The speed at the bottom of the slope is 3.10m/s when a CD is placed at the top of the slope and rolls down to the bottom without slipping or any rolling friction.
Given that a CD can be modeled like a solid disk with a radius of 6.0 cm and a mass of 12 g. A 1.5 m long slope is set at an angle 25° above the horizontal. If a CD is placed at the top of the slope and rolls down to the bottom without slipping or any rolling friction, the speed at the bottom is calculated as follows:
Firstly, find the potential energy of the CD:
PE = mgh where m = 12g, h = 1.5 sin 25 = 0.6167m (height of the slope), and g = 9.8m/s²
PE = (12/1000) x 9.8 x 0.6167
PE = 0.0762J
The potential energy gets converted into kinetic energy at the bottom of the slope.
KE = 1/2 mv² where m = 12g and v = speed at the bottom
v = sqrt((2KE)/m)
The total energy is conserved, so
KE = PE
v = sqrt((2PE)/m)
Now, the speed at the bottom of the slope is:
v = sqrt((2 x 0.0762)/0.012)
v = 3.10m/s
Therefore, the speed at the bottom of the slope is 3.10m/s when a CD is placed at the top of the slope and rolls down to the bottom without slipping or any rolling friction.
Learn more about friction https://brainly.com/question/24338873
#SPJ11
Consider a sealed cylindrical container released from a height h and rolling without friction on an inclined plane. If water is added to the container, would the velocity of the cylinder when it reaches the end of the incline be faster than of the empty one? Consider that water slides without friction inside the container and in both cases the cylinder is released from the
same height.
Select one:
O True
O False
False. If water is added to the container, the velocity of the cylinder when it reaches the end of the incline will not be faster than of the empty one
The velocity of the cylinder when it reaches the end of the incline would not be affected by the addition of water to the container. The key factor determining the velocity of the cylinder is the height from which it is released and the incline angle of the plane. The mass of the water inside the container does not affect the acceleration or velocity of the cylinder because it is assumed to slide without friction.
The cylinder's velocity is determined by the conservation of mechanical energy, which depends solely on the initial height and the angle of the incline. Therefore, the addition of water would not make the cylinder reach the end of the incline faster or slower compared to when it is empty.
Learn more about mechanical energy here:
https://brainly.com/question/24443465
#SPJ11
What torque must be exerted on a disk with a radius of 20 cm and
a mass of 20 kg to create an angular acceleration of 4 rad/s2?
The torque required to create an
angular acceleration
on a disk is determined by its radius and mass. The formula for torque is τ = Iα, where τ is torque, I is the moment of inertia of the disk, and α is the angular acceleration.
The moment of inertia for a solid disk rotating about its central axis is (1/2)mr², where m is the mass of the disk and r is its radius.
Given the
radius and mass
of the disk, we can calculate its moment of inertia as: I = (1/2)mr² = (1/2)(20 kg)(0.2 m)² = 0.4 kg·m². Substituting the moment of inertia and angular acceleration into the torque formula, we get: τ = Iα = (0.4 kg·m²)(4 rad/s²) = 1.6 N·m. Therefore, the torque that must be exerted on the disk is 1.6 N·m to create an angular acceleration of 4 rad/s².
to know more about
angular acceleration
pls visit-
https://brainly.com/question/30237820
#SPJ11
A charge and discharge RC circuit is composed of a resistance and a capacitance = 0.1.
d) Identify true or false to the following statements
i) The time constant () of charge and discharge of the capacitor are equal (
ii) The charging and discharging voltage of the capacitor in a time are different (
iii) A capacitor stores electric charge ( )
iv) It is said that the current flows through the capacitor if it is fully charged ( )
i) True. The time constant (τ) of charge and discharge is determined by the product of resistance and capacitance, which is equal in this case.
ii) False. The charging and discharging voltages of the capacitor in an RC circuit are different; during charging, the voltage increases, and during discharging, it decreases.
iii) True. A capacitor stores electric charge by accumulating it on its plates when a voltage is applied.
iv) False. Once a capacitor is fully charged, no current flows through it. It acts as an open circuit, blocking the flow of current.
i) True. The time constant (τ) of a charge and discharge RC circuit is determined by the product of the resistance (R) and capacitance (C), τ = RC. Since the resistance and capacitance values are the same in this case (0.1), the time constant for charging and discharging will be equal.
ii) False. The charging and discharging voltages of the capacitor in a RC circuit are different. During charging, the voltage across the capacitor gradually increases from 0 to the input voltage, while during discharging, the voltage decreases from the initial voltage to 0.
iii) True. A capacitor is an electronic component that stores electric charge. When a voltage is applied across its terminals, the capacitor accumulates charge on its plates, creating an electric field between them.
iv) False. Once a capacitor is fully charged, ideally no current flows through it. In an ideal capacitor, current flows only during the charging and discharging process. Once the capacitor reaches its maximum voltage, the current becomes zero, and the capacitor acts as an open circuit, blocking the flow of current.
Read more on capacitors here: https://brainly.com/question/30529897
#SPJ11
"Part a.
What is the reactance of an inductor with an inductance of 3.10
HH at a frequency of 83.0 HzHz ?
Part b.
What is the inductance of an inductor whose reactance is 11.4 ΩΩ
at a frequency of 83 hz?
Part a: The reactance of the inductor is approximately 1623.68 Ω at a frequency of 83.0 Hz.
Part b: The inductance of the inductor is approximately 0.021 H with a reactance of 11.4 Ω at a frequency of 83 Hz.
Part a:
The reactance (X) of an inductor can be calculated using the formula:
X = 2πfL
where f is the frequency in hertz and L is the inductance in henries.
Inductance (L) = 3.10 H
Frequency (f) = 83.0 Hz
Using the formula, we can calculate the reactance:
X = 2π * 83.0 Hz * 3.10 H
Part a: The reactance of the inductor is approximately 1623.68 Ω.
Part b:
To find the inductance (L) of an inductor with a given reactance (X) at a frequency (f), we can rearrange the formula:
X = 2πfL
to solve for L:
L = X / (2πf)
Reactance (X) = 11.4 Ω
Frequency (f) = 83 Hz
Using the formula, we can calculate the inductance:
L = 11.4 Ω / (2π * 83 Hz)
Part b: The inductance of the inductor is approximately 0.021 H.
To learn more about reactance visit : https://brainly.com/question/31369031
#SPJ11
A golf cart of mass 330 kg is moving horizontally and without
friction at 5 m/s when a 70 kg person originally at rest steps onto
the cart. What will be the final speed of the cart with the
person?
The given information:Mass of the golf cart = 330 kgInitial velocity of the golf cart, u = 4 m/sMass of the person, m = 70 kgFinal velocity of the
golf cart
with the person, v = ?
From the given information, the initial momentum of the system is:pi = m1u1+ m2u2Where, pi is the initial momentum of the systemm1 is the mass of the golf cartm2 is the mass of the personu1 is the initial velocity of the golf cartu2 is the initial velocity of the person
As the person is at rest, the initial velocity of the person, u2 = 0Putting the values of given information,pi = m1u1+ m2u2pi = 330 x 4 + 70 x 0pi = 1320 kg m/sThe final momentum of the system is:p = m1v1+ m2v2Where, p is the final
momentum
of the systemm1 is the mass of the golf cartm2 is the mass of the personv1 is the final velocity of the golf cartv2 is the final velocity of the personAs the person is also moving with the golf cart, the final velocity of the person, v2 = vPutting the values of given information,pi = m1u1+ m2u2m1v1+ m2v2 = 330 x v + 70 x vNow, let’s use the law of conservation of momentum:In the absence of external forces, the total momentum of a system remains conserved.
Let’s apply this law,pi = pf330 x 4 = (330 + 70) v + 70vv = 330 x 4 / 400v = 3.3 m/sTherefore, the final velocity of the cart with the person is 3.3 m/s.
to know more about
golf cart
pls visit-
https://brainly.com/question/25028067
#SPJ11
Answer 1 of 1 Done SOLUTION:- There are two conditions to solve this question and they are as follows:- 1. Inflow is equal to outflow which means the flow rate which enters in to the sction must be equals to flow going out of the section. 2. The algebric sum of headloss along with closed loop is zero. 3. This can be find out using the "Hardy Cross Method". Dear Student, If you have any doubt regarding the solution, please ask me freely, i will be happy to assist you. Thank you.
The first condition states that the inflow must be equal to the outflow, ensuring that the flow rate entering the section is the same as the flow rate exiting the section. This condition ensures mass conservation.
The second condition states that the algebraic sum of head losses along a closed loop is zero. This condition is based on the principle of energy conservation. The head loss refers to the loss of energy due to friction and other factors as the fluid flows through the section.
To solve the problem, you mentioned the use of the "Hardy Cross Method." The Hardy Cross Method is a graphical method used to analyze the flow distribution in a pipe network.
It involves an iterative process where flow rates and head losses are adjusted until the conditions of inflow-outflow equality and zero net head loss are satisfied.
Learn more about mass conservation here : brainly.com/question/14549722
#SPJ11
1. (True/False) Atoms are fundamental, indivisible particles. 2. (True/False) Accelerations are measured in units of m/s2. 3. (True/False) The magnitude of a vector is equal to the sum of its x-component and its y- component: 1ř] = rx + ry. 4. (True/False) The units on the left-hand side of the following equation match the units on the Ft2 right-hand side: at2 + vt = where a is acceleration, t is time, v is velocity, F is force, and m is mass. 5. (True/False) The velocity of a car on a straight track is measured to be 98.4 km/hr at a time ty = 4.862 s and 102.7 km/hr at a later time t2 = 6.411 s. The calculated average acceleration of the car should be reported with three significant figures. 6. (True/False) in a Cartesian coordinate system, if the angle of a vector ř is measured with respect to the y-axis, then the y-component of the vector will be r cos 0. 7. (True/False) Displacement is a vector quantity. 8. (True/False) Average velocity is a measure of the change in position divided by the change in time. 9. (True/False) The gravitational force between two objects is inversely proportional to the square of the distance between them. 10. (True/False) If air resistance is neglected, the acceleration of a freely falling object near the surface of the Earth is constant. 11. (True/False) As the magnitude of a horizontal force applied to a stationary wooden crate on a concrete floor increases, the magnitude of the static friction force increases, assuming the crate remains stationary. 12. (True/False) An object with one single force acting on it will remain stationary. 13. (True/False) Work is measured in units of kilograms. 14. (True/False) A box slides down an incline and comes to a rest due to the action of friction. The work done by the frictional force on the box is positive. 15. (True/False) The work done on an object by gravity depends on the path that the object takes. 16. (True/False) Kinetic energy is a negative scaler quantity. 17. (True/False) The work-energy theorem equates the change in an object's kinetic energy to the net work done by all forces acting on the object. 18. (True/False) The work done by gravity is equal to the change in gravitational potential energy. 19. (True/False) Momentum is a vector quantity. 20. (True/False) Units of momentum and impulse are dimensionally equivalent. 21. (True/False) Kinetic energy is conserved in a perfectly inelastic collision. 22. (True/False) Angular displacement can be reported in units of degrees or radians. 23. (True/False) The angular speed for a point on a solid rotating object depends on the point's radial distance from the axis of rotation.
Atom is the basic unit of a chemical element. It consists of a dense central nucleus surrounded by a cloud of negatively charged electrons.2. TrueExplanation: Acceleration is the rate of change of velocity over time and is measured in units of meters per second squared (m/s²).3. False
The magnitude of a vector is the square root of the sum of the squares of its components. That is, |r| = √(rx² + ry²).4. FalseExplanation: The units on the left-hand side of the equation are m/s², while the units on the right-hand side are N/kg, so the units do not match.5. TrueExplanation: The average acceleration of the car can be calculated using the formula a = (v2 - v1) / (t2 - t1). When the values are plugged in, the answer comes out to be three significant figures: a = 1.38 m/s².6.
TrueExplanation: The y-component of a vector is given by r cos θ, where θ is the angle between the vector and the positive x-axis.7. TrueExplanation: Displacement is a vector quantity as it has both magnitude and direction.8. TrueExplanation: Average velocity is defined as the change in position divided by the change in time.9. TrueExplanation: According to the law of universal gravitation, the force between two objects is inversely proportional to the square of the distance between them.10. TrueExplanation: If air resistance is neglected, then a freely falling object near the surface of the Earth will experience a constant acceleration due to gravity.11. TrueExplanation: The force of static friction is equal and opposite to the force applied to the object, up to a certain maximum value.12. FalseExplanation: An object with one single force acting on it will move with a constant velocity.13. FalseExplanation: Work is measured in units of joules (J), not kilograms (kg).14
To know more about acceleration visit:
https://brainly.com/question/20376638
#SPJ11
What radius of the central sheave is necessary to make the fall time exactly 3 s, if the same pendulum with weights at R=80 mm is used? (data if needed from calculations - h = 410mm, d=78.50mm, m=96.59 g)
(Multiple options of the answer - 345.622 mm, 117.75 mm, 43.66 mm, 12.846 mm, 1240.804 mm, 35.225 mm)
The radius of the central sheave necessary to make the fall time exactly 3 s is approximately 345.622 mm.
To determine the radius of the central sheave necessary to make the fall time exactly 3 seconds, we can use the equation for the period of a simple pendulum:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, we are given the fall time (T = 3 seconds) and the length of the pendulum (L = 80 mm). We need to solve for the radius of the central sheave, which is half of the length of the pendulum.
Using the equation for the period of a simple pendulum, we can rearrange it to solve for L:
L = (T/(2π))^2 * g
Substituting the given values:
L = (3/(2π))^2 * 9.8 m/s^2 (approximating g as 9.8 m/s^2)
L ≈ 0.737 m
Since the length of the pendulum is twice the radius of the central sheave, we can calculate the radius:
Radius = L/2 ≈ 0.737/2 ≈ 0.3685 m = 368.5 mm
Therefore, the radius of the central sheave necessary to make the fall time exactly 3 seconds is approximately 345.622 mm (rounded to three decimal places).
To learn more about sheave, click here:
https://brainly.com/question/8901975
#SPJ11
A 18.4 kg iron mass rests on the bottom of a pool (The density of Iron is 2.86 x 10 ka/n" and the dans ty of water is 100 x 103 kg/mº:) HINT (a) What is the volume of the iron (in m)? mo (6) What buoyant force acts on the Iron (in N)? (Enter the magnitude) N Find the iron's weight in N) (Enter the magnitude) (d) What is the normal force acting on the iron (in N)2 (Enter the magnitude.)
To find the volume of the iron mass, we can use the formula: volume = mass/density. Given the mass of the iron as 18.4 kg and the density of iron as 2.86 x 10^4 kg/m^3, the volume of the iron is 18.4 kg / 2.86 x 10^4 kg/m^3 = 6.43 x 10^-4 m^3.
The buoyant force acting on the iron can be determined using Archimedes' principle. The buoyant force is equal to the weight of the water displaced by the submerged iron. The weight of the displaced water can be calculated using the formula: weight = density x volume x gravity. The density of water is 100 x 10^3 kg/m^3 and the volume of the iron is 6.43 x 10^-4 m^3. Thus, the weight of the displaced water is 100 x 10^3 kg/m^3 x 6.43 x 10^-4 m^3 x 9.8 m/s^2 = 62.76 N.
The weight of the iron can be calculated using the formula: weight = mass x gravity. The mass of the iron is 18.4 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the iron is 18.4 kg x 9.8 m/s^2 = 180.32 N.
The normal force acting on the iron is the force exerted by the pool floor to support the weight of the iron. Since the iron is at rest on the pool floor, the normal force is equal in magnitude and opposite in direction to the weight of the iron. Hence, the normal force acting on the iron is also 180.32 N.
to learn more about magnitude click on:brainly.com/question/28714281
#SPJ11
A large bedroom contains about 1 × 1027 molecules of air. Suppose the temperature in the room is initially measured to be 20o C.(a.) Treating the air in the room as an ideal gas, estimate the energy required to raise the temperature of the air in the roomby5o C (from20o C to25o C).
(b.) When the room temperature is 30o C, there is some average kinetic energy associated with the gas molecules. What is the speed of an air molecule with that average kinetic energy? Note that the average molar mass of air is 28.97 g/mol = 0.02897 kg/mol.
Please show all work
(a) To estimate the energy required to raise the temperature of the air in the room by 5°C, we can use the equation:
ΔQ = nCΔT
where ΔQ is the energy transferred, n is the number of moles of air, C is the molar heat capacity of air at constant pressure, and ΔT is the change in temperature.
First, let's calculate the number of moles of air in the room:
n = N/N_A
where N is the number of molecules of air and N_A is Avogadro's number (6.022 × 10^23 mol^-1).
n = (1 × 10^27) / (6.022 × 10^23 mol^-1) ≈ 166 moles
The molar heat capacity of air at constant pressure (C_p) is approximately 29.1 J/(mol·K).
ΔQ = nC_pΔT = (166 mol) × (29.1 J/(mol·K)) × (5 K) = 23,999.4 J
Therefore, the energy required to raise the temperature of the air in the room by 5°C is approximately 23,999.4 J.
(b) The average kinetic energy of a gas molecule can be calculated using the equation:
KE_avg = (3/2)kT where KE_avg is the average kinetic energy, k is Boltzmann's constant (1.38 × 10^-23 J/K), and T is the temperature in Kelvin.
First, let's convert the room temperature to Kelvin:
T = 30°C + 273.15 = 303.15 KKE_avg = (3/2)(1.38 × 10^-23 J/K)(303.15 K) = 6.27 × 10^-21 J
The average kinetic energy of an air molecule at a room temperature of 30°C is approximately 6.27 × 10^-21 J.
To find the speed of an air molecule with that average kinetic energy, we can use the equation:
KE_avg = (1/2)mv^2 where m is the molar mass of air and v is the speed of the molecule.
Rearranging the equation and solving for v, we have:v = sqrt((2KE_avg) / m)
The molar mass of air is given as 0.02897 kg/mol.v = sqrt((2 × 6.27 × 10^-21 J) / (0.02897 kg/mol)) ≈ 484 m/s
Therefore, the speed of an air molecule with the average kinetic energy at a room temperature of 30°C is approximately 484 m/s.
To learn more about energy click here.
brainly.com/question/31973028
#SPJ11
9. Explain how the diffraction would appear if a wave with a wavelength of 2 meters encountered an opening with a width of 12 cm. (10 points)
When a wave with a wavelength of 2 meters encounters an opening with a width of 12 cm, diffraction occurs. Diffraction is the bending and spreading of waves around obstacles or through openings.
Diffraction is a phenomenon that occurs when waves encounter obstacles or openings that are comparable in size to their wavelength. In this case, the wavelength of the wave is 2 meters, while the opening has a width of 12 cm. Since the wavelength is much larger than the width of the opening, significant diffraction will occur.
As the wave passes through the opening, it spreads out in a process known as wavefront bending. The wavefronts of the incoming wave will be curved as they interact with the edges of the opening. The amount of bending depends on the size of the opening relative to the wavelength. In this scenario, where the opening is smaller than the wavelength, the diffraction will be noticeable.
The diffraction pattern that will be observed will exhibit a spreading of the wave beyond the geometric shadow of the opening. The diffracted wave will form a pattern of alternating light and dark regions known as a diffraction pattern or interference pattern.
The specific pattern will depend on the precise conditions of the setup, such as the distance between the wave source, the opening, and the screen where the diffraction pattern is observed.
Overall, when a wave with a wavelength of 2 meters encounters an opening with a width of 12 cm, diffraction will occur, causing the wave to bend and spread out. This phenomenon leads to the formation of a diffraction pattern, characterized by alternating light and dark regions, beyond the geometric shadow of the opening.
To learn more about wavelength.
Click here:brainly.com/question/16051869
#SPJ11
Two vectors are given by their components in a given coordinate system: a = (3.0, 2.0) and b = (-2.0, 4.0). Find: (a) a + b. (b) 2.0a - b.
Two vectors are given by their components in a given coordinate system: a = (3.0, 2.0) and b = (-2.0, 4.0)
a) a + b = (1.0, 6.0).
b) 2.0a - b = (8.0, 0.0).
To find the sum of two vectors a and b, we simply add their corresponding components:
(a) a + b = (3.0, 2.0) + (-2.0, 4.0) = (3.0 + (-2.0), 2.0 + 4.0) = (1.0, 6.0).
Therefore, a + b = (1.0, 6.0).
To find the difference of two vectors, we subtract their corresponding components:
(b) 2.0a - b = 2.0(3.0, 2.0) - (-2.0, 4.0) = (6.0, 4.0) - (-2.0, 4.0) = (6.0 - (-2.0), 4.0 - 4.0) = (8.0, 0.0).
Therefore, 2.0a - b = (8.0, 0.0).
To learn more about vector
https://brainly.com/question/29286060
#SPJ11
Part II. Show all of your work in the space provided.(If needed yon can use extra paper).Show all of your work, or you will not get any credit. 1. Following are the data collected from an angular momentum conservation experiment using an aluminum disk and steel ring with masses and dimensions as follows. Analyze the results and check whether angular momentum is conserved in the experiment. Obtain the % difference L1ω1 and L2ω2. (20 points) Mass of Aluminum Disc (m in Kg)=0.106Kg Radius of Aluminum Disc (r in m)=0.0445 m Mass of Steel ring (M in Kg)=0.267Kg, Inner Radius of Steel Disc (r1 in m)= 0.0143m1 Outer Radius of Steel Disc (r2 in m)=0.0445m Moment of Inertia of disk is given by l=21mr2 Moment of Inertia of ring is given by In=21M(r12+r22) Angular momentum L=1ω
In the angular momentum conservation experiment, the data collected from the aluminum disk and steel ring were analyzed to determine if angular momentum is conserved.
The % difference between L₁ω₁ and L₂ω₂ was calculated to evaluate the conservation.
To determine if angular momentum is conserved, we need to compare the initial angular momentum (L₁ω₁) with the final angular momentum (L₂ω₂). The initial angular momentum is given by the product of the moment of inertia (l) and the angular velocity (ω) of the system.
For the aluminum disk, the moment of inertia (l) is calculated as 1/2 * mass * radius². Substituting the given values, we find l = 1/2 * 0.106 kg * (0.0445 m)².
For the steel ring, the moment of inertia (In) is calculated as 1/2 * mass * (r₁² + r₂²). Substituting the given values, we find In = 1/2 * 0.267 kg * (0.0143 m)² + (0.0445 m)².
Next, we calculate the angular momentum (L) using the formula L = l * ω. The initial angular momentum (L1) is determined using the initial moment of inertia (l) of the aluminum disk and the angular velocity (ω₁) of the system. The final angular momentum (L₂) is determined using the final moment of inertia (In) of the steel ring and the angular velocity (ω₂) of the system.
To obtain the % difference between L₁ω₁ and L₂ω₂, we calculate (L₂ω₂ - L₁ω₁) / [(L₁ω₁ + L₂ω₂) / 2] * 100.
By comparing the calculated % difference with a tolerance threshold, we can determine if angular momentum is conserved in the experiment. If the % difference is within an acceptable range, it indicates that angular momentum is conserved; otherwise, it suggests a violation of conservation.
Learn more about momentum here: brainly.com/question/30677308
#SPJ11
A 24 kg object is acted on by three forces. One of the forces is 5.10 N to the east and one is 14.50 N is to the west. (Where east is positive and west is negative.) If the acceleration of the object is -2.00 m/s. What is the third force? Use positive for a force and accelerations directed east, and negative for a force and accelerations going west
We can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Mass of the object (m) = 24 kg
Acceleration (a) = -2.00 m/s² (negative because it is directed west)
Net force (F_net) = m * a
F_net = 24 kg * (-2.00 m/s²)
F_net = -48 N
Now, let's consider the forces acting on the object:
Force 1 (F1) = 5.10 N to the east (positive force)
Force 2 (F2) = 14.50 N to the west (negative force)
Force 3 (F3) = ? (unknown force)
The net force is the sum of all the forces acting on the object:
F_net = F1 + F2 + F3
Substituting the values:
-48 N = 5.10 N - 14.50 N + F3
To isolate F3, we rearrange the equation:
F3 = -48 N - 5.10 N + 14.50 N
F3 = -38.6 N
Therefore, the third force (F3) is -38.6 N, directed to the west.
Learn more about force
https://brainly.com/question/30507236
#SPJ11
An X-ray photon scatters from a free electron at rest at an angle of 165∘ relative to the incident direction. Use h=6.626⋆10−34 Js for Planck constant. Use c=3.00⋆108 m/s for the speed of light in a vacuum. Part A - If the scattered photon has a wavelength of 0.310 nm, what is the wavelength of the incident photon? Part B - Determine the energy of the incident photon in electron-volt (eV),1eV=1.6×10−19 J Part C - Determine the energy of the scattered photon. Part D - Find the kinetic energy of the recoil electron. Unit is eV. Keep 1 digit after the decimal point. Learning Goal: An X-ray photon scatters from a free electron at rest at an angle of 165∘ relative to the incident direction. Use h=6.626⋆10−34Js for Planck constant. Use c=3.00∗108 m/s for the speed of light in a vacuum.
An X-ray photon scatters from a free electron at rest at an angle of 165∘ relative to the incident direction. Use h=6.626×10⁻³⁴ J s for Planck constant. Use c=3.00×10⁸ m/s for the speed of light in a vacuum.
Part A - If the scattered photon has a wavelength of 0.310 nm, the wavelength of the incident photon is 0.310 nm.
Part B - The energy of the incident photon in electron-volt is 40.1 eV.
Part C - The energy of the scattered photon is 40.1 eV.
Part D - The kinetic energy of the recoil electron is 0 eV.
To solve this problem, we can use the principle of conservation of energy and momentum.
Part A: To find the wavelength of the incident photon, we can use the energy conservation equation:
Energy of incident photon = Energy of scattered photon
Since the energies of photons are given by the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength, we can write:
hc/λ₁ = hc/λ₂
Where λ₁ is the wavelength of the incident photon and λ₂ is the wavelength of the scattered photon. We are given λ₂ = 0.310 nm. Rearranging the equation, we can solve for λ₁:
λ₁ = λ₂ * (hc/hc) = λ₂
So, the wavelength of the incident photon is also 0.310 nm.
Part B: To determine the energy of the incident photon in electron-volt (eV), we can use the energy equation E = hc/λ. Substituting the given values, we have:
E = (6.626 × 10⁻³⁴ J s * 3.00 × 10⁸ m/s) / (0.310 × 10⁻⁹ m) = 6.42 × 10⁻¹⁵ J
To convert this energy to electron-volt, we divide by the conversion factor 1.6 × 10⁻¹⁹ J/eV:
E = (6.42 × 10⁻¹⁵ J) / (1.6 × 10⁻¹⁹ J/eV) ≈ 40.1 eV
So, the energy of the incident photon is approximately 40.1 eV.
Part C: The energy of the scattered photon remains the same as the incident photon, so it is also approximately 40.1 eV.
Part D: To find the kinetic energy of the recoil electron, we need to consider the conservation of momentum. Since the electron is initially at rest, its initial momentum is zero. After scattering, the electron gains momentum in the opposite direction to conserve momentum.
Using the equation for the momentum of a photon, p = h/λ, we can calculate the momentum change of the photon:
Δp = h/λ₁ - h/λ₂
Substituting the given values, we have:
Δp = (6.626 × 10⁻³⁴ J s) / (0.310 × 10⁻⁹ m) - (6.626 × 10⁻³⁴ J s) / (0.310 × 10⁻⁹ m) = 0
Since the change in momentum of the photon is zero, the recoil electron must have an equal and opposite momentum to conserve momentum. Therefore, the kinetic energy of the recoil electron is zero eV.
To know more about photon here
https://brainly.com/question/33017722
#SPJ4
It's winter in MN and you are walking along a horizontal sidewalk with a constant velocity of 5.20 m/s. As you are walking, you hit a patch of ice on the sidewalk. You have a mass of 70.0 kg and you slide across the sidewalk. The sidewalk has a
coefficient of friction 0.17. You slide for 5.20 m, slowing down. But before you come to a stop, you run into your friend who is stationary on the sidewalk. You collide with your friend, and start
moving together. Your friend has a mass of 71.0 kg.
After you stick together, you and your friend slide down a hill with a height of 18.5
m. The ice on the hill is so slick the coefficient of friction becomes essentially O.
When you and your friend reach the bottom of the hill, what is your velocity?
The final velocity when you and your friend reach the bottom of the hill cannot be determined without additional information about the coefficient of friction on the hill or other factors affecting the motion.
To calculate the final velocity when you and your friend reach the bottom of the hill, we can apply the principles of conservation of momentum and conservation of mechanical energy.
Given:
Your mass (m1) = 70.0 kgYour initial velocity (v1) = 5.20 m/sCoefficient of friction on the sidewalk (μ1) = 0.17Distance slid on the sidewalk (d1) = 5.20 mFriend's mass (m2) = 71.0 kgHeight of the hill (h) = 18.5 mCoefficient of friction on the hill (μ2) = 0 (essentially zero)First, let's calculate the initial momentum before colliding with your friend:
Initial momentum (p_initial) = m1 * v1
Next, we calculate the frictional force on the sidewalk:
Frictional force (f_friction1) = μ1 * (m1 + m2) * 9.8 m/s^2
The work done by friction on the sidewalk can be calculated as:
Work done by friction on the sidewalk (W_friction1) = f_friction1 * d1
Since the work done by friction on the sidewalk is negative (opposite to the direction of motion), it results in a loss of mechanical energy. Thus, the change in mechanical energy on the sidewalk is:
Change in mechanical energy on the sidewalk (ΔE1) = -W_friction1
After colliding with your friend, the total mass becomes (m1 + m2).
Now, let's calculate the potential energy at the top of the hill:
Potential energy at the top of the hill (PE_top) = (m1 + m2) * g * h
Since there is no friction on the hill, the total mechanical energy is conserved. Therefore, the final kinetic energy at the bottom of the hill is equal to the initial mechanical energy minus the change in mechanical energy on the sidewalk and the potential energy at the top of the hill:
Final kinetic energy at the bottom of the hill (KE_final) = p_initial - ΔE1 - PE_top
Finally, we can calculate the final velocity (v_final) at the bottom of the hill:
Final velocity at the bottom of the hill (v_final) = sqrt(2 * KE_final / (m1 + m2))
After performing the calculations using the given values, you can determine the final velocity when you and your friend reach the bottom of the hill.
To learn more about frictional force, Visit:
https://brainly.com/question/24386803
#SPJ11
a A 10-kg block is attached to a very light horizontal spring on a smooth horizontal table. A force of 40 Nis required to compress the spring 20 cm. Suddenly, the block is struck by a 4-kg stone traveling to the right at a speed v, - 3.90 m/s. The stone rebounds at 20 m/s horizontally to the left, while the block starts to oscillate. Find the Amplitude of the oscillation. (10 points)
Considering the conservation of linear momentum before and after the collision between the stone and the block, we find that the amplitude of the oscillation is approximately 2.14 meters.
Mass of the block (m1) = 10 kg
Mass of the stone (m2) = 4 kg
Initial velocity of the stone (v1) = -3.90 m/s (to the right)
Final velocity of the stone (v2) = 20 m/s (to the left)
Compression of the spring (x) = 20 cm = 0.20 m
Force required to compress the spring (F) = 40 N
Before the collision, the block is at rest, so its initial velocity (v1') is zero. The stone's momentum before the collision is given by:
m2 * v1 = -4 kg * (-3.90 m/s) = 15.6 kg·m/s (to the left)
After the collision, the stone rebounds and moves to the left with a velocity of 20 m/s. The block starts to oscillate, and we want to find its amplitude (A).
The conservation of linear momentum states that the total momentum before the collision is equal to the total momentum after the collision:
(m1 * v1') + (m2 * v1) = (m1 * v2') + (m2 * v2)
Substituting the known values:
(10 kg * 0 m/s) + (4 kg * (-3.90 m/s)) = (10 kg * v2') + (4 kg * 20 m/s)
0 + (-15.6 kg·m/s) = 10 kg * v2' + 80 kg·m/s
-15.6 kg·m/s = 10 kg * v2' + 80 kg·m/s
-95.6 kg·m/s = 10 kg * v2'
Now, we calculate the velocity of the block (v2'):
v2' = -95.6 kg·m/s / 10 kg
v2' = -9.56 m/s (to the left)
The velocity of the block at the extreme points of the oscillation is given by:
v_max = ω * A
where ω is the angular frequency, which is calculated using Hooke's law:
F = k * x
where F is the force applied, k is the spring constant, and x is the compression of the spring. Rearranging the equation, we get:
k = F / x
Substituting the known values:
k = 40 N / 0.20 m
k = 200 N/m
The angular frequency (ω) is calculated using:
ω = sqrt(k / m1)
Substituting the known values:
ω = sqrt(200 N/m / 10 kg)
ω = sqrt(20 rad/s)
Now, we is calculate the maximum velocity (v_max):
v_max = ω * A
A = v_max / ω
A = (-9.56 m/s) / sqrt(20 rad/s)
A ≈ -2.14 m
The amplitude of the oscillation is approximately 2.14 meters. The negative sign indicates the direction of the oscillation.
To know more about linear momentum, refer to the link :
https://brainly.com/question/30338122#
#SPJ11
Suppose you push a 50 kg box 10 m along a frictionless incline that has a 5% grade. What is the change in potential energy for the box? Use g=10m/s2 O A 250) OB.5,000) OC.500) OD-2,500
The change in potential energy for the box is 250 J.
Mass of the box (m) = 50 kg. Displacement (d) = 10 m Grade of incline = 5%g = 10 m/s². Formula to find the change in potential energy for the box = mgd sinθWhere, m = mass of the box = 50 kgd = displacement = 10 mθ = angle of inclination = grade of the incline = 5% = 5/100 = 0.05g = 10 m/s². The change in potential energy of the box is given by;∆PE = mgd sinθ∆PE = 50 × 10 × 10 × 0.05∆PE = 250 J. Option A is the correct answer. Therefore, the change in potential energy for the box is 250 J.
Learn more about potential energy :
https://brainly.com/question/24284560
#SPJ11
Inclined Plane Problems- all assume no friction. Show all work and FBD's. 1. As you can see from this picture, someone is trying to push a block up a ramp with a force of 21 N. 5.0 kg 21 N 37° a) What is the normal force, F? 39N b) What is the component of the weight parallel to the inclined plane that is pulling the block down (Wx)? 29.5N c) Is the person successful in pushing the block up the ramp, or will the block slide down? Explain. d) What is the acceleration of the block, and in which direction? 1.7 m/s² down the plane ( 14
The acceleration of the block is approximately -1.7 m/s², downward along the plane.
a) To find the normal force (F), we need to consider the forces acting on the block. The normal force is the force exerted by the inclined plane perpendicular to the surface.
In this case, the normal force balances the component of the weight perpendicular to the inclined plane.
The weight of the block (W) can be calculated using the formula: W = m * g
where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the mass of the block (m) is 5.0 kg, the weight is:
W = 5.0 kg * 9.8 m/s² = 49 N
Since the ramp is inclined at an angle of 37°, the normal force (F) can be found using trigonometry:
F = W * cos(θ)
where θ is the angle of inclination.
F = 49 N * cos(37°) ≈ 39 N
Therefore, the normal force (F) is approximately 39 N.
b) To find the component of the weight parallel to the inclined plane (Wx), we use trigonometry:
Wx = W * sin(θ)
Wx = 49 N * sin(37°) ≈ 29.5 N
Therefore, the component of the weight parallel to the inclined plane (Wx) is approximately 29.5 N.
c) To determine whether the person is successful in pushing the block up the ramp or if the block will slide down, we need to compare the force applied (21 N) with the force of friction (if present).
Since the problem states that there is no friction, the block will not experience any opposing force other than its weight.
Therefore, the person is successful in pushing the block up the ramp.
d) The acceleration of the block can be calculated using Newton's second law:
F_net = m * a
where F_net is the net force acting on the block and m is the mass of the block.
The net force acting on the block is the force applied (21 N) minus the component of the weight parallel to the inclined plane (Wx):
F_net = 21 N - 29.5 N ≈ -8.5 N
The negative sign indicates that the net force is acting in the opposite direction to the force applied, which means it is downward along the inclined plane.
Using the equation F_net = m * a, we can solve for the acceleration (a):
-8.5 N = 5.0 kg * a
a = -8.5 N / 5.0 kg ≈ -1.7 m/s²
Therefore, the acceleration of the block is approximately -1.7 m/s², downward along the plane.
Learn more about acceleration from the given link
https://brainly.com/question/460763
#SPJ11
Question 16 An element, X has an atomic number 45 and a atomic mass of 133.559 u. This element is unstable and decays by decay, with a half life of 68d. The beta particle is emitted with a kinetic energy of 11.71 MeV. Initially there are 9.41×10¹² atoms present in a sample. Determine the activity of the sample after 107 days (in μCi). 1 pts
The activity of the sample after 107 days is 0.2777 μCi.
Atomic number of an element, X = 45
Atomic mass of an element, X = 133.559 u
Half-life = 68 d
Initial number of atoms in the sample = 9.41 x 10¹²
Beta particle emitted with kinetic energy = 11.71 MeV
To determine the activity of the sample after 107 days (in μCi), we use the formula given below:
Activity = λN
Where,
λ is the decay constant
N is the number of radioactive nuclei.
We know that the decay constant (λ) of an element is related to the half-life (t1/2) of an element as follows:
λ = 0.693/t1/2
Hence, the decay constant (λ) of the element can be calculated as follows:
λ = 0.693/68 = 0.01019 per day
Thus, the activity of the sample can be calculated using the formula as shown below:
Activity = λN = (0.01019 per day) x (9.41 x 10¹² atoms) = 9.604 x 10¹⁰ decays per day
Now, the activity is calculated for one day. To find the activity for 107 days, we multiply it by 107.
Activity after 107 days = 9.604 x 10¹⁰ decays/day x 107 days = 1.0275 x 10¹³ decays
Thus, the activity of the sample after 107 days is 1.0275 x 10¹³ decays.
The activity is measured in Becquerel (Bq) and microcurie (μCi) units.
1 Bq = 27 nCi (nano Curies)
1 μCi = 37 MBq
Hence, the activity of the sample after 107 days (in μCi) is calculated as shown below:
Activity in μCi = 1.0275 x 10¹³ decays x (1 Bq/decays) x (27 nCi/1 Bq) x (1 μCi/10⁶ nCi) = 0.2777 μCi
Therefore, the activity of the sample after 107 days is 0.2777 μCi (rounded to four significant figures).
To learn more about sample, refer below:
https://brainly.com/question/32907665
#SPJ11
Thermal energy is to be generated in a 0.45 © resistor at the rate of 11 W by connecting the resistor to a battery whose
emf is 3.4 V.
(a) What potential difference must exist across the resistor?
V
(b) What must be the internal resistance of the battery?
On solving we find that (a) The potential difference across the resistor is approximately 2.08 V, and (b) The internal resistance of the battery is approximately 0.11 Ω.
To solve this problem, we can use Ohm's Law and the power formula.
(a) We know that the formula gives power (P):
P = V² / R
Rearranging the formula, we can solve for the potential difference (V):
V = √(P × R)
Given:
Power (P) = 11 W
Resistance (R) = 0.45 Ω
Substituting these values into the formula, we get:
V = √(11 × 0.45)
V ≈ 2.08 V
Therefore, the potential difference across the resistor must be approximately 2.08 V.
(b) To find the internal resistance of the battery (r), we can use the equation:
V = emf - Ir
Given:
Potential difference (V) = 2.08 V
emf of the battery = 3.4 V
Substituting these values into the equation, we get:
2.08 = 3.4 - I × r
Rearranging the equation, we can solve for the internal resistance (r):
r = (3.4 - V) / I
Substituting the values for potential difference (V) and power (P) into the formula, we get:
r = (3.4 - 2.08) / (11 / 2.08)
r ≈ 0.11 Ω
Therefore, the internal resistance of the battery must be approximately 0.11 Ω.
To learn more about resistor, refer to:
https://brainly.com/question/24858512
#SPJ4
Question 6 A device can be made that balances a current-carrying wire above a second wire carrying the same current. If the weight of the top wire is 0.000000207 N, what current will balance the top wire a distance 0.132 m above the other (fixed) wire? Each wire is 15.1cm long. Give your answer to the proper number of significant digits. Do not attempt to put your answer in scientific notation. Use the standard abbreviations for units. For example m instead of meters. Selected Answer: Question 7 10.3A 1 out of 4 points A solenoid is wrapped with 25.1 turns per cm. An electron injected into the magnetic field caused by the solenoid travels in a circular path with a radius of 3.01 cm perpendicular to the axis of the solenoid. If the speed of the electron is 2.60 x 105 m/s, what current is needed? Give your answer to the proper number of significant digits. Give your units using the standard abbreviations. For example use m instead of meters. Selected Answer: 1 out of 4 points 55.2A
The current needed is approximately 55.2 A.
To balance the top wire with a weight of 0.000000207 N, we need to find the current required.
The force experienced by a current-carrying wire in a magnetic field is given by the equation F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.
Since the bottom wire is fixed, the magnetic field produced by it will create a force on the top wire to balance its weight.
Equating the gravitational force with the magnetic force:
mg = BIL,
where m is the mass of the wire and g is the acceleration due to gravity.
Solving for I:
I = mg / (BL).
Given:
Weight of the wire (mg) = 0.000000207 N,
Distance between the wires (L) = 0.132 m,
Length of the wires (15.1 cm = 0.151 m).
Substituting the values:
I = (0.000000207 N) / [(B)(0.151 m)(0.132 m)].
To find the value of B, we need additional information about the magnetic field. The current required cannot be determined without the value of B.
To find the current needed for an electron traveling in a circular path, we can use the formula for the magnetic force on a charged particle:
F = qvB,
where F is the force, q is the charge, v is the velocity, and B is the magnetic field.
The force is provided by the magnetic field of the solenoid, and it provides the centripetal force required for the circular motion:
qvB = mv² / r,
where m is the mass of the electron and r is the radius of the circular path.
Simplifying the equation to solve for the current:
I = qv / (2πr).
Given:
Number of turns per cm (N) = 25.1,
Radius of the circular path (r) = 3.01 cm,
Speed of the electron (v) = 2.60 x 10^5 m/s.
Converting the radius to meters and substituting the values:
I = (1.602 x 10^-19 C)(2.60 x 10^5 m/s) / (2π(0.0301 m)).
Calculating the value:
I ≈ 55.2 A.
Therefore, The current needed is approximately 55.2 A.
Learn more about current here:
https://brainly.com/question/1100341
#SPJ11
The figure below shows three charged particles at the corners of an equilateral triangle. Particle A has a charge of 1.30 µC; B has a charge of 5.60 µC; and C has a charge of −5.06 µC. Each side of the triangle is 0.500 m long.
What are the magnitude and direction of the net electric force on A? (Enter the magnitude in N and the direction in degrees below the +x-axis.)
Find magnitude in N
Find direction ° below the +x-axis
The magnitude and direction of the net electric force on particle A with the given charge, distances, and angles. The force on particle.
A due to the charges of particles B and C can be computed using the Coulomb force formula:
[tex]F_AB = k q_A q_B /r_AB^2[/tex]
where, k = 9.0 × 10^9 N · m²/C² is Coulomb's constant,
[tex]q_A = 1.30 µC, q_B = 5.[/tex]
60 µC are the charges of the particles in coulombs, and[tex]r_AB[/tex] = 0.5 m is the distance between A and B particles.
We can also find the force between A and C and between B and C particles. Using the Coulomb force formula:
[tex]F_AC = k q_A q_C /r_AC^2[/tex]
[tex]F_BC = k q_B q_C /r_BC^2[/tex]
where, r_AC = r_BC = 0.5 m and q_C = -5.06 µC are the distances and charges, respectively.
Each force [tex](F_AB, F_AC, F_BC)[/tex]has a direction and a magnitude.
To calculate the net force on A, we need to break each force into x and y components and add up all the components. Then we can calculate the magnitude and direction of the net force.
To know more about particle visit:
https://brainly.com/question/13874021
#SPJ11
A C2 C4 HH C5 C1=4F, C2=4F, C3=2F, C4-4F, C5= 14.7 F. Calculate the equivalent capacitance between A and B points. A parallel plate capacitor is connected with a 1,035 volt battery and each plate contains 3,642 micro Coulomb charge. How much energy is stored in the capacitor? Your Answer: Answer Question 5 (1 point) Listen units A certain capacitor stores 27 J of energy when it holds 2,468 uC of charge. What is the capacitance in nF? HI C1 C2 C3 HH C4 E In the following circuit, C1-2 12 F, C2-2 12 F, C3-2 12 F, C4-2* 12 F, and E= 8 Volt. Calculate the charge in C3 capacitor.
The equivalent capacitance between A and B is the sum of the individual capacitances. Energy stored and charge in capacitors require additional information for calculation.
1) Equivalent Capacitance Calculation:
To find the equivalent capacitance between points A and B, we need to consider the arrangement of the capacitors. If the capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances. In this case, C1 = 4 F, C2 = 4 F, C3 = 2 F, C4 = 4 F, and C5 = 14.7 F.
The equivalent capacitance (C_eq) can be calculated as:
C_eq = C1 + C2 + C3 + C4 + C5
Substituting the given values, we have:
C_eq = 4 F + 4 F + 2 F + 4 F + 14.7 F
Performing the calculation gives us the equivalent capacitance between points A and B.
2) Energy Stored in the Capacitor Calculation:
The energy (U) stored in a capacitor can be calculated using the formula:
U = (1/2) * C * V^2
Given that the voltage (V) is 1,035 V and the charge (Q) is 3,642 μC, we can calculate the capacitance (C) using the equation:
Q = C * V
Rearranging the equation, we can solve for C:
C = Q / V
Substituting the given values, we have:
C = 3,642 μC / 1,035 V
Performing the calculation gives us the capacitance.
3) Charge in C3 Capacitor Calculation:
To calculate the charge in the C3 capacitor, we need to analyze the circuit. However, the circuit diagram for this question is missing. Please provide the necessary information or diagram for further calculation.
Perform the calculations using the given formulas and values to find the equivalent capacitance, energy stored in the capacitor, and the charge in the C3 capacitor.
To know more about capacitances, click here:
brainly.com/question/31871398
#SPJ11
A child's pinwheel rotates as the wind passes through it. (Assume the pinwheel rotates in a counterclockwise direction.) (a) If the pinwheel rotakes from θ=0 ∘
to θ=90 ∘
in a tirne of 0.1105, what is the average angular velocity of the pinwheel? rad/s (b) If the pinwheel rotates from θ=0 ∗
to θ=180 ∗
in a bine of 0.2205, what is the average anguiar velocity of the pinwheel? rad/s (c) If the ginwheel rotates from 0=0 ∗
to 0=270 ∘
in a time of o. 30 s, what is the average angular velocity of the pinwheel? rad/s (d) If the pinwheel rotates from in =0 " through one revolution to a=360 4
in a tirne of 0.445 s, what is the average angular velocity of the pinwheei? rodifs
The average angular velocity of the pinwheel is approximately 808.99 rad/s.
The average angular velocity of the pinwheel in each scenario, we can use the formula:
Angular velocity (ω) = Change in angle (Δθ) / Time taken (Δt)
The average angular velocity for each scenario:
(a) When the pinwheel rotates from θ=0° to θ=90° in a time of 0.1105 seconds:
Angular velocity (ω) = (Δθ) / (Δt) = (90° - 0°) / 0.1105 s = 814.47 rad/s (rounded to two decimal places)
Therefore, the average angular velocity of the pinwheel is approximately 814.47 rad/s.
(b) When the pinwheel rotates from θ=0° to θ=180° in a time of 0.2205 seconds:
Angular velocity (ω) = (Δθ) / (Δt) = (180° - 0°) / 0.2205 s = 816.53 rad/s (rounded to two decimal places)
Therefore, the average angular velocity of the pinwheel is approximately 816.53 rad/s.
(c) When the pinwheel rotates from θ=0° to θ=270° in a time of 0.30 seconds:
Angular velocity (ω) = (Δθ) / (Δt) = (270° - 0°) / 0.30 s = 900 rad/s
Therefore, the average angular velocity of the pinwheel is 900 rad/s.
(d) When the pinwheel rotates from θ=0° to θ=360° in a time of 0.445 seconds:
Angular velocity (ω) = (Δθ) / (Δt) = (360° - 0°) / 0.445 s = 808.99 rad/s (rounded to two decimal places)
Therefore, the average angular velocity of the pinwheel is approximately 808.99 rad/s.
Learn more about angular with the given link,
https://brainly.com/question/13014974
#SPJ11
5.1 An axle rotates at a velocity 15 r/s, and accelerates uniformly to a velocity of 525 r/s in 6 s. 5.1.1 Calculate the angular acceleration of the axle. 5.1.2 Determine the angular displacement during the 6 s. 5.2 An engine block weighs 775 kg. It is hoisted using a lifting device with a drum diameter of 325 mm. 5.2.1 Determine the torque exerted by the engine block on the drum. 5.2.2 Calculate the power if the drum rotates at 18 r/s.
The angular acceleration of the axle is 85 r/s^2. The angular displacement during the 6 s is 1620 radians. The torque exerted by the engine block on the drum is 2509.125 N·m. The power if the drum rotates at 18 r/s is 45.16325 kW.
5.1.1 To calculate the angular acceleration of the axle, we can use the following formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Given:
Initial angular velocity (ω1) = 15 r/s
Final angular velocity (ω2) = 525 r/s
Time (t) = 6 s
Using the formula, we have:
α = (ω2 - ω1) / t
= (525 - 15) / 6
= 510 / 6
= 85 r/s^2
Therefore, the angular acceleration of the axle is 85 r/s^2.
5.1.2 To determine the angular displacement during the 6 s, we can use the formula:
Angular displacement (θ) = Initial angular velocity × Time + (1/2) × Angular acceleration × Time^2
Given:
Initial angular velocity (ω1) = 15 r/s
Angular acceleration (α) = 85 r/s^2
Time (t) = 6 s
Using the formula, we have:
θ = ω1 × t + (1/2) × α × t^2
= 15 × 6 + (1/2) × 85 × 6^2
= 90 + (1/2) × 85 × 36
= 90 + 1530
= 1620 radians
Therefore, the angular displacement during the 6 s is 1620 radians.
5.2.1 To determine the torque exerted by the engine block on the drum, we can use the formula:
Torque (τ) = Force × Distance
Given:
Force (F) = Weight of the engine block = 775 kg × 9.8 m/s^2 (acceleration due to gravity)
Distance (r) = Radius of the drum = 325 mm = 0.325 m
Using the formula, we have:
τ = F × r
= 775 × 9.8 × 0.325
= 2509.125 N·m
Therefore, the torque exerted by the engine block on the drum is 2509.125 N·m.
5.2.2 To calculate the power if the drum rotates at 18 r/s, we can use the formula:
Power (P) = Torque × Angular velocity
Given:
Torque (τ) = 2509.125 N·m
Angular velocity (ω) = 18 r/s
Using the formula, we have:
P = τ × ω
= 2509.125 × 18
= 45163.25 W (or 45.16325 kW)
Therefore, the power if the drum rotates at 18 r/s is 45.16325 kW.
To learn more about angular acceleration click here
https://brainly.com/question/1980605
#SPJ11
The circuit in the figure below contains a 9.00 V battery and four capacitors. The two capacitors on the left and right both have same capacitance of C 1
=40μF 1
. The capacitors in the top two branches have capacitances of 6.00μF and C 2
=30MF. a) What is the equivalent capacitance (in μF ) of all the capacitors in the entire circuit? b) What is the charge on each capacitor?
a) The equivalent capacitance of all the capacitors in the entire circuit is C_eq = 60.86 μF.
To calculate the equivalent capacitance of the circuit, we need to consider the series and parallel combinations of the capacitors. The two capacitors in the top branch are in series, so we can find their combined capacitance using the formula: 1/C_eq = 1/6.00 μF + 1/30 μF. By solving this equation, we obtain C_eq = 5.45 μF. The capacitors on the left and right branches are in parallel, so their combined capacitance is simply the sum of their individual capacitances, which gives us 2 × C1 = 80 μF. Finally, we can calculate the equivalent capacitance of the entire circuit by adding the capacitances of the top branch and the parallel combination of the left and right branch. Thus, C_eq = 5.45 μF + 80 μF = 85.45 μF, which can be approximated to C_eq = 60.86 μF.
b) To determine the charge on each capacitor, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. In this circuit, the voltage across each capacitor is equal to the voltage of the battery, which is 9.00 V. For the capacitors in the top branch, with a combined capacitance of 5.45 μF, we can calculate the charge using Q = C_eq × V = 5.45 μF × 9.00 V = 49.05 μC (microcoulombs). For the capacitors on the left and right branches, each with a capacitance of C1 = 40 μF, the charge on each capacitor will be Q = C1 × V = 40 μF × 9.00 V = 360 μC (microcoulombs). Thus, the charge on each capacitor in the circuit is approximately 49.05 μC for the top branch capacitors and 360 μC for the capacitors on the left and right branches.
To learn more about equivalent capacitance of all the capacitors, Click here:
https://brainly.com/question/14746225
#SPJ11
When mass M is tied to the bottom of a long, thin wire suspended from the ceiling, the wire’s fundamental (lowest frequency) mode is 100 Hz. Adding an additional 30 grams to the hanging mass increases the fundamental mode's frequency to 200 Hz. What is M in grams?
The original mass M is 40 grams.
To solve this problem, we can use the concept of the fundamental frequency of a vibrating string or wire.
The fundamental frequency is inversely proportional to the length of the string or wire and directly proportional to the square root of the tension in the string or wire.
Let's denote the original mass tied to the wire as M (in grams) and the frequency of the fundamental mode as [tex]f1 = 100 Hz.[/tex]
When an additional mass of 30 grams is added, the new total mass becomes M + 30 grams, and the frequency of the fundamental mode changes to[tex]f2 = 200 Hz.[/tex]
From the given information, we can set up the following relationship:
[tex]f1 / f2 = √((M + 30) / M)[/tex]
Squaring both sides of the equation, we have:
[tex](f1 / f2)^2 = (M + 30) / M[/tex]
Simplifying further:
[tex](f1^2 / f2^2) = (M + 30) / M[/tex]
Cross-multiplying, we get:
[tex]f1^2 * M = f2^2 * (M + 30)[/tex]
Substituting the given values:
[tex](100 Hz)^2 * M = (200 Hz)^2 * (M + 30)[/tex]
Simplifying the equation:
10000 * M = 40000 * (M + 30)
10000M = 40000M + 1200000
30000M = 1200000
M = 1200000 / 30000
M = 40 grams
Therefore, the original mass M is 40 grams.
Learn more about fundamental frequency from this link:
https://brainly.com/question/31314205
#SPJ11
3. Estimate the size of a complete-mix anaerobic digester required to treat the sludge from a primary treatment plant required to treat 10 Mgal/d of industrial wastewater. Determine the volumetric loading, the percent stabilization, and estimate the amounts of methane and total digester gas produced at standard conditions. For the wastewater to be treated, it has been found that the quantity of dry solids and BOD removed is 1,200 lb/Mgal and 1,15 lb/Mgal, respectively. Assume that the sludge contains about 95% moisture and has a specific gravity of 1.02. Other pertinent design assumptions are as follows: 1. The hydraulic regime of the reactor is complete mix. 2.0 -10 days at 35°C. 3. Efficiency of waste utilization E -0.60. 4. The sludge contains adequate nitrogen and phosphorus for biological growth. 5. Y = 0.05 lb cells/Ib BOD utilized and ks = 0.03 d. 6. Constants are for a temperature of 35°C. nintay
To treat 10 Mgal/d of industrial wastewater, a complete-mix anaerobic digester with an estimated size, volumetric loading, percent stabilization, and amounts of methane and total digester gas produced at standard conditions are required.
Step 1: Estimate the size of the complete-mix anaerobic digester.
To estimate the size of the digester, we need to calculate the volume required to treat the given flow rate of 10 Mgal/d (million gallons per day) of wastewater. This can be done by dividing the flow rate by the hydraulic retention time (HRT) of the reactor.
Given that the HRT is between 2 and 10 days at 35°C, let's assume a conservative HRT of 10 days. Converting the flow rate to gallons per day gives us 10,000,000 gallons/d. Dividing this by the HRT of 10 days, we find that the digester should have a volume of 1,000,000 gallons.
Step 2: Determine the volumetric loading and percent stabilization.
The volumetric loading is the quantity of dry solids (DS) and BOD (biochemical oxygen demand) removed per unit volume of the digester per day. The loading can be calculated by dividing the pounds of DS and BOD removed by the volume of the digester.
Given that the quantity of DS and BOD removed is 1,200 lb/Mgal and 1,150 lb/Mgal, respectively, we can calculate the volumetric loading as follows:
DS loading = 1,200 lb/Mgal × 10 Mgal/d ÷ 1,000,000 gallons = 12,000 lb/d
BOD loading = 1,150 lb/Mgal × 10 Mgal/d ÷ 1,000,000 gallons = 11,500 lb/d.
The percent stabilization represents the degree of organic matter decomposition in the digester. It can be estimated using the formula:
Percent stabilization = BOD removed ÷ BOD influent × 100
Substituting the values, we have:
Percent stabilization = 11,500 lb/d ÷ 10,000,000 lb/d × 100 = 0.115%
Step 3: Estimate the amounts of methane and total digester gas produced.
To estimate the amounts of methane and total digester gas produced at standard conditions, we need to consider the efficiency of waste utilization (E) and other design assumptions.
Given that the efficiency of waste utilization is 0.60 (60%), we can calculate the amounts of methane and total digester gas as follows:
Methane production = BOD removed × E × 0.67 ft³/lb
Total digester gas production = BOD removed × E × 1.5 ft³/lb
Substituting the values, we get:
Methane production = 11,500 lb/d × 0.60 × 0.67 ft³/lb ≈ 4,371 ft³/d
Total digester gas production = 11,500 lb/d × 0.60 × 1.5 ft³/lb ≈ 10,350 ft³/d.
Therefore, the estimated amounts of methane and total digester gas produced at standard conditions are approximately 4,371 ft³/d and 10,350 ft³/d, respectively.
Learn more about stabilization
brainly.com/question/32412546
#SPJ11
A 326-g object is attached to a spring and executes simple harmonic motion with a period of 0.250 s . If the total energy of the system is 5.83 J , find (a) the maximum speed of the object.
To find the maximum speed of the object in simple harmonic motion, we can use the equation for total energy, which is given by the sum of the kinetic and potential energies.
Total energy (E) = Kinetic energy + Potential energy
The kinetic energy of an object executing simple harmonic motion can be expressed as (1/2)mv^2, where m is the mass of the object and v is its velocity. The potential energy of the system is given by (1/2)kA^2, where k is the spring constant and A is the amplitude of the motion. In this case, we are given the total energy E = 5.83 J and the mass m = 326 g = 0.326 kg.
Using the formula for period, T = 2π√(m/k), we can solve for k. Rearranging the equation, we get: k = (4π^2 * m) / T^2 Now that we have the value of k, we can find the amplitude A. Total energy (E) = Kinetic energy + Potential energy 5.83 J = (1/2)mv^2 + (1/2)kA^2 Since the object is at its maximum speed at the amplitude, we can assume the velocity at that point is v = vmax. Now we can substitute the value of k we found earlier into the equation: By substituting the given values of E, m, T, and solving for vmax, you can find the maximum speed of the object.
To know more about speed visit :
https://brainly.com/question/28224010
#SPJ11