Q: A construction worker lifts a 20 kg steel beam vertically upward a distance of 3 m at a constant speed. What is the work done by the worker on the beam? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$W = 20 \times 9.8 \times 3 = 588\ \mathrm{J}$$

Q: A box is pulled 5 m across a horizontal floor by a constant force of 40 N that acts at an angle of $$30^\circ$$ above the horizontal. What is the work done by the force?

$$W = 40 \times 5 \times \cos 30^\circ = 173\ \mathrm{J}$$

Q: A 2 kg object is moving at 3 m/s. What is its kinetic energy?

$$K = \frac{1}{2} \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Q: A car accelerates from 10 m/s to 20 m/s. If its mass is 1000 kg, what is the change in its kinetic energy?

$$\Delta K = \frac{1}{2} \times 1000 \times (20^2$ - 10^2$) = 150,000\ \mathrm{J}$$

Q: A spring with force constant $$k = 200\ \mathrm{N/m} is $$stretched 0.1 m from equilibrium. How much work is required to stretch the spring?

$$W = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Q: A cyclist applies a constant force of 100 N to move a bike at a constant velocity of 5 m/s. What is the instantaneous power output?

$$P = Fv = 100 \times 5 = 500\ \mathrm{W}$$

Q: A 60 kg student runs up a flight of stairs 4 m high in 5 seconds. What is the average power output? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$P_{av} = \frac{60 \times 9.8 \times 4}{5} = 470.4\ \mathrm{W}$$

Question 1

A construction worker lifts a 20 kg steel beam vertically upward a distance of 3 m at a constant speed. What is the work done by the worker on the beam? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = 20 	imes 9.8 	imes 3 = 588\ \mathrm{J}$$

Question 2

A box is pulled 5 m across a horizontal floor by a constant force of 40 N that acts at an angle of $$30^\circ$$ above the horizontal. What is the work done by the force?

Accepted Answer

$$W = 40 	imes 5 	imes \cos 30^\circ = 173\ \mathrm{J}$$

Question 3

Which of the following scenarios results in zero work being done by the applied force?

Accepted Answer

A person holds a heavy suitcase stationary above the ground.

Question 4

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 5

A car accelerates from 10 m/s to 20 m/s. If its mass is 1000 kg, what is the change in its kinetic energy?

Accepted Answer

$$\Delta K = \frac{1}{2} 	imes 1000 	imes (20^2$ - 10^2$) = 150,000\ \mathrm{J}$$

Question 6

A force $$F_x = 4x (in $$newtons, with $$x in $$meters) acts on a particle as it moves from $$x = 0 to$$ $$x = 2 m. $$What is the work done by this force?

Accepted Answer

$$W = \$$int_0$$^2 4x\ dx = 8\ \mathrm{J}$$

Question 7

A spring with force constant $$k = 200\ \mathrm{N/m} is $$stretched 0.1 m from equilibrium. How much work is required to stretch the spring?

Accepted Answer

$$W = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 8

A cyclist applies a constant force of 100 N to move a bike at a constant velocity of 5 m/s. What is the instantaneous power output?

Accepted Answer

$$P = Fv = 100 	imes 5 = 500\ \mathrm{W}$$

Question 9

A 60 kg student runs up a flight of stairs 4 m high in 5 seconds. What is the average power output? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P_{av} = \frac{60 	imes 9.8 	imes 4}{5} = 470.4\ \mathrm{W}$$

Question 10

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy depends on the mass and the square of the speed of the object.

Question 11

A force acts perpendicular to the displacement of an object. What is the work done by this force?

Accepted Answer

$$W = 0$$

Question 12

A 10 kg box is pushed across a rough floor with a force of 50 N at an angle of $$60^\circ to $$the horizontal for a distance of 4 m. What is the work done by the force?

Accepted Answer

$$W = 50 	imes 4 	imes \cos 60^\circ = 100\ \mathrm{J}$$

Question 13

A car engine delivers 100 kW of power. How much work does it do in 10 seconds?

Accepted Answer

$$W = P 	imes t = 100,000 	imes 10 = 1,000,000\ \mathrm{J}$$

Question 14

A force $$\vec{F}$$ acts on a particle moving with velocity $$\vec{v}. $$Which expression gives the instantaneous power delivered to the particle?

Accepted Answer

$$p = \vec{F} \cdot \vec{v}$$

Question 15

A 5 kg object moves along a curved path under a varying force. The total work done by the force is 40 J. If the object started from rest, what is its final speed?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 40}{5}} = 4\ \mathrm{m/s}$$

Question 16

A person pushes a stalled car (mass 1200 kg) with a force of 300 N over a distance of 10 m. If the car starts from rest and friction is negligible, what is the car's final speed?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 300 	imes 10}{1200}} = 2.24\ \mathrm{m/s}$$

ch 6:Work and Kinetic Energy

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