Question 1

An object of mass 20.0 kg is lifted vertically through 1.00 m by a 400 N force. How much work is done by the net force in lifting this object? Use g = 10.0 m/s².

Accepted Answer

Work done by a force = force x distance x cos(theta).

Here, the force and displacement are in the same direction, so cos(theta) = 1.

Work done = 400 N x 1.00 m = 400 J.

Note that the weight of the object does not need to be considered since it is not doing any work in this scenario.

Question 2

A person drops a brick from the top of a building. The height of the building is 400 m and the mass of the brick is 2.00 kg. What will be the speed of the brick right before it touches the ground? Use g = 10.0 m/s².

Accepted Answer

The potential energy of the brick at the top of the building is given by:

PE = mgh = (2.00 kg)(10.0 m/s^2)(400 m) = 8000 J

At the bottom of the building, all of this potential energy will be converted into kinetic energy:

KE = 1/2 mv^2

Rearranging this equation gives:

v = sqrt(2KE/m)

Substituting in the values for KE and m and solving for v gives:

v = sqrt(2(8000 J)/(2.00 kg)) = 89.4 m/s

Therefore, the speed of the brick right before it touches the ground is approximately 89.4 m/s.

Question 3

FIGURE 8-4  An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/sS1U1P12S1S1P0.
-Refer to Figure 8-4. What is the kinetic energy of the object at the top of the wedge?

Accepted Answer

At the top of the wedge, the object has only potential energy and no kinetic energy since it has not yet been released. Therefore, the kinetic energy at the top of the wedge is 0 J.

Question 4

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². What is the kinetic energy of the object as it reaches its maximum height?

Accepted Answer

At the maximum height, the object's velocity is zero, which means its kinetic energy is also zero because KE = 1/2 mv^2. Therefore, the correct answer is 0 J.

Question 5

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released. What is the amount of work required to compress the spring?

Accepted Answer

The answer of A mass of 1.0 kg is pushed...

Question 6

A force of 4.0 N applied to a spring compresses it by 8.0 cm. What is the amount of work done to compress the spring by an additional amount of 5.0 cm?

Accepted Answer

The work done to compress a spring is given by the formula:

W = (1/2)kx^2

where W is the work done, k is the spring constant, and x is the displacement.

First, we can use Hooke's Law to find the spring constant:

F = kx 
4.0 N = k(0.08 m) 
k = 50 N/m

Next, we can plug in the values for the additional compression:

W = (1/2)(50 N/m)((0.08 m + 0.05 m)^2 - (0.08 m)^2) 
W = 0.26 J

Therefore, the answer is B.

Question 7

An object of mass 2.00 kg is held at a position A, a vertical height of 20.0 m above the ground. Point B is 8.00 m directly below A. Neglect air resistance and use g = 10.0 m/s². (a) What is the speed of the object at position B when it falls from position A? (b) What is the speed of the object just before it touches the ground? (c) What is the ratio of the total energy of the object at position A to position B?

Accepted Answer

The answer of An object of mass 2.00 kg is...

Question 8

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope. When the skier reaches the bottom of the hill, her speed is 30.0 m/s.
(a) How much work is done by friction as the skier comes down the hill?
(b) What is the magnitude of the friction force if the skier travels directly down the hill?

Accepted Answer

The answer of A 50.0-kg skier starting from rest travels...

Question 9

FIGURE 8-4  An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/sS1U1P12S1S1P0.
-Refer to Figure 8-4. What is the speed of the object just before it reaches the bottom of the wedge?

Accepted Answer

The potential energy at the top of the wedge is converted into kinetic energy at the bottom, assuming no energy is lost to friction or other non-conservative forces.

Using conservation of energy:

Potential energy at top = Kinetic energy at bottom

mgh = 1/2 mv^2

where m = 2 kg, h = 4 m (height of triangle), g = 10 m/s^2

Solving for v:

v = sqrt(2gh) = sqrt(2*10*4) = 4sqrt(5)

Rounded to one significant figure, the speed is approximately 8 m/s. So the correct answer is (B).

Question 10

FIGURE 8-4  An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/sS1U1P12S1S1P0.
-Refer to Figure 8-4. What is the amount of work done by the gravitational force as the object comes to the bottom of the wedge?

Accepted Answer

The answer of FIGURE 8-4  An object of mass...

Question 11

An object of mass 20 kg is raised vertically through a distance of 8.0 m above ground level. Using g = 10 m/s² what is the potential energy of this object at this position?

Accepted Answer

Potential energy = mgh 
Where m = mass, g = acceleration due to gravity, h = height 
Plugging in the values, 
Potential energy = (20 kg) x (10 m/s^2) x (8.0 m) = 1600 J 
Therefore, the answer is D (1600 J).

Question 12

As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s².

Accepted Answer

Since the ramp is frictionless, there is no change in mechanical energy. Therefore, the initial kinetic energy (K) of the object at point A is converted into potential energy (U) at point B.

K = (1/2)mv^2 = (1/2)(60 kg)(20 m/s)^2 = 12,000 J

At point B, the object is at its highest point, so all of its initial kinetic energy has been transformed into potential energy:

U = K = 12,000 J

Therefore, the potential energy of the object at point B is 12 × 10^3 J or 12,000 J. The answer is (D).

Question 13

(a) A force of 15 N applied to a spring compresses it by 4 cm. What is the potential energy of the spring in the compressed position?
(b) A force of 15 N applied to a spring stretches it by 4 cm. What is the potential energy of the spring in the stretched position?

Accepted Answer

The answer of (a) A force of 15 N applied...

Question 14

FIGURE 8-5  A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/sS1U1P12S1S1P0.
-Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

Accepted Answer

The bead is at rest at point A, so its velocity is 0 and therefore its kinetic energy is also 0.

Question 15

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

Accepted Answer

The change in gravitational potential energy is calculated using the formula ΔPE = m * g * Δh. Here, m = 20 kg, g = 10 m/s², and Δh = 8.7 m - 1.6 m = 7.1 m. Thus, ΔPE = 20 * 10 * 7.1 = 1420 J.

Question 16

A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position.
(a) What is the maximum angle away from the lowest position the pendulum will reach?
(b) What is the speed of the mass when the pendulum is 45° above its lowest position?

Accepted Answer

The answer of A simple pendulum of length 2.00 m...

Question 17

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s².

Accepted Answer

The total energy (kinetic + potential) of the child will remain constant throughout the slide, so we can equate the initial potential energy to the final kinetic energy:

mgh = (1/2)mv^2

where m is the mass of the child, g is the acceleration due to gravity and h is the height of the slide.
Rearranging the equation for h, we get:

h = (v^2)/(2g)

Substituting the given values, we get:

h = (15.0^2)/(2×10) = 11.3 m

Therefore, the height of the slide should be 11.3 m so that a child will reach the bottom of the slide with a speed of 15.0 m/s. Therefore, the correct answer is C) 11.3 m.

Question 18

An object of mass 4.00 kg is sitting at the top of an inclined plane of height h and angle θ with the horizontal. The object slides down the inclined plane and right before it reaches the bottom of the plane, it has speed of 16.0 m/s. Neglect friction and use g = 10.0 m/s². (a) What is the height of the inclined plane? (b) If the height of the inclined plane is raised to 15.0 m, what is the speed of the object right before it reaches the bottom of the inclined plane?

Accepted Answer

The answer of An object of mass 4.00 kg is...

Question 19

FIGURE 8-4  An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/sS1U1P12S1S1P0.
-Refer to Figure 8-4. What is the gravitational potential energy of the object at the top of the wedge?

Accepted Answer

The answer of FIGURE 8-4  An object of mass...

Question 20

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released.
(a) What is the amount of potential energy acquired by the spring when it is compressed?
(b) What is the kinetic energy of the mass after the mass is released and it is no longer in contact with the spring?

Accepted Answer

The answer of A mass of 1.0 kg is pushed...

Quiz 8: Potential Energy and Conservation of Energy

An object of mass 20.0 kg is lifted vertically through 1.00 m by a 400 N force. How much work is done by the net force in lifting this object? Use g = 10.0 m/s².

A person drops a brick from the top of a building. The height of the building is 400 m and the mass of the brick is 2.00 kg. What will be the speed of the brick right before it touches the ground? Use g = 10.0 m/s².

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². What is the kinetic energy of the object as it reaches its maximum height?

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released. What is the amount of work required to compress the spring?

A force of 4.0 N applied to a spring compresses it by 8.0 cm. What is the amount of work done to compress the spring by an additional amount of 5.0 cm?

An object of mass 20 kg is raised vertically through a distance of 8.0 m above ground level. Using g = 10 m/s² what is the potential energy of this object at this position?

As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s².

(a) A force of 15 N applied to a spring compresses it by 4 cm. What is the potential energy of the spring in the compressed position? (b) A force of 15 N applied to a spring stretches it by 4 cm. What is the potential energy of the spring in the stretched position?

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s². -Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s².

Quiz 8: Potential Energy and Conservation of Energy

An object of mass 20.0 kg is lifted vertically through 1.00 m by a 400 N force. How much work is done by the net force in lifting this object? Use g = 10.0 m/s2.

A person drops a brick from the top of a building. The height of the building is 400 m and the mass of the brick is 2.00 kg. What will be the speed of the brick right before it touches the ground? Use g = 10.0 m/s2.

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s2. What is the kinetic energy of the object as it reaches its maximum height?

A mass of 1.0 kg is pushed against a spring with a spring constant of 25 N/m. As a result, the spring is compressed by 20 cm. The mass is then released. What is the amount of work required to compress the spring?

A force of 4.0 N applied to a spring compresses it by 8.0 cm. What is the amount of work done to compress the spring by an additional amount of 5.0 cm?

An object of mass 20 kg is raised vertically through a distance of 8.0 m above ground level. Using g = 10 m/s2 what is the potential energy of this object at this position?

As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s2.

(a) A force of 15 N applied to a spring compresses it by 4 cm. What is the potential energy of the spring in the compressed position? (b) A force of 15 N applied to a spring stretches it by 4 cm. What is the potential energy of the spring in the stretched position?

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s2. -Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s2.

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s2.

An object of mass 20.0 kg is lifted vertically through 1.00 m by a 400 N force. How much work is done by the net force in lifting this object? Use g = 10.0 m/s².

A person drops a brick from the top of a building. The height of the building is 400 m and the mass of the brick is 2.00 kg. What will be the speed of the brick right before it touches the ground? Use g = 10.0 m/s².

An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s². What is the kinetic energy of the object as it reaches its maximum height?

An object of mass 20 kg is raised vertically through a distance of 8.0 m above ground level. Using g = 10 m/s² what is the potential energy of this object at this position?

As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s².

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s². -Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

A 20-kg object is resting at the top of a table 1.6 m above ground level. The object is then picked up and moved to a height of 8.7 m above ground level. What is the change in the gravitational potential energy of this object? Use g = 10 m/s².

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s².