A machine gun with a mass of 5kg fires a 50g bullet at a speed of 100m/s. what Is the recoil of the machine gun
Explanation:
Using conservation of momentum
the bullets momentum must equal the rifle's momnetum
5 000 gm * v = 50 gm * 100 m/s
v = 1 m/s
What quantity in moles of LiBr are in 77.0 grams of LiBr?
Using stoichiometry, use the conversion factor of 1 mol/molar mass of LiBr
Molar mass of Li = 6.941 g
Molar mass of Br = 79.904 g
Molar mass of LiBr = 6.941 g + 79.904 g
Molar mass of LiBr = 86.845 g
[tex]77.0 g LiBr(\frac{1 mol LiBr}{86.845g LiBr})\\\\0.886637112096[/tex]
There are 0.886637112096 moles of LiBr in 77.0 grams of LiBr.
The molecular mass of Lithium Bromide (LiBr) is found by adding the atomic masses of Lithium and Bromide. Given a mass of 77.0 grams of LiBr, by converting this to moles using the molecular mass, we find there are 0.887 moles of LiBr.
Explanation:The process to solve this involves finding the molecular mass of Lithium Bromide (LiBr), which allows us to convert grams to moles. The atomic mass of Lithium (Li) is approximately 6.94 g/mol, and Bromide (Br) is 79.9 g/mol. Hence, the molecular mass of LiBr = 6.94 g/mol + 79.9 g/mol = 86.84 g/mol.
To calculate the quantity of moles, we use the formula: Moles = mass (grams) / molecular weight (g/mol). Given a mass of 77.0 grams, the quantity in moles = 77.0 g / 86.84 g/mol = approximately 0.887 moles of LiBr.
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from the diameter and effective surface temperature of the sun, estimate the rate at which it emits energy. what fraction of this emitted energy is intercepted by the earth? estimate the solar constant, given the mean earth-sun distance
The rate at which the Sun emits energy is calculated using P = σ * A * T⁴. The fraction of emitted energy intercepted by Earth is (π * R_earth²) / (4 * π * R_earth-sun²). The solar constant is P * Fraction.
Step 1: Use the Stefan-Boltzmann Law
The Stefan-Boltzmann Law states that the power (energy emitted per unit time) of a blackbody is given by:
P = σ * A * T⁴
where P is the power, σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴), A is the surface area, and T is the effective surface temperature.
Step 2: Calculate the surface area of the Sun
The surface area of a sphere is given by:
A = 4 * π * R²
where R is the radius. Since the diameter is given, we can find the radius as half of the diameter:
R = diameter / 2
Step 3: Calculate the power emitted by the Sun
Using the surface area and temperature, calculate the power:
P = σ * A * T⁴
Step 4: Calculate the fraction of emitted energy intercepted by Earth
The fraction of emitted energy intercepted by Earth can be found by calculating the ratio of the cross-sectional area of Earth to the surface area of a sphere with a radius equal to the Earth-Sun distance.
Fraction = (π * R_earth²) / (4 * π * R_earth-sun²)
Step 5: Estimate the solar constant
The solar constant is the amount of solar energy received per unit area at the mean Earth-Sun distance. It can be calculated using the power emitted by the Sun and the fraction of emitted energy intercepted by Earth:
Solar constant = P * Fraction
By following these steps, you can estimate the rate at which the Sun emits energy, the fraction of emitted energy intercepted by Earth, and the solar constant, given the diameter and effective surface temperature of the Sun and the mean Earth-Sun distance.
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two monochromatic light sources can interfere constructively or destructively, depending on their phase difference. one consequence of this phenomenon is
One phenomenon that we see when two monochromatic light source interfere constructively or destructively is the colors that are observed on the surface of a soap bubble. So option A is correct.
Constructive interference is when two light waves overlap and combines to form a larger wave. Destructive interference is when the waves cancel each other. Constructive interference occurs when the waves are in phase with each other, and destructive occurs when they are out of phase.
A soap bubble will have an internal and an external surface. Both these surface reflects light that falls in it regardless of the source. When these two reflected waves constructively or destructively interfere, we could see colors on the surface even the light reflected by both surfaces are white.
So the correct answer is option A.
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The complete question is
We have seen that two monochromatic light waves can interfere constructively or destructively, depending on their phase difference. One consequence of this phenomenon is
A) the colors you see when white light is reflected from a soap bubble.
B) the appearance of a mirage in the desert.
C) a rainbow.
D) the way in which Polaroid sunglasses work.
E) the formation of an image by a converging lens, such as the lens in your eye
Please Help! Thanks!
Study the scenario.
System 1 has a large number of particles, moving slowly on average. System 2 has a smaller number of particles, but they are moving faster on average.
Which system has a higher temperature?
Responses:
There is not enough data to tell. The larger number of particles in System 1 may or may not outweigh the increase in movement in System 2.
System 1 has a higher temperature because the particles are moving slowly. The particles in System 1 have greater kinetic energy than System 2.
System 1 has a higher temperature because there are more particles. A greater number of particles have more kinetic energy than a smaller number of particles.
System 2 has a higher temperature because the particles are moving with greater speed. The particles in System 2 have greater kinetic energy than System 1.
System 2 has a higher temperature because the particles are moving with greater speed. The particles in System 2 have greater kinetic energy than System 1.
What is kinetic energy?
Kinetic energy is a form of energy that an object possesses by virtue of its motion. It is defined as the energy an object possesses due to its motion and is determined by its mass and velocity. The greater an object's mass and velocity, the greater its kinetic energy.
What is velocity?
Velocity is a vector quantity that describes the rate at which an object changes its position in a specific direction. It is defined as the displacement of an object per unit of time and is measured in meters per second (m/s) or other appropriate units of distance over time. Velocity takes into account both the speed of the object and its direction of motion, making it a more precise measurement than speed.
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a merry-go-round is a common piece of playground equipment. a 2.77 diameter merry-go-round with a mass of 264 kg is spinning at 24 rpm. john runs tangent to the merry-go-round at 4.44 m/s, in the same direction that it is turning, and jumps onto the outer edge. john's mass is 35.4 kg. what is the merry-go-round's angular velocity, in rpm, after john jumps on?
A 264 kg merry-go-round spinning at 24 rpm has its angular velocity reduced to 14.3 rpm after a 35.4 kg person jumps on.
To tackle this issue, we really want to utilize protection of precise energy. At first, the carousel is turning at a specific precise speed and has a specific snapshot of dormancy. At the point when John bounces onto the carousel, he expands the snapshot of inactivity, which makes the carousel delayed down. Notwithstanding, since precise energy is monitored, the result existing apart from everything else of dormancy and rakish speed should stay steady.
To begin with, we should track down the snapshot of idleness of the carousel:
I =[tex](1/2)mr^2[/tex]
where
m = 264 kg (mass of the carousel)
r = 1.385 m (span of the carousel, which is half of the width)
I = [tex](1/2)(264 kg)(1.385 m)^2[/tex] = 255 kg[tex]m^2[/tex]
Then, how about we convert the underlying precise speed of the carousel from rpm to rad/s:
w_i = (24 rpm)(2π rad/1 rev)(1 min/60 s) = 2.51 rad/s
The underlying precise force of the framework is then:
L_i = Iw_i = (255 kg [tex]m^2[/tex])(2.51 rad/s) = 642.05 kg [tex]m^2/s[/tex]
At the point when John hops onto the carousel, the snapshot of inactivity of the framework increments to:
I_f = I + m*[tex]r^2[/tex]
where
m = 35.4 kg (mass of John)
r = 1.385 m (span of the carousel)
I_f = (264 kg)[tex](1.385 m)^2[/tex] + (35.4 kg)[tex](1.385 m)^2[/tex]= 429.78 kg [tex]m^2[/tex]
To find the last precise speed of the framework, we can utilize protection of rakish energy:
L_i = L_f
Iw_i = I_fw_f
Settling for w_f, we get:
w_f = (Iw_i)/I_f = (255 kg [tex]m^2/s[/tex])(2.51 rad/s)/(429.78 kg [tex]m^2[/tex]) = 1.50 rad/s
At long last, we can change over the last precise speed from rad/s back to rpm:
w_f = (1.50 rad/s)(60 s/2π rad)(1 fire up/1 turn) = 14.3 rpm
Consequently, the rakish speed of the carousel, in rpm, after John hops on is 14.3 rpm.
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under what condition is the angular momentum of an object conserved? under what condition is the angular momentum of an object conserved? if there is no net torque acting on it. if it is a point particle. if there is no net force acting on it. if there are no torques acting on it.
The angular momentum of an object conserved A. if there is no net torque acting on it.
Angular momentum is defined as the rotational analog of linear momentum, which is a measure of the amount of rotation an object has. The law of conservation of angular momentum states that the angular momentum of an object is conserved when there is no external torque acting on the object.
Mathematically, it can be expressed as, L = IωWhere L is the angular momentum of an object, I is its moment of inertia, and ω is its angular velocity. The angular momentum of an object is conserved when there is no net torque acting on it. This means that the total external torque acting on an object must be zero. If there is no external torque acting on an object, its angular momentum will be conserved, meaning that it will remain constant in magnitude and direction over time.
If an object experiences a torque, its angular momentum will change, and the rate of change of angular momentum will be equal to the magnitude of the torque acting on the object. Hence, if there is no net torque acting on an object, the angular momentum of that object will be conserved. An object that has no net force acting on it is not necessarily conserved, since it may still experience a torque that will cause its angular momentum to change.
However, if an object is a point particle, it can be treated as having zero moments of inertia, and its angular momentum will be conserved if there is no net torque acting on it. Therefore the correct option is A
The Question was Incomplete, Find the full content below :
under what condition is the angular momentum of an object conserved?
a. if there is no net torque acting on it.
b. if it is a point particle.
c. if there is no net force acting on it.
d. if there are no torques acting on it
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how does a diode behave in a circuit? include how the behavior is different for positive and negative voltages
A diode is an electronic component that allows current to flow in one direction and blocks it in the opposite direction.
A diode is a semiconductor device that allows current to flow in only one direction. When the voltage across the diode is positive (forward bias), the diode conducts current easily and has a very low resistance, allowing current to flow through the diode. However, when the voltage across the diode is negative (reverse bias), the diode has a very high resistance and will not conduct any significant current.
In practical circuits, the diode is often used as a rectifier, allowing current to flow in one direction and blocking current in the opposite direction. In forward bias, the diode acts as a closed switch, allowing current to flow freely in the forward direction. In reverse bias, the diode acts as an open switch, blocking any current flow in the reverse direction.
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when will another full moon appear
Answer: Thursday, April 6, at 12:34 a.m.
Explanation:
a long, straight wire with current flowing through it produces magnetic field strength at its surface. if the wire has a radius r, where within the wire is the field strength equal to of the field strength at the surface of the wire? assume that the current density is uniform throughout the wire. a) 0.36 r b) 0.060 r c) 0.64 r d) 0.030 r
The answer to this question is 0.64 r (option c).To calculate the magnetic field inside the wire, we can use Ampere's Law.
Calculation of magnetic field:The magnetic field can be calculated by
1: Calculate the magnetic field strength at the surface using Ampere's Law for a long, straight wire.
2: Find the equation for the magnetic field strength at a distance x from the center of the wire.
3: Equate the magnetic field strength at distance x to half the magnetic field strength at the surface.
4: Solve for x in terms of the wire's radius r.
The answer is x = 0.64 r, which corresponds to option c) 0.64 r.
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A copy machine uses a lens to make an image of a page in the physics textbook to print a copy. When the print is regular size, both the book and its image are 16.0 cm from the lens.
What is the focal length of this lens?
If the lens is moved so that it is 24 cm from the book, what is the distance to the new image?
This new image will be magnified, reduced, or the same size compared to the original book?
How do you know?
a parallel-plate capacitor is connected to a battery. what happens if the plate separation is doubled while the capacitor remains connected to the battery? (a) the stored energy remains the same. (b) the stored energy is doubled. (c) the stored energy decreases by a factor of 2. (d) the stored energy decreases by a factor of 4. (e) the stored energy increases by a factor of 4.
When a parallel-plate capacitor is connected to a battery, if the plate separation is doubled the stored energy decreases by a factor of 2 while the capacitor remains connected to the battery. The correct option is (c)
The stored energy in a capacitor can be computed from the amount of charge stored on the plates and the voltage difference between them.
It is given by the formula E=½QV, where E is the energy, Q is the charge, and V is the voltage between the plates.
A capacitor stores energy in its electric field, which is created by the charge distribution on its plates.
When the plate separation is increased while the capacitor is connected to a battery, the electric field inside the capacitor decreases since the voltage across it is constant. This results in a reduced potential energy, as well as a decrease in stored energy.
As a result, the stored energy of the capacitor is reduced by a factor of 2 when the plate separation is doubled, as the electric field in the capacitor decreases by half. Therefore,option (c) is correct.
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from what height should a circular hoop of radius r be released on the same slope in order to equal the sphere's speed at the bottom?
To ensure that the speed of a circular hoop of radius r is equal to that of a sphere at the bottom, the hoop must be released from a height of r/2 above the sphere's release point.
Circular hoops are a set of steel or aluminum rings with an inner diameter of 16 inches, making them ideal for use with woven or braided nets. They are used to support the net and provide a framework for the ball to pass through. For balls up to 18 feet in diameter, we recommend a minimum of four hoops. The motion of rolling without slipping: The motion of rolling without slipping is the movement of an object without slipping.
Rolling without slipping is the motion of a circular object where there is a rolling motion of the object without slipping, meaning that the point on the outer edge of the circular object contacts the ground while rolling. The distance traveled by an object rolling without slipping can be calculated using the formula
S = Rθ
when it travels a distance θ with a radius R.
The answer to the question is that the circular hoop of radius r should be released from a height of r/2 above the sphere's release point in order to match the speed of the sphere at the bottom.
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I NEED HELP ASAP
Which of the following best explains how the location of the fossils provides evidence of continental plate movement?
A.
Fossil evidence suggests that South America and Africa were once joined together in one land mass.
B.
Fossil evidence suggests that South America and Africa were never joined together in one land mass.
C.
Fossil evidence suggests that South America and Africa are currently one land mass with the Atlantic Ocean covering part of the continent.
D.
Fossil evidence cannot be used as evidence of continental plate movement.
According to fossil evidence, South America and Africa were formerly part of a single geographical mass.
Which two fossils provide evidence in favour of continental drift?The eastern Greenland and Appalachian mountain ranges' similarity is scientists evidence for the theory of continental drift. In rocks that are the same age but on continents that are currently far apart, ancient fossils of the same species of extinct plants and animals can be found.s.
What evidence demonstrates the historical ties between South America and Africa?The most convincing proof, in his opinion, that the two continents were formerly connected is the existence of identical fossil species along the coasts of South America and Africa.
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1) a) What is the total resistance of three resistors connected in series if they have values of R1 20 ohm, R2 = 30 ohm and R3 = 10 ohm?
Answer:
60 Ω
Explanation:
When when there is a series connection, the resistances of the resistors are added together;
R = R1 + R2 + R3
R = 20 Ω + 30 Ω + 10 Ω = 60 Ω
what are jet streams? what are jet streams? bands of low-speed wind found at elevations of 9-15 km bands of low-speed wind found at elevations of 5-9 km bands of high-speed wind found at elevations of 9-15 km bands of high-speed wind found at elevations of 5-9 km
Jet streams are bands of high-speed wind found at elevations of 9-15 km. This wind current, referred to as jet streams, is formed by a combination of atmospheric temperature, Earth's rotation, and pressure differences in the atmosphere.
What are jet streams, Jet streams are fast-flowing, narrow air currents located in the upper atmosphere or the troposphere, generally around 8 to 9 miles high in the Earth's atmosphere.
They are formed due to the combination of the Earth's rotation, temperature, and atmospheric pressure.The temperature of the air in the atmosphere decreases with increasing altitude. Because the Earth's rotation is faster at the equator than at the poles, the temperature difference causes high-altitude air to flow from west to east, resulting in a jet stream.
The band of high-speed wind called the jet stream can influence the weather in the areas they pass over. They push high and low-pressure systems around, affecting weather patterns. Jet streams are caused by differences in atmospheric pressure, Earth's rotation, and atmospheric temperature.
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what is the magnitude of the force per meter of length on a straight wire carrying an 8.50- a current when perpendicular to a 0.75- t uniform magnetic field?
The magnitude of the force per meter of length on the wire is 6.375 N/m when the wire is carrying an 8.50-A current perpendicular to a 0.75-T uniform magnetic field.
The magnitude of the force per meter of length on a straight wire carrying an 8.50-A current when perpendicular to a 0.75-T uniform magnetic field can be calculated using the formula F = BIL, where F is the magnitude of the force, B is the magnetic field strength, I is current, and L is the length of the wire.
Substituting the given values, we get:
F = (0.75 T) x (8.50 A) x 1 m
F = 6.375 N/m
This force is known as the Lorentz force, which describes the force experienced by a charged particle, such as an electron when moving in a magnetic field. In this case, the moving charges are the electrons in the wire, and the magnetic field causes them to experience a force perpendicular to their direction of motion.
This force can be used in various applications, such as electric motors and generators, where the motion of electrons in a magnetic field is utilized to produce mechanical work or generate electricity.
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explain why a patch of light appears at a specific point on the floor
Answer:
a patch of light appears at a specific point on the floor due to reflection from a nearby surface. This phenomenon occurs due to the law of reflection, which states that when light hits a surface, it reflects off at an angle equal to the angle at which it struck.
Explanation:
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tha a) Name the type of logic gate shown in a Figure 5.88a. Write down its truth table. b) Show that when its two inputs are joined together as in Figure 5.88b it will act as a NOT gate.
The logic gate in figure 5.88a is NAND gate. When two inputs are joined together it will act as a NOT gate. This is shown in figure 5.88b.
What is the truth table of NAND gate? How do both inputs joined give a NOT gate?A truth table is a table that shows the output of a logic gate for all possible combinations of its input values.
a. Truth table of NAND gate is:
A B Output
0 0 1
0 1 1
1 0 1
1 1 0
b. When one input each is given to two different NOT gates and these two gates are connected to an AND gate, a NOT gate is formed.
This is the truth table for these gates:
A B ~A ~B ~A AND ~B
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
As you can see from the truth table, the output of the AND gate is 1 (logic high) only when both inputs to the NOT gates are 0 (logic low). In all other cases, the output of the AND gate is 0 (logic low). Therefore, the output of the entire circuit is the negation of the input A. This is the behavior of a NOT gate.
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The image of the question is attached.
If you pull something horizontally at a constant speed with a force meter, what is the net force on the object?
The forces operating on the thing in question are considered to be into equilibrium when there is no net force on it.
What is the best way to define acceleration?The rate at which velocity changes is referred to as acceleration. velocity change over time is measured by acceleration (a). As a result, any change in direction or speed will result in a change to velocity, which will then result in acceleration.
The acceleration formula as what?According for the equation that a = v/t, acceleration (a) equals the product of the alteration in velocity (v) and a change in time (t).
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if a violin string vibrates at 400 hz as its fundamental frequency, what are the frequencies of the first four harmonics?
The first four harmonics of a violin string vibrating at 400 Hz are 400 Hz, 800 Hz, 1200 Hz, and 1600 Hz, with each harmonic having a frequency that is a multiple of the fundamental frequency.
The first four harmonics of a violin string, which has a fundamental frequency of 400 Hz, can be computed as follows: The basic frequency, 400 Hz, is represented by the first harmonic, where n = 1. The frequency of the second harmonic (n = 2) is two times that of the main frequency. Consequently, the second harmonic's frequency is: 400 Hz + 2 f1 = 2 = 800 Hz The frequency of the third harmonic (n = 3) is three times that of the main frequency. Consequently, the third harmonic's frequency is: 400 Hz + 3 f1 = 3 = 1200 Hz The frequency of the fourth harmonic (n = 4) is four times that of the main frequency. Consequently, the fourth harmonic's frequency.
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in 1897, a refracting telescope was built at the yerkes observatory in williams bay, wisconsin. at the time it was the largest telescope in the world, and is actually used till this day. the telescope has an objective lens of 1 m diameter with the focal length of 19 m. what should the focal length of the eyepiece lens be to give a magnification of magnitude 250?
The focal length of the eyepiece lens should be 0.076 m to give a magnification of magnitude 250.According to the magnification formula, Magnification = focal length of the objective lens / focal length of the eyepiece lens.
Magnification = 250focal length of the objective lens = 19 m Magnification = focal length of the objective lens / focal length of the eyepiece lens.250 = 19 / focal length of the eyepiece lens Rearranging the above equation to get the focal length of the eyepiece lens: focal length of the eyepiece lens = 19 / 250focal length of the eyepiece lens = 0.076 m Therefore, the focal length of the eyepiece lens should be 0.076 m to give a magnification of magnitude 250.
To achieve a magnification of 250 with a telescope at Yerkes Observatory in Wisconsin, you can use the formula.
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describe how contacts associated with relays, timers, motor starts, and the like are represented on a ladder diagram.
In a ladder diagram, these symbols are organized into horizontal rungs, which represent parallel circuits, and vertical rails, which represent power supply lines.
In a ladder diagram, contacts associated with relays, timers, motor starters, and similar devices are represented using specific symbols and notations to show their function and status. Here's a step-by-step explanation of how they are represented:
1. Normally open (NO) contact: This is represented by two parallel lines, similar to an open switch. It indicates that the contact is open when the device (relay, timer, motor starter, etc.) is not energized. The symbol is (| |).
2. Normally closed (NC) contact: This is represented by two parallel lines with a diagonal line across them, similar to a closed switch. It indicates that the contact is closed when the device is not energized. The symbol is (|/|).
3. Relay coil: A relay coil is represented by a circle with the relay's identification (usually a letter and number) inside it. When the coil is energized, it causes the associated contacts to change their state (NO contacts close, NC contacts open).
4. Timer: Timers are represented by a square or rectangle with the timer's identification inside it, and sometimes the time delay setting. Timer contacts can be either normally open (| |) or normally closed (|/|), and their state will change after the specified time delay.
5. Motor starter: A motor starter is represented by a circle with an "M" inside it. Motor starters have both normally open and normally closed contacts, depending on the function (e.g., for starting or stopping the motor). The contacts are connected in series or parallel with the motor and other control devices.
In a ladder diagram, these symbols are organized into horizontal rungs, which represent parallel circuits, and vertical rails, which represent power supply lines. The diagram provides a clear and concise way to visualize the operation and interconnection of these devices in a control circuit.
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write an equation to help stacy find the gravitational force on an object if she knows the mass. in the equation let w represent gravitational force m represent mass and g represent the ratio you found in part s test your equation using a set of values from the table to be sure it works
The gravitational force on the object with a mass of 5 kg on the surface of the Earth is 49.05 N.
The equation that can help Stacy find the gravitational force on an object if she knows its mass is:
F = w = m x g
where:
F is the gravitational force (in Newtons, N)
m is the mass of the object (in kilograms, kg)
g is the acceleration due to gravity (in meters per second squared, [tex]m/s^2)[/tex]
The value of g varies depending on the location of the object, but on the surface of the Earth, it is approximately 9.81 [tex]m/s^2.[/tex]
To test the equation using a set of values from the table, let's say we have an object with a mass of 5 kg. Using the value of g on the surface of the Earth, we can calculate the gravitational force on the object as:
F = 5 kg x 9.81[tex]m/s^2[/tex]
F = 49.05 N.
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a penny is dropped from the top of a tall stairwell. what is the velocity of the penny after it has fallen for 2 s? show your work.
Explanation:
Vf = Vo + at Vo = 0 a = 9.81 m/s t = 2
Vf = 0 + 9.81 (2) = 19.62 m/s
The velocity of the penny after it has fallen for 2 seconds is approximately 19.6 m/s.
When an object is dropped from rest, its velocity increases due to the acceleration of gravity. The acceleration of gravity on Earth is approximately 9.8 m/s².
The distance fallen by the penny after 2 seconds can be calculated using the formula:
d = 1/2 * g * t²
where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.
Substituting the values, we get:
d = 1/2 * 9.8 m/s² * (2 s)²
d = 19.6 m
Thus, the penny falls a distance of 19.6 meters in 2 seconds.
The velocity of the penny can be calculated using the formula:
v = √(2 * g * d)
where v is the velocity of the penny and d is the distance fallen.
Substituting the values, we get:
v = √(2 * 9.8 m/s² * 19.6 m)
v = √(384.16)
v = 19.6 m/s (approximately)
Therefore, the penny's speed is around 19.6 meters per second when it has been falling for 2 seconds.
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light from a laser of wavelength 780 nm falls on a diffraction grating containing 3300 lines per centimeter. what are the angles of the principle maxima?
The required angle of principle maxima when wavelength and diffraction grating are given is calculated to be 15.07°.
The wavelength is given as 780 nm = 780 × 10⁻⁹ m
It is given that the diffraction grating contains 3300 lines per centimetre.
Distance between the slits d = 1 cm/3300 lines = 10⁻² m/3300 lines = 3×10⁻⁶ m
The angles of principle maxima are to be found out.
We know that,
d sin θ = m λ
where,
d is the distance between slits
θ is the angle with respect to the path of the incident light
m is the order of interference
sin θ = m λ/d
θ = sin⁻¹(m λ/d) = sin⁻¹[(1× 780 × 10⁻⁹)/(3×10⁻⁶)] = sin⁻¹ (26× 10⁻²) = sin⁻¹(0.26) = 15.07°
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the big bang theory suggests that the universe formed as a result of the sudden expansion of a singularity. what observations about galaxies in the universe provide support for this suggestion?
One of the most compelling pieces of evidence is the cosmic microwave background radiation (CMB), which is a faint glow of electromagnetic radiation that fills the entire universe.
This radiation is thought to be the afterglow of the Big Bang and is consistent with the predictions of the theory. Additionally, observations of the distribution and movement of galaxies in the universe suggest that the universe is expanding. Finally, the observed abundance of light elements in the universe, such as hydrogen and helium, is also consistent with the predictions of the Big Bang theory. Together, these observations provide strong evidence that the universe began with a sudden expansion from a singularity.
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A starter cord for a generator is 1m long. It is wound on to a drum with a diameter of 10cm. A person starts pulling with a force of 100N. How much work does he do?
The person does 31.4 Joules of work when pulling the starter cord.
To calculate the work done by the person pulling the starter cord, we need to find the distance that the cord moves as it is pulled.
The circumference of the drum can be calculated as:
C = 2πr = 2 x 3.14 x 0.1m = 0.628m
So, each complete turn of the drum will wind or unwind the cord by a distance of 0.628m.
Assuming that the person pulls the cord with a constant force of 100N, the work done can be calculated as:
Work = Force x Distance
where distance is the length of cord pulled.
Since the cord is wound on the drum, the distance pulled will be equal to the length of the cord unwound from the drum.
Length of cord unwound = π x diameter of drum
= π x 10cm = 0.314m
Therefore, the work done by the person is:
Work = Force x Distance = 100N x 0.314m = 31.4 Joules (J)
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if olaf catches the ball, with what speed vf do olaf and the ball move afterward? express your answer numerically in meters per second.
If Olaf catches the ball, the speed with which Olaf and the ball move afterward can be determined using the principle of conservation of momentum. The total momentum of a system remains constant if no external force acts on it.
the ball's momentum before being caught by Olaf equals the combined momentum of Olaf and the ball after the catch. The expression that represents this concept is pi= pf, where pi is the initial momentum of the ball (which is equal to the final momentum), and pf is the final momentum of the ball and Olaf. In general, momentum is defined as:p = mv where,m is the mass of the object in kg,v is the velocity of the object in m/sandp is the momentum of the object in kg m/s.Applying the conservation of momentum principle:pi= pf m1v1= m1v1'+m2v2', where,m1 is the mass of the ball,v1 is the velocity of the ball before being caught by Olaf,v1' is the velocity of the ball and Olaf after the catch,m2 is the mass of Olaf, andv2' is the velocity of Olaf after the catch.The velocity of Olaf before the catch is assumed to be zero because it is not mentioned in the problem statement. The problem statement asks for the velocity of Olaf and the ball after the catch, which we will represent asv1'.So, using the above formula, we get:0.5 × 3.0 kg × 20.0 m/s = 0.5 × 3.0 kg × v1' + 20.0 kg × 0 m/sHere,m1 = 0.5 kg, v1 = 20 m/s, m2 = 20 kg, andv2' = 0 m/sSolving forv1', we get:v1' = (0.5 × 3.0 kg × 20.0 m/s)/ (0.5 × 3.0 kg + 20.0 kg)= 2.73 m/sTherefore, if Olaf catches the ball, the speed with which Olaf and the ball move afterwards is 2.73 m/s.
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You have two capacitors in series, C1 = 300 nF = 300x10-'F and C2 100 nF = 100x10-'F, and you connect them in series to a 1000-2 (ohm) resistor. What is the time constant of this RC circuit?
The time constant of the RC circuit with two capacitors in series and a 1000 Ω resistor is 0.75 seconds.
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In regards to the provided student question, here is an answer:In order to determine the time constant of the RC circuit that has two capacitors in series, we must first use the formula for the equivalent capacitance of a series circuit,
which is given by 1/Ceq = 1/C1 + 1/C2, where Ceq represents the equivalent capacitance of the circuit, C1 represents the capacitance of the first capacitor, and C2 represents the capacitance of the second capacitor.Using this formula,
we can calculate the equivalent capacitance of the circuit as follows:1/Ceq = 1/300x10^-9 + 1/100x10^-9 = (100x10^-9 + 300x10^-9) / (100x10^-9 x 300x10^-9) = 4/3 x 10^-9Ceq = 3/4 x 10^9 FNow that we have the equivalent capacitance of the circuit,
we can use the formula for the time constant of an RC circuit, which is given by RC, where R represents the resistance of the circuit and C represents the capacitance of the circuit.Using the given resistance of 1000 Ω and the calculated equivalent capacitance of 3/4 x 10^9 F,
we can calculate the time constant of the circuit as follows:RC = 1000 Ω x 3/4 x 10^9 F = 0.75 s
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