Q: A box of mass $$m = 10\ \mathrm{kg} is $$pushed up a frictionless incline of $$5^\circ by a $$constant force $$F = 85\ \mathrm{N}$$ parallel to the incline over a distance $$d = 6.0\ \mathrm{m}. $$What is the work done by the force $$F on $$the box?

$$W = Fd \cos \theta = 85 \times 6.0 \times \cos 5^\circ = 510\ \mathrm{J}$$

Q: A $$2.0\ \mathrm{kg}$$ cart is pulled by a force with a horizontal component of $$80\ \mathrm{N}$$ and a vertical component of $$60\ \mathrm{N}$$ over a horizontal distance of $$2.0\ \mathrm{m}. $$What is the work done by the force?

$$W = F_x d = 80 \times 2.0 = 160\ \mathrm{J}$$

Q: A spring with spring constant $$k = 860\ \mathrm{N/m} is $$stretched $$x = 0.47\ \mathrm{m}$$ from its equilibrium position. What is the elastic potential energy stored in the spring?

$$U_{\mathrm{spring}} = \frac{1}{2} k x^2$ = \frac{1}{2} \times 860 \times (0.47)^2$ = 94.9\ \mathrm{J}$$

Q: A $$60.0\ \mathrm{kg}$$ woman runs up a $$3.0\ \mathrm{m}$$ high flight of stairs in $$2.5\ \mathrm{s}$$, starting from rest and reaching a final speed of $$2.0\ \mathrm{m/s}. $$What is her average power output?

$$P = \frac{mgh + \frac{1}{2}mv^2$}{t} = \frac{60 \times 9.8 \times 3.0 + \frac{1}{2} \times 60 \times (2.0)^2$}{2.5} = 756\ \mathrm{W}$$

Q: A $$1600\ \mathrm{kg}$$ elevator carries $$200\ \mathrm{kg} of $$passengers and is lifted at constant speed by a motor against a constant retarding force of $$4000\ \mathrm{N}. $$What power must the motor deliver to lift the elevator at $$3.00\ \mathrm{m/s}$$?

$$P = (mg + F_{\mathrm{retard}})v = (1800 \times 9.8 + 4000) \times 3.00 = 73,920\ \mathrm{W}$$

Q: A $$0.5\ \mathrm{kg}$$ mass is dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before hitting the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Question 1

A box of mass $$m = 10\ \mathrm{kg} is $$pushed up a frictionless incline of $$5^\circ by a $$constant force $$F = 85\ \mathrm{N}$$ parallel to the incline over a distance $$d = 6.0\ \mathrm{m}. $$What is the work done by the force $$F on $$the box?

Accepted Answer

$$W = Fd \cos 	heta = 85 	imes 6.0 	imes \cos 5^\circ = 510\ \mathrm{J}$$

Question 2

Which of the following best describes the work-energy theorem?

Accepted Answer

The net work done on an object is equal to the change in its kinetic energy: $$W_{\mathrm{net}} = K_f - K_i$$

Question 3

A $$2.0\ \mathrm{kg}$$ cart is pulled by a force with a horizontal component of $$80\ \mathrm{N}$$ and a vertical component of $$60\ \mathrm{N}$$ over a horizontal distance of $$2.0\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$W = F_x d = 80 	imes 2.0 = 160\ \mathrm{J}$$

Question 4

A spring with spring constant $$k = 860\ \mathrm{N/m} is $$stretched $$x = 0.47\ \mathrm{m}$$ from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_{\mathrm{spring}} = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 860 	imes (0.47)^2$ = 94.9\ \mathrm{J}$$

Question 5

A $$60.0\ \mathrm{kg}$$ woman runs up a $$3.0\ \mathrm{m}$$ high flight of stairs in $$2.5\ \mathrm{s}$$, starting from rest and reaching a final speed of $$2.0\ \mathrm{m/s}. $$What is her average power output?

Accepted Answer

$$P = \frac{mgh + \frac{1}{2}mv^2$}{t} = \frac{60 	imes 9.8 	imes 3.0 + \frac{1}{2} 	imes 60 	imes (2.0)^2$}{2.5} = 756\ \mathrm{W}$$

Question 6

A skier of mass $$m$$ starts at rest at the top of a frictionless ramp at height $$H$$ and descends to a lower point at height $$D. $$What is her speed $$v at $$the lower point?

Accepted Answer

$$v = \sqrt{2g(H - D)}$$

Question 7

Which of the following statements about conservative and non-conservative forces is correct?

Accepted Answer

Work done by a conservative force depends only on the initial and final positions, not the path taken.

Question 8

A block of mass $$m = 0.080\ \mathrm{kg} is $$launched up a frictionless ramp by a spring with $$k = 36\ \mathrm{N/m}$$ compressed $$x = 0.042\ \mathrm{m}. $$How far $$d up $$the ramp does the block travel before coming to rest?

Accepted Answer

$$d = \frac{kx^2$}{2mg}$$

Question 9

A leaf falls to the ground at constant speed. Comparing its initial mechanical energy ($$U_i + K_i) to $$its final mechanical energy ($$U_f + K_f$$), what can you conclude?

Accepted Answer

The final mechanical energy is less than the initial mechanical energy due to work done by non-conservative forces (air resistance).

Question 10

Which of the following is NOT a form of energy present in a wind farm at sunset?

Accepted Answer

Nuclear energy

Question 11

A $$1600\ \mathrm{kg}$$ elevator carries $$200\ \mathrm{kg} of $$passengers and is lifted at constant speed by a motor against a constant retarding force of $$4000\ \mathrm{N}. $$What power must the motor deliver to lift the elevator at $$3.00\ \mathrm{m/s}$$?

Accepted Answer

$$P = (mg + F_{\mathrm{retard}})v = (1800 	imes 9.8 + 4000) 	imes 3.00 = 73,920\ \mathrm{W}$$

Question 12

If only gravity does work on a falling object, which equation correctly relates the change in kinetic energy to the change in gravitational potential energy?

Accepted Answer

$$\Delta K = -\Delta U_{\mathrm{grav}}$$

Question 13

A $$0.5\ \mathrm{kg}$$ mass is dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

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

Question 14

Which of the following is true about the potential energy of a spring?

Accepted Answer

It is given by $$U_{\mathrm{spring}} = \frac{1}{2} k x^2$, where x$ is the displacement from equilibrium.

Question 15

A $$5.0\ \mathrm{kg}$$ object is moving at $$4.0\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 5.0 	imes (4.0)^2$ = 40\ \mathrm{J}$$

Question 16

A $$10\ \mathrm{kg}$$ crate is pulled up a $$5^\circ$$ incline by a force of $$85\ \mathrm{N}$$ parallel to the incline. The crate moves $$6.0\ \mathrm{m}$$ and the friction force is $$56\ \mathrm{N}. $$What is the net work done on the crate?

Accepted Answer

$$W_{\mathrm{net}} = W_{\mathrm{applied}} + W_{\mathrm{gravity}} + W_{\mathrm{friction}}$$

Question 17

Which of the following scenarios involves negative work being done?

Accepted Answer

A person applies a force opposite to the direction of motion to bring a moving cart to a halt.

Question 18

A projectile is accelerated from rest to a launch speed $$v in $$time $$t. $$How much power is required to accelerate the same projectile to $$2v in $$time $$2t$$?

Accepted Answer

The required power is the same: $$P = \frac{\frac{1}{2} m (2v)^2$}{2t} = \frac{2mv^2$}{2t} = \frac{mv^2$}{t}$$

Chapter 7: Work and Energy – Physics Study Notes

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