Question 1

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of unstable equilibrium are:

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The answer of The diagram shows a plot of the...

Question 2

The first graph shows the potential energy U(x) for a particle moving on the x axis. Which of the following five graphs correctly gives the force F exerted on the particle?

Accepted Answer

The force on a particle is equal to the negative derivative of the potential energy with respect to position, i.e. F = -dU(x)/dx. This means that the graph of the force is simply the negative gradient of the potential energy graph, which is shown in Option D.

Question 3

The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

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The answer of The potential energy of a body of...

Question 4

The potential energy of a particle moving along the x axis is given by U(x) = (8.0J/m²)x² + (2.0J/m4)x⁴. If the total mechanical energy is 9.0 J, the limits of motion are:

Accepted Answer

The limits of motion are found by setting the potential energy U(x) equal to the total mechanical energy (9.0 J) and solving for x. Solving the equation (8.0)x^2 + (2.0)x^4 = 9.0 gives x = ±0.96 m.

Question 5

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

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The answer of Three identical blocks move either on a...

Question 6

The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x¹² - B/x⁶, where A and B are constants and x is the interatomic distance. The magnitude of the force of one atom exerts on the other is:

Accepted Answer

To find the force, we need to take the derivative of the potential energy with respect to the distance x: F = -dU/dx = -A (1/x^2) ¹³ - B (1/x^2) ⁷ Simplifying, we get: F = -A/x^2 ¹³ - B/x^2 ⁷ Multiplying numerator and denominator of the first term by x gives: F = -A/|x|¹³ + B/x⁷ Multiplying numerator and denominator of the second term by |x| gives: F = 12A/|x|¹³ - 6B/|x|⁷ Therefore, the correct answer is A.

Question 7

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is

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The answer of A 25-g ball is released from rest...

Question 8

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²)x²+ (2.0J/m⁴)x^4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

Accepted Answer

To find the point where the particle stops, we need to find the point where the kinetic energy of the particle is zero. At that point, all the initial kinetic energy of the particle is converted to potential energy given by U(x).

The kinetic energy of the particle when it is at x = 1.0 m is given by (1/2)mv^2 = (1/2) x 0.20 kg x (5.0 m/s)^2 = 2.5 J.

Let's find the point where U(x) = 2.5 J.

U(x) = (8.0 J/m^(1/2)) x^(3/2) + (2.0 J/m^(1/4)) x^(4)

Equating U(x) to 2.5 J, we get:

(8.0 J/m^(1/2)) x^(3/2) + (2.0 J/m^(1/4)) x^(4) = 2.5 J

Solving this equation numerically, we get x = 1.1 m or x = -2.3 m. Since the particle starts at x = 1.0 m and is moving in the positive direction, it must turn around at x = 1.1 m. Therefore, the answer is choice C.

Question 9

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

Accepted Answer

Thermal energy is associated with the motion of individual particles within a system. In this case, the thermal energy would be a result of the motions of the particles within the ball and the air. The gravitational interaction (A) and the kinetic energy of the ball and Earth as a whole (B and E) do not contribute to thermal energy in the same way that the motions of individual particles do. The motion of particles within the ball (C) would contribute to thermal energy but does not account for the whole system.

Question 10

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:

Accepted Answer

The thermal energy of the block and the table top increases due to the work done against friction. The kinetic energy of the block is converted into elastic potential energy stored in the spring and thermal energy due to friction. The increase in thermal energy can be calculated by finding the initial kinetic energy of the block and the potential energy stored in the spring. The initial kinetic energy (KE) is given by $ \frac{1}{2}mv^2 $, where $ m = 0.75 $ kg and $ v = 3.5 $ m/s. The potential energy (PE) stored in the spring is given by $ \frac{1}{2}kx^2 $, where $ k = 1200 $ N/m and $ x = 0.057 $ m (since 5.7 cm = 0.057 m). The difference between the initial kinetic energy and the potential energy stored in the spring is the increase in thermal energy.Calculating the initial kinetic energy:$$ KE = \frac{1}{2} \times 0.75 \times (3.5)^2 = 4.59375 \, \text{J} $$Calculating the potential energy stored in the spring:$$ PE = \frac{1}{2} \times 1200 \times (0.057)^2 = 1.9442 \, \text{J} $$The increase in thermal energy is the difference between the initial kinetic energy and the potential energy stored in the spring:$$ \Delta E_{thermal} = KE - PE = 4.59375 - 1.9442 = 2.64955 \, \text{J} $$This is approximately 2.6 J, so the thermal energy of the block and the table top has increased by 2.6 J.

Question 11

A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is:

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Question 12

Objects A and B interact with each other via both conservative and nonconservative forces. Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy. If no external agent does work on the objects then:

Accepted Answer

In a system where objects interact through both conservative and nonconservative forces, without external work being done, the total mechanical energy (kinetic plus potential) is not conserved due to the presence of nonconservative forces. However, the total energy, which includes kinetic energy, potential energy, and internal energy (accounting for energy lost or gained through nonconservative forces), remains conserved. This is because energy can neither be created nor destroyed, only transformed.

Question 13

Given a potential energy function U(x), the corresponding force  is in the positive x direction if:

Accepted Answer

The relationship between potential energy and force is given by the equation F=-dU/dx, where F is the force and U is the potential energy function. Taking the derivative of U with respect to x results in dU/dx. If this derivative is negative, which is the case for a decreasing function, then the force will be positive in the x direction. Therefore, the correct answer is D.

Question 14

A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25 °  above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the thermal energy of the projectile and air is:

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The answer of A 5-kg projectile is fired over level...

Question 15

As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

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The answer of As a particle moves along the x...

Question 16

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are:

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The answer of The diagram shows a plot of the...

Question 17

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x) shown. The particle:

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The answer of A particle is released from rest at...

Question 18

A block slides across a rough horizontal table top. The work done by friction changes:

Accepted Answer

Friction converts kinetic energy into thermal energy.

Question 19

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of neutral equilibrium are:

Accepted Answer

The answer of The diagram shows a plot of the...

Question 20

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²)x²+ (2.0J/m⁴)x^4. When the particle is at x = 1.0 m its magnituede of its acceleration is:

Accepted Answer

The answer of The potential energy of a 0.20-kg particle...

Quiz 8: Potential Energy and Conservation of Energy

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of unstable equilibrium are:

The first graph shows the potential energy U(x) for a particle moving on the x axis. Which of the following five graphs correctly gives the force F exerted on the particle?

The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

The potential energy of a particle moving along the x axis is given by U(x) = (8.0J/m²) x² + (2.0J/m4) x⁴. If the total mechanical energy is 9.0 J, the limits of motion are:

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x¹² - B/x⁶, where A and B are constants and x is the interatomic distance. The magnitude of the force of one atom exerts on the other is:

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²) x²+ (2.0J/m⁴) x^4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:

A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is:

Objects A and B interact with each other via both conservative and nonconservative forces. Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy. If no external agent does work on the objects then:

Given a potential energy function U(x) , the corresponding force is in the positive x direction if:

A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25 ° above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the thermal energy of the projectile and air is:

As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are:

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x) shown. The particle:

A block slides across a rough horizontal table top. The work done by friction changes:

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of neutral equilibrium are:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²) x²+ (2.0J/m⁴) x^4. When the particle is at x = 1.0 m its magnituede of its acceleration is:

Quiz 8: Potential Energy and Conservation of Energy

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of unstable equilibrium are:

The first graph shows the potential energy U(x) for a particle moving on the x axis. Which of the following five graphs correctly gives the force F exerted on the particle?

The potential energy of a body of mass m is given by U = -mgx + 1/2kx2. The corresponding force is:

The potential energy of a particle moving along the x axis is given by U(x) = (8.0J/m2) x2 + (2.0J/m4) x4. If the total mechanical energy is 9.0 J, the limits of motion are:

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.

The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x12 - B/x6, where A and B are constants and x is the interatomic distance. The magnitude of the force of one atom exerts on the other is:

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m2) x2 + (2.0J/m4) x4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:

A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is:

Objects A and B interact with each other via both conservative and nonconservative forces. Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the internal energy. If no external agent does work on the objects then:

Given a potential energy function U(x) , the corresponding force is in the positive x direction if:

A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25 ° above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the thermal energy of the projectile and air is:

As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of stable equilibrium are:

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x) shown. The particle:

A block slides across a rough horizontal table top. The work done by friction changes:

The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of neutral equilibrium are:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m2) x2 + (2.0J/m4) x4. When the particle is at x = 1.0 m its magnituede of its acceleration is:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

The potential energy of a particle moving along the x axis is given by U(x) = (8.0J/m²) x² + (2.0J/m4) x⁴. If the total mechanical energy is 9.0 J, the limits of motion are:

The potential energy for the interaction between the two atoms in a diatomic molecule is U = A/x¹² - B/x⁶, where A and B are constants and x is the interatomic distance. The magnitude of the force of one atom exerts on the other is:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²) x²+ (2.0J/m⁴) x^4. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 5.0 m/s. It next stops momentarily to turn around at x =

Objects A and B interact with each other via both conservative and nonconservative forces. Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy. If no external agent does work on the objects then:

The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) =(8.0J/m²) x²+ (2.0J/m⁴) x^4. When the particle is at x = 1.0 m its magnituede of its acceleration is: