When the Achilles tendon is stretched to a length of 17.1 cm, the tension in the tendon is approximately 2.22 newtons. By multiplying the stress by the cross-sectional area of the tendon, we determine the tension in the tendon.
The strain (ε) in the tendon can be calculated using the formula ε = (ΔL / L), where ΔL is the change in length and L is the original length. In this case, the original length is 16.0 cm, and the change in length is 17.1 cm - 16.0 cm = 1.1 cm.
Using Hooke's Law, stress (σ) is related to strain by the equation σ = E * ε, where E is the Young's modulus of the material. In this case, the Young's modulus is given as 1.65 x 10^10 Pa.
To find the tension (F) in the tendon, we need to multiply the stress by the cross-sectional area (A) of the tendon. The cross-sectional area can be calculated using the formula A = π * (r^2), where r is the radius of the tendon. The diameter of the tendon is given as 5.00 mm, so the radius is 2.50 mm = 0.25 cm.
By plugging in the calculated values, we can determine the strain, stress, and ultimately the tension in the tendon.
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(10%) Problem 2: The image shows a rocket sled, In the top image all four forward thrusters are engaged, creating a total forward thrust of magnitude 47, where T =519 N. In the bottom image, in addition to the four forward thrusters, one reverse thruster is engaged, creating a reverse thrust of magnitude 7. In both cases a backward force (friction and air drag) of magnitude f = 20 Nacts on the sled. 7 What is the ratio of the greater acceleration to the lesser acceleration?
The ratio of the greater acceleration to the lesser acceleration is approximately 0.985.
In the top image where all four forward thrusters are engaged, the total forward thrust exerted on the sled is 519 N. The backward force due to friction and air drag is 20 N. Using Newton's second law, we can calculate the acceleration in this case:
Forward thrust - Backward force = Mass * Acceleration
519 N - 20 N = Mass * Acceleration₁
In the bottom image, in addition to the four forward thrusters, one reverse thruster is engaged, creating a reverse thrust of magnitude 7 N. The backward force of friction and air drag remains the same at 20 N. The total forward thrust can be calculated as:
Total forward thrust = Forward thrust - Reverse thrust
Total forward thrust = 519 N - 7 N = 512 N
Again, using Newton's second law, we can calculate the acceleration this case:
Total forward thrust - Backward force = Mass * Acceleration
512 N - 20 N = Mass * Acceleration₂
To find the ratio of the greater acceleration (Acceleration₂) to the lesser acceleration (Acceleration₁), we can divide the equations:
(Acceleration₂) / (Acceleration₁) = (512 N - 20 N) / (519 N - 20 N)
Simplifying the expression, we get:
(Acceleration₂) / (Acceleration₁) = 492 N / 499 N
(Acceleration₂) / (Acceleration₁) ≈ 0.985
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On a frictionless surface, an 80 gram meter stick lies at rest on a frictionless surface. The origin lies at the 60-cm mark and is along x axis. At the 100 cm mark, there is an 80 gram lump of clay. Also, there is another 80 gram lump of clay moving 2.50 m/s in positive y direction. This second lump of clay collides and sticks at the 12 cm mark. What is angular momentum around center of stick?
What quantities are conserved in collision accounting for angular momentum, energy, momentum, and rotational energy? Give an explanation for each.
2. Calculate the moment of inertia for the two lumps of clay + stick after collision.
3. Calculate the velocity of the center of mass of the meter stick after the collision?
4. Calculate the angular velocity of the stick after collision.
5. Calculate where the center of the stick is after it has completed one rotation?
A friction less surface, an 80 gram meter stick lies at rest on a friction less surface. The origin lies at the 60-cm mark and is along x axis. At the 100 cm mark, there is an 80 gram lump of clay.( 1)) The angular momentum around the center of the stick is zero.(2)The moment of inertia for the two lumps of clay + stick after collision is 0.08 kg×m^2.(3)The velocity of the center of mass of the meter stick after the collision is 0 m/s.(4) The angular velocity of the stick after collision is 4.3 rad/s.(5)The center of the stick will be at the 60 cm mark after it has completed one rotation
The following solution are :
1. This is because the initial angular momentum of the system is zero, and there are no external torques acting on the system after the collision.
2)The quantities conserved in the collision are angular momentum, energy, and momentum. Angular momentum is conserved because there are no external torques acting on the system. Energy is conserved because the collision is elastic. Momentum is conserved because the collision is head-on and there is no net external force acting on the system.
The moment of inertia for the two lumps of clay + stick after collision is 0.08 kg×m^2. This is calculated using the equation I = mr^2, where m is the mass of the system (160 g) and r is the distance from the center of mass to the axis of rotation (58 cm).
3) The velocity of the center of mass of the meter stick after the collision is 0 m/s. This is because the center of mass of the system does not move in a collision.
4) The angular velocity of the stick after collision is 4.3 rad/s. This is calculated using the equation ω = L/I, where L is the angular momentum of the system (0.16 kg.m^2rad/s) and I is the moment of inertia of the system (0.08 kg×m^2).
5) The center of the stick will be at the 60 cm mark after it has completed one rotation. This is because the center of mass of the system does not move in a collision.
Here are the steps in more detail:
The initial angular momentum of the system is zero. This is because the first lump of clay is not rotating, and the second lump of clay has no angular momentum because it is moving in a straight line. There are no external torques acting on the system after the collision. This is because the surface is friction less, so there is no frictional force acting on the system. There are also no other forces acting on the system, so the net torque is zero. The angular momentum of the system is conserved because there are no external torques acting on the system. This means that the angular momentum of the system after the collision must be equal to the angular momentum of the system before the collision, which is zero. The energy of the system is conserved because the collision is elastic. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision. The momentum of the system is conserved because the collision is head-on and there is no net external force acting on the system. This means that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. The center of mass of the meter stick does not move in a collision. This is because the collision is perfectly elastic, and there are no external forces acting on the system. The angular velocity of the stick after collision is calculated using the equation ω = L/I, where L is the angular momentum of the system (0.16 kgm^2rad/s) and I is the moment of inertia of the system (0.08 kg×m^2). This gives us an angular velocity of 4.3 rad/s. The center of the stick will be at the 60 cm mark after it has completed one rotation. This is because the center of mass of the system does not move in a collision.To learn more about angular momentum visit: https://brainly.com/question/4126751
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A capacitor with a capacitance of C = 6.00x10-5 F
is charged by connecting it to a 11.5 - V battery. The capacitor is then disconnected from the batten
and connecteo across an inauctor wit an
inductance of L = 1.55 H.
What is the angular frequency w of the electrical oscillations?
The angular frequency (w) of the electrical oscillations can be calculated using the formula w = 1 / sqrt(LC).
The angular frequency (w) of the electrical oscillations can be calculated using the formula w = 1 / sqrt(LC), where L is the inductance and C is the capacitance. In this case, the capacitance (C) is given as 6.00x10^(-5) F and the inductance (L) is given as 1.55 H.
Plugging in these values into the formula, we have w = 1 / sqrt(1.55 * 6.00x10^(-5)). Simplifying further, w = 1 / sqrt(9.3x10^(-5)). Taking the square root, we get w = 1 / (9.64x10^(-3)). Evaluating this expression, we find w ≈ 103.91 rad/s. Therefore, the angular frequency of the electrical oscillations is approximately 103.91 rad/s.
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Four point charges are located at the comers of a square. Fach charge has magnitude 1 , a0 nc and the square has sides of length 3.00 om. Find the magnitude of the ei of the square of all of the charges are positive and three of illve charges are pesittve and one is negative. (a) sis the charges are positive N/C (b) three of the charges are pesitive and one is negative Nre (a) ill the tharges are jotitive Nye (b) three of the charges are Dettive aref ene is negative N'C
The problem is related to Coulomb's law, which describes the interaction of charges with one another. It is necessary to consider four point charges located at the corners of a square. Each charge has a magnitude of 1 and is positioned a0 nc away from the square, which has sides of length 3.00 om.
The task is to determine the magnitude of the electric field generated by the square of charges if all charges are positive and three are positive, and one is negative. (a) is the charges are positive N/C (b) three of the charges are positive and one is negative Nre (a) ill the charges are positive Nye (b) three of the charges are Dettive aref ene is negative N'C.
Electric field is a vector quantity that is denoted by E. The formula of electric field is E = F / q. The electric field is the force per unit charge acting on a charge placed in the electric field, where F is the force acting on the charge and q is the magnitude of the charge.In the case where all four charges are positive, the magnitude of the electric field generated by the square of charges isE = k * Q / r²The total electric field due to four charges of magnitude q is the vector sum of the individual fields created by each of the charges.E = E1 + E2 + E3 + E4.
We know that the charges at opposite corners of the square have a net electric field of zero because they lie on the same diagonal line. So, we only need to consider the fields created by the two charges along the same diagonal line. Let's say that the charges on this diagonal line are q1 and q2. The distance between them is a, and the distance from each charge to the midpoint of the line is b.
The electric field generated by each of the charges isE = k * q / r²E1 = k * q1 / b²E2 = k * q2 / b²The net electric field at the midpoint of the line isE = E1 - E2 = k * (q1 - q2) / b²The magnitude of the electric field isE = k * (q1 - q2) / b²The distance b is equal to half the length of the diagonal of the square, which isL = √(3² + 3²) = 3√2.
The magnitude of the electric field at the midpoint of the diagonal isE = k * (q1 - q2) / (3√2)²E = k * (q1 - q2) / 18. The electric field at the midpoint of the opposite diagonal is the same magnitude and in the opposite direction. So, the net electric field at the center of the square is zero. So, in this case, the answer is (c) all charges are positive Nye.
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QUESTION 1 0.25 points A student measures the diameter (D) of a cylindrical wire using micrometer of accuracy (0.01mm) as shown in the figure. What is the reading of the measured diameter? a. 5.53 b.3
The reading of the measured diameter is 2.0151 mm which is closest to option b. 3.
Given,Accuracy = 0.01mmDiameter of a cylindrical wire = DWe know that,Error = (Accuracy / 2)So, error in the measurement of diameter = (0.01 / 2) = 0.005 mmAs per the given diagram, the reading on the micrometer scale is 3.51 mm.The main scale reading is 2 mm.
So,Total reading on micrometer = main scale reading + circular scale reading= 2 + 1.51= 3.51 mmThe final reading of the diameter D is obtained by adding the main scale reading to the product of the circular scale reading and the least count of the instrument.
Least Count = 0.01 mmSo, D = Main scale reading + (Circular scale reading x Least count)= 2 + (1.51 × 0.01)= 2 + 0.0151= 2.0151 mm
Therefore, the reading of the measured diameter is 2.0151 mm which is closest to option b. 3.
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13. At each instant, the ratio of the magnitude of the electric field to the magnetic field in an electromagnetic wave in a vacuum is equal to the speed of light. a. Real b. False
b. False.The statement is false. In an electromagnetic-wave in a vacuum, the ratio of the magnitude of the electric field to the magnitude of the magnetic field is not equal to the speed of light.
Instead, the ratio is determined by the impedance of free space, which is a fundamental constant in electromagnetism. The impedance of free space, denoted by the symbol "Z₀," is approximately equal to 377 ohms and represents the ratio of the electric field amplitude to the magnetic-field amplitude in an electromagnetic wave. It is not equal to the speed of light, which is approximately 3 x 10^8 meters per second in a vacuum. Therefore, the correct answer is false.
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An infinitely long cylinder with radius R1 and charge density rho has a small cylinder (length L=50 cm, radius R2
r(R₂) ≈ √(L₂ + R₁₂) + 2kρL ln(R₁ / R₂) / √(L₂ + R1₂). The electric field at point P is then: E = kρ / r₂ ≈ kρ / [L₂ + R₁₂ + 2kρL ln(R₁ / R₂)]. The contribution of a small element of the cylinder with length dx, charge density ρ, and radius x to the electric field at point P is : dE = k · ρ · dx / r
The contribution of a small element of the cylinder with length dx, charge density ρ, and radius x to the electric field at point P is : dE = k · ρ · dx / r, where k is Coulomb's constant. We can use the Pythagorean theorem to relate r and x: r₂= L₂ + (R₁ - x)₂
Squaring both sides and differentiating with respect to x yields: 2r · dr / dx = -2(R₁ - x)
Therefore, dr / dx = -(R₁ - x) / r
Integrating this expression from x = 0 to x = R₂,
we obtain: r(R₂) - r(0) = -∫0R₂(R₁ - x) / r dx
We can use the substitution u = r₂ to simplify the integral:∫1r₁ du / √(r₁₂ - u) = -∫R₂₀(R₁ - x) dx / xR₁ > R₂, the integral can be approximated as: ∫R₂₀(R₁ - x) dx / x ≈ 2(R₁ - R₂) ln (R₁ / R₂)
Therefore: r(R₂) ≈ √(L₂ + R₁₂) + 2kρL ln(R₁ / R₂) / √(L₂ + R1₂)
The electric field at point P is then: E = kρ / r₂ ≈ kρ / [L₂ + R₁₂ + 2kρL ln(R₁ / R₂)]
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A 13-width rectangular loop with 15 turns of wire and a 17 cm length has a current of 1.9 A flowing through it. Two sides of the loop are oriented parallel to a 0.058 uniform magnetic field, and the other two sides are perpendicular to the magnetic field. (a) What is the magnitude of the magnetic moment of the loop? (b) What torque does the magnetic field exert on the loop?
The magnitude of the magnetic moment of the loop is 45.81 Am². The torque exerted on the loop by the magnetic field is 2.66 Nm.
Rectangular loop width, w = 13 cm
Total number of turns of wire, N = 15
Current flowing through the loop, I = 1.9 A
Length of the loop, L = 17 cm
Strength of uniform magnetic field, B = 0.058 T
The magnetic moment of the loop is defined as the product of current, area of the loop and the number of turns of wire.
Therefore, the formula for magnetic moment can be given as;
Magnetic moment = (current × area × number of turns)
We can also represent the area of the rectangular loop as length × width (L × w).
Hence, the formula for magnetic moment can be written as:
Magnetic moment = (I × L × w × N)
The torque (τ) on a magnetic dipole in a uniform magnetic field can be given as:
Torque = magnetic moment × strength of magnetic field sinθ
where θ is the angle between the magnetic moment and the magnetic field.So, the formula for torque can be given as:
T = MB sinθ
(a) The magnetic moment of the loop can be calculated as follows:
Magnetic moment = (I × L × w × N)
= 1.9 × 17 × 13 × 15 × 10^-2Am^2
= 45.81 Am^2
The magnitude of the magnetic moment of the loop is 45.81 Am².
(b)The angle between the magnetic moment and the magnetic field is θ = 90° (as two sides of the loop are perpendicular to the magnetic field)
So sin θ = sin 90° = 1
Torque = M B sinθ
= 45.81 × 0.058 × 1
= 2.66 Nm
Therefore, the torque exerted on the loop by the magnetic field is 2.66 Nm.
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1.15-k22 resistor and a 570-nH inductor are connected in series to a 1500-Hx generator with an rms voltage of 12.1 V What is the rms current in the circuit? What capacitance must be inserted in series with the resistor and inductor to reduce the rms current to half the value found in part A?
The rms current in the circuit is approximately 2.3 A.
To find the rms current in the circuit, we can use Ohm's law and the impedance of the series combination of the resistor and inductor.
The impedance (Z) of an inductor is given by Z = jωL, where j is the imaginary unit, ω is the angular frequency (2πf), and L is the inductance.
In this case, the impedance of the inductor is Z = j(2πf)L = j(2π)(1500 Hz)(570 nH).
The impedance of the resistor is simply the resistance itself, R = 0.15 kΩ.
The total impedance of the series combination is Z_total = R + Z.
The rms current (I) can be calculated using Ohm's law, V_rms = I_rms * Z_total, where V_rms is the rms voltage.
Plugging in the given values, we have:
12.1 V = I_rms * (0.15 kΩ + j(2π)(1500 Hz)(570 nH))
Solving for I_rms, we find that the rms current in the circuit is approximately 2.3 A.
(b) Brief solution:
To reduce the rms current to half the value found in part A, a capacitance must be inserted in series with the resistor and inductor. The value of the capacitance can be calculated using the formula C = 1 / (ωZ), where ω is the angular frequency and Z is the impedance of the series combination of the resistor and inductor.
To reduce the rms current to half, we need to introduce a reactive component that cancels out a portion of the inductive reactance. This can be achieved by adding a capacitor in series with the resistor and inductor.
The value of the capacitance (C) can be calculated using the formula C = 1 / (ωZ), where ω is the angular frequency (2πf) and Z is the impedance of the series combination.
In this case, the angular frequency is ω = 2π(1500 Hz), and the impedance Z is the sum of the resistance and inductive reactance.
Once the capacitance value is calculated, it can be inserted in series with the resistor and inductor to achieve the desired reduction in rms current.
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A block, W 180 lbs rests on a rough level plane. The coefficient of friction is 0.42, what horizontal push will cause the block to move? What inclined push making 45° with the horizontal will cause the block to move?
The inclined push making a 45° angle with the horizontal should satisfy the equation: Horizontal component = inclined push × cos(45°) ≥ Frictional force
To determine the horizontal push required to make the block move, we need to consider the force of friction acting on the block. The force of friction can be calculated using the formula:
Frictional force = coefficient of friction × normal force
The normal force is equal to the weight of the block, which is 180 lbs. Therefore, the normal force is 180 lbs × acceleration due to gravity.
To find the horizontal push, we need to overcome the force of friction. The force of friction is given by the equation:
Frictional force = coefficient of friction × normal force
Let's calculate the force of friction:
Frictional force = 0.42 × (180 lbs × acceleration due to gravity)
Now we can calculate the horizontal push:
Horizontal push = Frictional force
To Know the inclined push making a 45° angle with the horizontal, we need to consider the force components acting on the block. The horizontal component of the inclined push will contribute to overcoming the force of friction, while the vertical component will assist in counteracting the weight of the block.
Since the inclined push makes a 45° angle with the horizontal, the horizontal component can be calculated using the formula:
Horizontal component = inclined push × cos(45°)
To make the block move, the horizontal component of the inclined push should be equal to or greater than the force of friction calculated previously.
Therefore, the inclined push making a 45° angle with the horizontal should satisfy the equation:
Horizontal component = inclined push × cos(45°) ≥ Frictional force
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Determine the current in the 15-V emf.
A.
1.3A
b.
2.7A
c.
2.3A
d
0.30A
e.
2.5A
The answer is e. 2.5A, the current in the 15-V emf is 2.5A. This is because the voltage across the circuit is 15 volts and the resistance of the
is 6 ohms.
The current is calculated using the following equation: I = V / R
where:
I is the current (amps)V is the voltage (volts)R is the resistance (ohms)In this case, the voltage is 15 volts and the resistance is 6 ohms, so the current is: I = 15 / 6 = 2.5A
The current in a circuit is the amount of charge that flows through the circuit per unit time. The voltage across a circuit is the difference in electrical potential between two points in the circuit. The resistance of a circuit is the opposition to the flow of current in the circuit.
The current in a circuit can be calculated using the following equation:
I = V / R
where:
I is the current (amps)V is the voltage (volts)R is the resistance (ohms)In this case, the voltage is 15 volts and the resistance is 6 ohms, so the current is: I = 15 / 6 = 2.5A, Therefore, the current in the 15-V emf is 2.5A.
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Electrons from the main beam at the Stanford Linear Accelerator Center can reach speeds as large as 0.9999999997 c. Let these electrons enter a detector 1 m long. Calculate the length of the detector in the rest frame of one of the particles.
The length of the detector in the rest frame of one of the particles is 0.010129 m.
Stanford Linear Accelerator Center is a research institute that has developed an accelerator to generate high-energy electron and positron beams. These beams are then collided with each other or a fixed target to investigate subatomic particles and their properties. The electrons at this facility can reach a velocity of 0.9999999997 c.
The length of the detector in the rest frame of one of the particles is calculated as follows:Let’s start by calculating the velocity of the electrons. V= 0.9999999997 c.
Velocity can be defined as distance traveled per unit time. Hence, it is necessary to use the Lorentz factor to calculate the length of the detector in the rest frame of one of the particles.
Lorentz factor γ is given byγ = 1 / √(1 – v²/c²)where v is the velocity of the particle and c is the speed of light.γ = 1 / √(1 – (0.9999999997c)²/c²)γ = 98.7887
Now that we have the value of γ, we can calculate the length of the detector in the rest frame of one of the particles.The length of the detector as seen by an observer at rest is L = 1 m.
So, the length of the detector in the rest frame of one of the particles is given byL' = L / γL' = 1 m / 98.7887L' = 0.010129 m
Therefore, the length of the detector in the rest frame of one of the particles is 0.010129 m.
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Remaining Time: 24 minutes, 43 seconds. Question Completion Status: Question 2 0.5 points Save Answe A battery of 8-13 V is connected to a load resistor R-60. If the terminal voltage across the batter
Answer:
The terminal voltage across the battery is 7-13 V.
Explanation:
The terminal voltage of a battery is the voltage measured across its terminals when it is connected to a load. In this case, the battery has a voltage of 8-13 V, and it is connected to a load resistor of 60 Ω.
The terminal voltage of a battery can be affected by various factors, including the internal resistance of the battery and the current flowing through the load. When a load is connected to the battery, the internal resistance of the battery can cause a voltage drop, reducing the terminal voltage.
In this scenario, the terminal voltage across the battery is given as 8-13 V. This range indicates that the terminal voltage can vary between 8 V and 13 V depending on the specific conditions and the load connected to the battery.
To determine the exact terminal voltage across the battery, more information is needed, such as the current flowing through the load or the internal resistance of the battery. Without this additional information, we can only conclude that the terminal voltage across the battery is within the range of 8-13 V.
In summary, the terminal voltage across the battery connected to a load resistor of 60 Ω is 8-13 V. This range indicates the potential voltage values that can be measured across the battery terminals, depending on the specific conditions and factors such as the internal resistance and the current flowing through the load.
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A spaceship, 230-m long for those on board, moves by the Earth at 0.955c. What is its length as measured by an earthbound observer
The length of the spaceship as measured by an earthbound observer is approximately 68.69 meters.
To calculate the length of the spaceship as measured by an earthbound observer, we can use the Lorentz transformation for length contraction:
L' = L × sqrt(1 - (v²/c²))
Where:
L' is the length of the spaceship as measured by the earthbound observer,
L is the proper length of the spaceship (230 m in this case),
v is the velocity of the spaceship relative to the earthbound observer (0.955c),
c is the speed of light.
Substituting the given values:
L' = 230 m × sqrt(1 - (0.955c)²/c²)
To simplify the calculation, we can rewrite (0.955c)² as (0.955)² × c²:
L' = 230 m × sqrt(1 - (0.955)² × c²/c²)
L' = 230 m × sqrt(1 - 0.911025)
L' = 230 m sqrt(0.088975)
L' = 230 m × 0.29828
L' = 68.69 m
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the container shown has a the sape of a rectanglar soldid whena rock is submerged the water level rises 0.5 cm find the volume of the rock
Remember to convert the measurements to the same unit. Once you have the volume of the rock, express it in cubic centimeters (cm³) since the water level rise was given in centimeters.
To find the volume of the rock, we can use the concept of displacement. When the rock is submerged in the container, it displaces a certain amount of water equal to its own volume.
Given that the water level rises by 0.5 cm when the rock is submerged, we know that the volume of the rock is equal to the volume of water displaced, which can be calculated using the formula:
Volume of rock = Volume of water displaced
The volume of water displaced can be calculated using the formula:
Volume of water displaced = length × width × height
Since the shape of the container is a rectangular solid, the length, width, and height are already given. We can substitute the values into the formula to find the volume of the rock.
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ydro Electrical Funda COURSES SCHOOL OF ACCESS AND CONTINUING EDUCA PHYSICS: A REVIEW OF THE PHYSICS YOU WILL NEED TO CO Calculate the capacitive reactance of a capacitor through which 6A flows when 12VAC is applied. Select one: a. 2 ohms b. 0.7 ohms of is page nit 3 Oc. 4 ohms d. 2.7 ohms Jump to... · Next page Unit 4 ► : 7
Calculating the capacitive reactance of a capacitor through which 6A flows when 12VAC is applied.
The capacitive reactance can be calculated as follows: XC = V / I
Where, V = Voltage applied
I = Current flowing
XC = Capacitive reactance
Therefore, substituting the given values,V = 12VACI = 6AXC = V / IXC = 12VAC / 6A = 2 Ω
Thus, the capacitive reactance of a capacitor through which 6A flows when 12VAC is applied is 2 Ω.
The capacitive reactance of a capacitor can be calculated using the formula XC = V / I, where V is the voltage applied, I is the current flowing, and XC is the capacitive reactance. When 12VAC is applied to a capacitor through which 6A flows, the capacitive reactance is 2 Ω.
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An object with mass 3.2 kg is moving in one dimension subject to a time-dependent force given by the function F (1) = 3.172
At t = 1.0 s, the object is moving in the -x direction at a speed of 8.8 m/s.
What is the object's velocity at t = 2.1 s?
An object with mass 3.2 kg is moving in one dimension subject to a time-dependent force given by the function F (1) = 3.172. At t = 2.1 s, its velocity is -18.8 m/s in the -x direction.
To solve this problem, we can use the following equation:
F = ma
where
F is the force acting on the object
m is the mass of the object
a is the acceleration of the object
We know that the force acting on the object is given by the function F(t) = 3.172. We also know that the mass of the object is 3.2 kg. We can use these values to find the acceleration of the object:
a = F/m = 3.172 N/kg = 0.988 m/s²
We know that the object is moving in the -x direction at a speed of 8.8 m/s at t = 1.0 s. We can use this information to find the object's velocity at t = 2.1 s:
v = u + at
where
v is the object's velocity at t = 2.1 s
u is the object's velocity at t = 1.0 s
a is the acceleration of the object
Substituting the known values, we get:
v = -8.8 m/s + 0.988 m/s² * 2.1 s = -18.8 m/s
Therefore, the object's velocity at t = 2.1 s is -18.8 m/s.
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Consider a board meeting with n board members {1, 2, …, n}, each with a voting weight w_i (a positive integer) in the set W = {w_1, w_2, …, w_n}. When member i votes, their vote gets counted with weight w_i. A resolution being voted on by the board will pass if and only if the sum of the weights of `yes’ votes is a specific number T (a non-negative integer) – no more, no less.
Write an algorithm that will take as input the array W of weights (with w_i stored at index i) and the target sum T of voting weights and output TRUE if it is possible to pass a resolution with any combination of the input weights and FALSE otherwise. You may write the algorithm as pseudo-code or in a programming language of your choice
The required algorithm that will take as input the array W of weights (with w_i stored at index i) and the target sum T of voting weights and output TRUE if it is possible to pass a resolution with any combination of the input weights and FALSE otherwise is given below:
Algorithm: Function Can_Resolution_Passed (W, T)Initialize a Boolean variable Res with false.Set N as the length of array W. For i=1 to 2^N-1Iterate through the array W to find the sum of weights of the ith combination of the array W. Create a variable sum and initialize it with 0. For j=0 to N-1 If the jth bit of the binary representation of i is 1, then add W[j] to sum. End IfEnd For If sum is equal to T, then set Res to true and break the loop. End IfEnd ForReturn Res as the output.
End Function The above algorithm is checking all possible subsets of the array W, and for each subset, it is checking whether their sum is equal to the target sum T or not. If we get such a subset, then we return true, else we return false.The time complexity of the above algorithm is O(N*2^N), which is exponential.
But it is the best possible solution to the given problem because we need to check all possible subsets of the array W.
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A car drives at a constant speed of 21 m/s around a circle of radius 100m. What is the centripetal acceleration of the car
The centripetal acceleration of the car driving at a constant speed of 21 m/s around a circle with a radius of 100 m is calculated to be 4.41[tex]m/s^2.[/tex]
To find the centripetal acceleration of the car, we can use the formula:
a = [tex]v^2[/tex] / r
where "a" represents the centripetal acceleration, "v" is the velocity of the car, and "r" is the radius of the circular path.
Given that the car drives at a constant speed of 21 m/s and the radius of the circle is 100 m, we can substitute these values into the formula to calculate the centripetal acceleration.
a = (21[tex]m/s)^2[/tex]/ 100 m
a = 441 [tex]m^2/s^2[/tex]/ 100 m
a = 4.41 [tex]m/s^2[/tex]
Therefore, the centripetal acceleration of the car is 4.41[tex]m/s^2.[/tex] This centripetal acceleration represents the inward acceleration that keeps the car moving in a circular path, and its magnitude is determined by the square of the velocity divided by the radius of the circle.
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A 45μF air-filled capacitor is charged to a potential difference of 3304 V. What is the energy stored in it?
Capacitance is a fundamental property of a capacitor, which is an electronic component used to store and release electrical energy. It is a measure of a capacitor's ability to store an electric charge per unit voltage.Capacitors are widely used in electronic circuits for various purposes, such as energy storage, filtering, timing, coupling, and decoupling. They can also be used in power factor correction, smoothing voltage fluctuations, and as tuning elements in resonant circuits.
Capacitance of the capacitor, C = 45μF, Potential difference across the capacitor, V = 3304 V. Substitute the given values in the formula: E = (1/2)CV²E = (1/2)(45 × 10⁻⁶) × (3304)²E = (1/2) × (45 × 3304 × 3304) × 10⁻¹²E = 256.86 J.
Therefore, the energy stored in the given capacitor is 256.86 J.
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An RLC series circuit is connected to a 220V 60 Hz AC voltage. What is the phase angle op between V and 17 Consider R = 10 . L = 40 mH. and C = 90 pF. Select one: O a. 55.2° Ob 12.89 Oc 34.29 d. 21.0
The phase angle between the voltage (V) and current (I) in the RLC series circuit is 55.2°.
What is the phase angle?To find the phase angle between the voltage (V) and current (I) in an RLC series circuit, we can use the formula:
tan(φ) = (Xl - Xc) / R
where:
φ is the phase angleXl is the inductive reactanceXc is the capacitive reactanceR is the resistanceGiven:
R = 10 Ω
L = 40 mH = 40 * 10^-3 H
C = 90 pF = 90 * 10^-12 F
f = 60 Hz
V = 220 V
First, we need to calculate the inductive reactance (Xl) and capacitive reactance (Xc):
Xl = 2πfL
Xc = 1 / (2πfC)
Substituting the given values, we get:
Xl = 2π * 60 * 40 * 10⁻³
Xc = 1 / (2π * 60 * 90 * 10⁻¹²)
Xl ≈ 15.08 Ω
Xc ≈ 29.53 kΩ
Now we can calculate the phase angle (φ):
tan(φ) = (15.08 kΩ - 29.53 kΩ) / 10 Ω
tan(φ) ≈ -1.4467
Taking the inverse tangent (arctan) of both sides, we find:
φ ≈ -55.2°
Since the phase angle is negative, we take the absolute value:
|φ| ≈ 55.2°
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A charge Q is located some distance L from the center of a wire. A small charge −q with mass m is attached to the wire such that it can move along the wire but not perpendicular to it. The small charge −q is moved some small amount Δx<
The work done on the small charge -q when it is moved a small distance Δx along the wire can be determined by substituting the force equation into the work equation and solving for W
When the small charge -q is moved a small distance Δx along the wire, it experiences a force due to the electric field generated by the charge Q.
The direction of this force depends on the relative positions of the charges and their charges' signs. Since the small charge -q is negative, it will experience a force in the opposite direction of the electric field.
Assuming the small charge -q moves in the same direction as the wire, the work done on the charge can be calculated using the formula:
Work (W) = Force (F) × Displacement (Δx)
The force acting on the charge is given by Coulomb's Law:
Force (F) = k * (|Q| * |q|) / (L + Δx)²
Here, k is the electrostatic constant and |Q| and |q| represent the magnitudes of the charges.
Thus, the work done on the small charge -q when it is moved a small distance Δx along the wire can be determined by substituting the force equation into the work equation and solving for W.
It's important to note that the above explanation assumes the charge Q is stationary, and there are no other external forces acting on the small charge -q.
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discuss why we introduced the interaction picture for
time-dependent perturbation theory
The interaction picture is introduced in time-dependent perturbation theory to separate the effects of the unperturbed system and the perturbation, simplifying calculations. It allows for easier analysis of time-dependent perturbations by transforming the state vectors and operators according to a unitary transformation.
The interaction picture is introduced in time-dependent perturbation theory to simplify the analysis of systems undergoing time-dependent perturbations. In this picture, the Hamiltonian of the system is split into two parts: the unperturbed Hamiltonian and the perturbation Hamiltonian.
The unperturbed Hamiltonian describes the system's behavior in the absence of perturbation, while the perturbation Hamiltonian accounts for the time-dependent perturbation.
By working in the interaction picture, we can separate the time evolution due to the unperturbed Hamiltonian from the effects of the perturbation. This separation allows us to treat the perturbation as a small correction to the unperturbed system, making the calculations more manageable.
In the interaction picture, the state vectors and operators are transformed according to a unitary transformation to account for the time evolution due to the unperturbed Hamiltonian. This transformation simplifies the time dependence of the operators and allows for easier calculations of expectation values and transition probabilities.
Overall, the introduction of the interaction picture in time-dependent perturbation theory provides a convenient framework for studying the effects of time-dependent perturbations on quantum systems and simplifies the mathematical analysis of the problem.
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Submission 1 (0/1 points) Friday, May 6, 2022 07:58 PM PDT A liquid compound is not heated by microwaves the way water is. What can you conclude about the nature of the compound's molecules? O The compound must have a higher density than water. The compound's molecules must be polar. The compound must have a lower density than water. O The compound's molecules must not be polar. X Submission 2 (0/1 points) Friday, May 6, 2022 08:00 PM PDT A liquid compound is not heated by microwaves the way water is. What can you conclude about the nature of the compound's molecules? The compound must have a higher density than water. The compound's molecules must be polar. The compound must have a lower density than water. O The compound's molecules must not be polar.
The molecular type of the chemical can be deduced from the statement (b) "The compound's molecules must not be polar."
Microwaves heat substances by causing the molecules to rotate and generate heat through molecular friction. Water molecules, which are polar due to their bent structure and the presence of polar covalent bonds, readily absorb microwave radiation and experience increased molecular motion and heating.
In contrast, nonpolar compounds lack significant dipole moments and do not easily interact with microwaves. As a result, they are not heated by microwaves in the same way as polar molecules like water. Therefore, we can conclude that the compound in question must not have polar molecules.
Therefore : (b) "The compound's molecules must not be polar." is the correct answer.
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1) You are watering a garden using a garden hose connected to a large open tank of water. The garden hose has a circular cross-section with a diameter of 1.4 cm, and has a nozzle attachment at its end with a diameter of 0.80 cm. What is the gauge pressure at point A in the garden hose? (Ignore viscosity for this question.)
The gauge pressure at point A in the garden hose can be calculated as follows:The gauge pressure is the difference between the absolute pressure in the hose and atmospheric pressure.
The formula to calculate absolute pressure is given by;P = ρgh + P₀Where:P is the absolute pressureρ is the density of the liquid (water in this case)g is the acceleration due to gravity h is the height of the water column above the point A.
P₀ is the atmospheric pressure. Its value is usually 101325 Pa.The height of the water column above point A is equal to the height of the water level in the tank minus the length of the hose, which is 1 meter.
Let's assume that the tank is filled to a height of 2 meters above point A.
the height of the water column above point A is given by; h = 2 m - 1 m = 1 m
The density of water is 1000 kg/m³.
A.P = ρgh + P₀P
= (1000 kg/m³)(9.81 m/s²)(1 m) + 101325 PaP
= 11025 Pa
The absolute pressure at point A is 11025 Pa.
Gauge pressure = Absolute pressure - Atmospheric pressureGauge pressure
= 11025 Pa - 101325 PaGauge pressure
= -90299 Pa
Since the gauge pressure is negative, this means that the pressure at point A is below atmospheric pressure.
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The heating coil in an electric bea pot is made of nichrome wire with a radius of 0.400 mm. If the coil draws a current or 5.60 A when there is a 120 V potential oference across ta ende, find the following. (Take the resistivity of nicome to be 1.50 X 100m) (a) resistance of the col (in) (1) length or wire used to win the col tinm) m
The resistance of the coil is approximately 21.43 Ω, and the length of wire used to wind the coil is approximately 0.071 m.
To find the resistance of the coil, we can use the formula:
Resistance (R) = Resistivity (ρ) * Length (L) / Cross-sectional area (A)
Given the resistivity of nichrome wire as 1.50 × 10^−6 Ω·m and the radius of the wire as 0.400 mm, we can calculate the cross-sectional area (A) using the formula:
[tex]A = π * r^2[/tex]
where r is the radius of the wire.
Let's calculate the cross-sectional area first:
[tex]A = π * (0.400 mm)^2[/tex]
[tex]= π * (0.400 × 10^−3 m)^2[/tex]
[tex]≈ 5.03 × 10^−7 m^2[/tex]
Now, we can calculate the resistance (R) of the coil using the given formula:
[tex]R = ρ * L / A[/tex]
To find the length of the wire used in the coil (L), we rearrange the formula:
[tex]L = R * A / ρ[/tex]
Given that the current drawn by the coil is 5.60 A and the potential difference across the coil is 120 V, we can use Ohm's Law to find the resistance:
[tex]R = V / I[/tex]
Now, we can substitute the values into the formula for the length (L):
[tex]L = (21.43 Ω) * (5.03 × 10^−7 m^2) / (1.50 × 10^−6 Ω·m)[/tex]
Simplifying:
L ≈ 0.071 m
Therefore, the resistance of the coil is approximately 21.43 Ω, and the length of wire used to wind the coil is approximately 0.071 m.
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Determine the magnitudes and directions of the currents in each resistor shown in the figure. The batteries have emfs of ε1=7.4 V and ε2=11.4 V and the resistors have values of R1=30Ω=R2=32Ω, and R3=34Ω Figure 1 of 1 Assume each battery has internal resistance 1.5Ω. Express your answers using two significant figures. Enter your answers numerically separated by commas. Part F I1 is difected to the left. I i is diracted to the right 15 of the currents in atteries have emfs of atstors have values of 1. of 1 I1 is directed to the right. Part G I2 is directed to the left. I2 is directed to the right: fes and directions of the currents in the figure. The batteries have emils of 4 V and the resistors have values of , and R3=34Ω
To determine the magnitudes and directions of the currents in each resistor, we can analyze the circuit using Kirchhoff's laws and Ohm's law.
(a) Let's label the currents flowing through the resistors as I1, I2, and I3, as shown in the figure. We'll also consider the currents flowing in the batteries as Ia (for ε1) and Ib (for ε2).
Using Kirchhoff's loop rule for the outer loop, we have:
-ε1 + Ia(R1 + R2 + R3) - I2(R2 + R3) - I3R3 = 0
Using Kirchhoff's loop rule for the inner loop, we have:
-ε2 + Ib(R2 + R3) - I1R1 + I2(R2 + R3) = 0
We also know that the current in each resistor is related to the potential difference across the resistor by Ohm's law:
V = IR
Now, let's solve the system of equations: From the first equation, we can solve for Ia:
Ia = (ε1 + I2(R2 + R3) + I3R3) / (R1 + R2 + R3)
Substituting this value into the second equation, we can solve for Ib:
-ε2 + Ib(R2 + R3) - I1R1 + I2(R2 + R3) = 0
Ib = (ε2 + I1R1 - I2(R2 + R3)) / (R2 + R3)
Now, we can substitute the expressions for Ia and Ib into the equation for I1:
-ε1 + Ia(R1 + R2 + R3) - I2(R2 + R3) - I3R3 = 0
I1 = (ε1 - Ia(R1 + R2 + R3) + I2(R2 + R3) + I3R3) / R1
Finally, we can calculate the values of I1, I2, and I3 using the given values for ε1, ε2, R1, R2, and R3.
(b) Substituting the given values:
ε1 = 7.4 V
ε2 = 11.4 V
R1 = R2 = 32 Ω
R3 = 34 ΩI1 ≈ -0.122 A (directed to the left)
I2 ≈ 0.231 A (directed to the right)
I3 ≈ 0.070 A (directed to the right)
Therefore, the magnitudes and directions of the currents in each resistor are approximately:
I1 = 0.12 A (to the left)
I2 = 0.23 A (to the right)
I3 = 0.07 A (to the right)
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A lamp located 3 m directly above a point P on the floor of a
room produces at P an illuminance of 100 lm/m2. (a) What is the
luminous intensity of the lamp? (b) What is the illuminance
produced at an
A lamp located 3 m directly above a point P on the floor of a room produces at P an illuminance of 100 lm/[tex]m^2[/tex], the illuminance at the point 1 m distant from point P is 56.25 lm/[tex]m^2[/tex].
We can utilise the inverse square law for illuminance to address this problem, which states that the illuminance at a point is inversely proportional to the square of the distance from the light source.
(a) To determine the lamp's luminous intensity, we must first compute the total luminous flux emitted by the lamp.
Lumens (lm) are used to measure luminous flux. Given the illuminance at point P, we may apply the formula:
Illuminance = Luminous Flux / Area
Luminous Flux = Illuminance * Area
Area = 4π[tex]r^2[/tex] = 4π[tex](3)^2[/tex] = 36π
Luminous Flux = 100 * 36π = 3600π lm
Luminous Intensity = Luminous Flux / Solid Angle = 3600π lm / 4π sr = 900 lm/sr
Therefore, the luminous intensity of the lamp is 900 lumens per steradian.
b. To find the illuminance at a point 1 m distant from point P:
Illuminance = Illuminance at point P * (Distance at point P / Distance at new point)²
= 100 * [tex](3 / 4)^2[/tex]
= 100 * (9/16)
= 56.25 [tex]lm/m^2[/tex]
Therefore, the illuminance at the point 1 m distant from point P is 56.25 [tex]lm/m^2[/tex]
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Your question seems incomplete, the probable complete question is:
A lamp located 3 m directly above a point P on the floor of a room produces at Pan illuminance of 100 lm/m2. (a) What is the luminous intensity of the lamp? (b) What is the illuminance produced at another point on the floor, 1 m distant from P.
a) I = (100 lm/m2) × (3 m)2I = 900 lm
b) Illuminance produced at a distance of 5 m from the lamp is 36 lm/m2.
(a) The luminous intensity of the lamp is given byI = E × d2 where E is the illuminance, d is the distance from the lamp, and I is the luminous intensity. Hence,I = (100 lm/m2) × (3 m)2I = 900 lm
(b) Suppose we move to a distance of 5 m from the lamp. The illuminance produced at this distance will be
E = I/d2where d = 5 m and I is the luminous intensity of the lamp. Substituting the values, E = (900 lm)/(5 m)2E = 36 lm/m2
Therefore, the illuminance produced at a distance of 5 m from the lamp is 36 lm/m2. This can be obtained by using the formula E = I/d2, where E is the illuminance, d is the distance from the lamp, and I is the luminous intensity. Luminous intensity of the lamp is 900 lm.
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A 1530-kg automobile has a wheelbase (the distance between the axdes) of 3.30 m. The automobile's center of mass is on the centerline at a point 1.10 m behind the front axle. Find the force exerted by each front wheel KN each rear wheel
Front wheel exerts a force of approximately 5018 N, and each Rear wheel exerts a force of approximately 2509 N .
To find the force exerted by each front and rear wheel of the automobile, we can use the principle of moments and the concept of weight distribution.
Let's assume that the weight of the automobile is evenly distributed between the front and rear wheels. Since the center of mass is located 1.10 m behind the front axle, the weight of the automobile can be considered as acting at the center of mass.
The total weight of the automobile can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight = 1530 kg * 9.8 m/s^2
Weight ≈ 15054 N
Now, we can calculate the weight distribution between the front and rear wheels. Since the wheelbase is 3.30 m, the weight distribution can be determined using the principle of moments:
Weight_front * distance_front = Weight_rear * distance_rear
Weight_front * (3.30 m) = Weight_rear * (3.30 m - 1.10 m)
Weight_front * 3.30 = Weight_rear * 2.20
Weight_front/Weight_rear = 2.20/3.30
Weight_front/Weight_rear = 2/3
Since the weight distribution is proportional to the ratio of distances, we can calculate the weight on each wheel:
Weight_front = (2/3) * Total Weight
Weight_rear = (1/3) * Total Weight
Weight_front = (2/3) * 15054 N ≈ 10036 N
Weight_rear = (1/3) * 15054 N ≈ 5018 N
Finally, to calculate the force exerted by each front and rear wheel, we divide the weight by the number of wheels:
Force_front = Weight_front / 2
Force_rear = Weight_rear / 2
Force_front = 10036 N / 2 ≈ 5018 N
Force_rear = 5018 N / 2 ≈ 2509 N
Therefore, each front wheel exerts a force of approximately 5018 N (5.018 kN), and each rear wheel exerts a force of approximately 2509 N (2.509 kN).
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Dock The object in the figure is a depth d= 0.750 m below the surface of clear water. The index of refraction n of water is 1.33. d Water (n=1.33) Object D What minimum distance D from the end of the dock must the object be for it not to be seen from any point on the end of the dock? D = m Assume that the dock is 2.00 m long and the object is at a depth of 0.750 m. If you changed the value for index of refraction of the water to be then you can see the object at any distance beneath the dock. Dock The object in the figure is a depth d = 0.750 m below the surface of clear water. The index of refraction n of water is 1.33. d Water (n=1.33) Object D What minimum distance D from the end of the dock must the object be for it not to be seen from any point on the end of the dock? D= m m Assume that the dock is 2.00 m long and the object is at a depth of 0.750 m. If you changed the value for index of refraction of the water to be then you less than a maximum of beneath the dock. greater than a minimum of Dock The object in the figure is a depth d = 0.750 m below the surface of clear water. The index of refraction n of water is 1.33. d Water (n=1.33) Object D What minimum distance D from the end of the dock must the object be for it not to be seen from any point on the end of the dock? D = m Assume that the dock is 2.00 m long and the object is at a depth of 0.750 m. If you changed the value for index of refraction of the water to be then you can see the object at any distance b 1.07, lock 1.33, 1.00,
The image provided shows a dock with a length of 2.00 m, with an object placed at a depth d of 0.750 m below the surface of clear water having a refractive index of 1.33. We need to determine the minimum distance D from the end of the dock, such that the object is not visible from any point on the end of the dock.
The rays of light coming from the object move towards the surface of the water at an angle to the normal, gets refracted at the surface and continues its path towards the viewer's eye. The minimum distance D can be calculated from the critical angle condition. When the angle of incidence in water is such that the angle of refraction is 90° with the normal, then the angle of incidence in air is the critical angle. The angle of incidence in air corresponding to the critical angle in water is given by: sin θc = 1/n, where n is the refractive index of the medium with higher refractive index. In this case, the angle of incidence in air corresponding to the critical angle in water is:
[tex]sin θc = 1/1.33 ⇒ θc = sin-1(1/1.33) = 49.3°[/tex]As shown in the image below, the minimum distance D from the end of the dock can be calculated as :Distance[tex]x tan θc = (2.00 - D) x tan (90 - θc)D tan θc = 2.00 tan (90 - θc) - D tan (90 - θc)D tan θc + D tan (90 - θc) = 2.00 tan (90 - θc)D = 2.00 tan (90 - θc) / (tan θc + tan (90 - θc))D = 2.00 tan 40.7° / (tan 49.3° + tan 40.7°)D = 0.90 m[/tex]Therefore, the minimum distance D from the end of the dock, such that the object is not visible from any point on the end of the dock is 0.90 m .If the refractive index of the water is changed to be less than a maximum of 1.07, then we can see the object at any distance beneath the dock. This is because the critical angle will be greater than 90° in this case, meaning that all rays of light coming from the object will be totally reflected at the surface of the water and will not enter the air above the water.
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