Q: A 1600-kg car accelerates from 15.0 m/s to 40.0 m/s. What is the minimum energy required for this change in speed?

$$W = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} \times 1600 \times (40^2$ - 15^2$) = 1.19 \times 10^6$ \ \text{J}$$

Q: A 0.5-kg ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 150 N. If the ball's speed after being struck is 1 m/s, how long was the mallet in contact with the ball?

$$t = \frac{m v}{F} = \frac{0.5 \times 1}{150} = 0.0033 \ \text{s}$$

Question 1

A 1600-kg car accelerates from 15.0 m/s to 40.0 m/s. What is the minimum energy required for this change in speed?

Accepted Answer

$$W = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 1600 	imes (40^2$ - 15^2$) = 1.19 	imes 10^6$ \ 	ext{J}$$

Question 2

Which of the following best describes the work done by gravity on a pendulum bob as it swings from point A to point B?

Accepted Answer

The work is positive because gravity acts in the direction of displacement.

Question 3

A car skids to a stop along a level highway. In this example, the work done on the car is:

Accepted Answer

Negative, because friction removes kinetic energy from the car.

Question 4

Which of the following situations is an example of an object with a non-zero kinetic energy?

Accepted Answer

A satellite moving around the earth

Question 5

A roller coaster car starts at point A with $$PE = 30,000 \ 	ext{J}$$ and $$KE = 0. At $$point E, it is at a lower elevation than point A. At which point is the car's total mechanical energy ($$KE + PE) $$greatest?

Accepted Answer

It is the same everywhere (assuming no friction)

Question 6

A projectile is launched upward with some initial speed. As the projectile goes upward, what energy changes take place?

Accepted Answer

Kinetic energy decreases, potential energy increases.

Question 7

Two objects with different masses collide and stick to each other. Compared to before the collision, what can be said about the total momentum and total kinetic energy of the system?

Accepted Answer

The total momentum of the system is conserved, but the total kinetic energy is not.

Question 8

In an ELASTIC collision between two objects:

Accepted Answer

Both momentum and kinetic energy of the system are conserved.

Question 9

After a collision, two identical carts stick together and move to the right. Cart 1 was moving to the right and Cart 2 was at rest before the collision. Which statement is true?

Accepted Answer

Cart 1 and 2 move to the right with a speed less than Cart 1's original speed.

Question 10

A 0.5-kg ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 150 N. If the ball's speed after being struck is 1 m/s, how long was the mallet in contact with the ball?

Accepted Answer

$$t = \frac{m v}{F} = \frac{0.5 	imes 1}{150} = 0.0033 \ 	ext{s}$$

Question 11

A cart of mass 1.2 kg moves with a speed of 0.8 m/s on a frictionless air track and collides with an identical cart that is stationary. The carts stick together after the collision. What is the final kinetic energy of the system?

Accepted Answer

$$KE_f = \frac{1}{2} (2 	imes 1.2) \left( \frac{0.8}{2} \$$right)^2$$ = 0.192 \ 	ext{J}$$

Question 12

A 2.50-kg object traveling east at 20.0 m/s collides with a 1.00-kg object traveling west at 10.0 m/s. After the collision, the 2.50-kg object has a velocity 10.0 m/s to the west. How much kinetic energy was lost during the collision?

Accepted Answer

$$\Delta KE = KE_{initial} - KE_{final} = 625 - 176 = 449 \ 	ext{J}$$

Question 13

A box of mass 6.0 kg is pushed 8.0 m across a rough warehouse floor by an applied force of $$F = 214 \ 	ext{N}$$ directed at an angle of $$30.0^\circ$$ above the horizontal. The kinetic friction force between the floor and the box is $$90 \ 	ext{N}. $$What is the work done by the applied force?

Accepted Answer

$$W = F d \cos 	heta = 214 	imes 8.0 	imes \cos 30^\circ = 1,480 \ 	ext{J}$$

Question 14

A ball of mass 0.2 kg is dropped from a height of 10 m. What is its speed just before it hits the ground? (Assume $$g = 9.8 \ 	ext{m/s}^2$$ and neglect air resistance.)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14 \ 	ext{m/s}$$

Question 15

A spring stores 800 J of energy when compressed by 1.5 cm. What is the spring constant?

Accepted Answer

$$k = \frac{2E}{x^2$} = \frac{2 	imes 800}{(0.015)^2$} = 7.1 	imes 10^6$ \ 	ext{N/m}$$

Question 16

A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal ideal spring with spring constant $$2.0 	imes 10^4$ \ 	ext{N/m}. $$What is the maximum distance the spring compresses?

Accepted Answer

$$x = \sqrt{\frac{m v^2$}{k}} = \sqrt{\frac{1500 	imes 25^2$}{2.0 	imes 10^4$}} = 6.7 \ 	ext{m}$$

Question 17

A soccer ball is kicked with a force of 1100 N. If the player's foot is in contact with the ball for $$3.0 	imes 10$$^{-3}$$ s, what is the magnitude of the impulse delivered to the ball?

Accepted Answer

$$J = F \Delta t = 1100 	imes 3.0 	imes 10$$^{-3}$$ = 3.3 \ 	ext{N} \cdot 	ext{s}$$

Question 18

A sled having a certain initial speed on a horizontal surface comes to rest after traveling 19 m. If the coefficient of kinetic friction between the object and the surface is 0.30, what was the initial speed of the object?

Accepted Answer

$$v_0$$ = \sqrt{2 \mu_k g d} = \sqrt{2 	imes 0.30 	imes 9.8 	imes 19} = 10.6 \ 	ext{m/s}$$

Work, Energy, and Momentum: Review and Practice Problems

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