Q: A box is pushed across a floor by a force of $$F = 120\ \mathrm{N} at an $$angle of $$30^\circ$$ below the horizontal for a distance of $$d = 5.0\ \mathrm{m}. $$What is the work done by the force?

$$W = 120 \times 5.0 \times \cos 30^\circ = 600 \times 0.866 = 519.6\ \mathrm{J}$$

Q: A force of $$F = 200\ \mathrm{N}$$ acts perpendicular to the displacement of an object. What is the work done by this force over a displacement of $$d = 10\ \mathrm{m}$$?

$$W = 200 \times 10 \times \cos 90^\circ = 0\ \mathrm{J}$$

Q: A tractor pulls a sled with a force of $$5000\ \mathrm{N} at$$ $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}$$, while friction opposes with $$3500\ \mathrm{N}. $$What is the net work done on the sled?

$$W_{\text{net}} = (5000 \times 20 \times \cos 36.9^\circ) + (3500 \times 20 \times \cos 180^\circ) = 80,000 - 70,000 = 10,000\ \mathrm{J}$$

Q: A person lifts $$30\ \mathrm{kg}$$ boxes to a height of $$0.9\ \mathrm{m}$$ above the ground. How many boxes must be lifted per minute to achieve an average power output of at least $$0.50\ \mathrm{hp}$$ ($$1\ \mathrm{hp} = 746\ \mathrm{W}$$)?

$$N = \frac{P_{\text{avg}} \Delta t}{mgh} = \frac{(0.5 \times 746) \times 60}{30 \times 9.8 \times 0.9} \approx 84$$

Q: A spring with $$k = 100\ \mathrm{N/m} is $$compressed by $$x = 0.2\ \mathrm{m}. $$What is the work done ON the spring?

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} \times 100 \times 0.04 = 2\ \mathrm{J}$$

Question 1

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and is only done by the component of force parallel to the displacement.

Question 2

A box is pushed across a floor by a force of $$F = 120\ \mathrm{N} at an $$angle of $$30^\circ$$ below the horizontal for a distance of $$d = 5.0\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$W = 120 	imes 5.0 	imes \cos 30^\circ = 600 	imes 0.866 = 519.6\ \mathrm{J}$$

Question 3

A force of $$F = 200\ \mathrm{N}$$ acts perpendicular to the displacement of an object. What is the work done by this force over a displacement of $$d = 10\ \mathrm{m}$$?

Accepted Answer

$$W = 200 	imes 10 	imes \cos 90^\circ = 0\ \mathrm{J}$$

Question 4

A tractor pulls a sled with a force of $$5000\ \mathrm{N} at$$ $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}$$, while friction opposes with $$3500\ \mathrm{N}. $$What is the net work done on the sled?

Accepted Answer

$$W_{	ext{net}} = (5000 	imes 20 	imes \cos 36.9^\circ) + (3500 	imes 20 	imes \cos 180^\circ) = 80,000 - 70,000 = 10,000\ \mathrm{J}$$

Question 5

Which force does NO work on an object moving horizontally across a surface?

Accepted Answer

The normal force perpendicular to the displacement.

Question 6

A $$30\ \mathrm{kg}$$ box is pushed $$3.5\ \mathrm{m}$$ with a $$140\ \mathrm{N}$$ force at $$30^\circ$$ below the horizontal. The coefficient of kinetic friction is $$\mu_k = 0.25. $$What is the work done by friction?

Accepted Answer

$$W_f = -\mu_k n d = -(0.25)(364)(3.5) = -318.5\ \mathrm{J}$$

Question 7

A $$5\ \mathrm{kg}$$ block slides towards an unstretched spring ($$k = 200\ \mathrm{N/m}) $$and compresses it, coming to rest. How much is the spring compressed?

Accepted Answer

$$d = \sqrt{\frac{m v_i^2$}{k}}$$

Question 8

A box of mass $$m$$ slides down a frictionless ramp of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 9

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

Accepted Answer

The net work done on an object is equal to its change in kinetic energy: $$W_{	ext{net}} = \Delta K$$

Question 10

A person lifts $$30\ \mathrm{kg}$$ boxes to a height of $$0.9\ \mathrm{m}$$ above the ground. How many boxes must be lifted per minute to achieve an average power output of at least $$0.50\ \mathrm{hp}$$ ($$1\ \mathrm{hp} = 746\ \mathrm{W}$$)?

Accepted Answer

$$N = \frac{P_{	ext{avg}} \Delta t}{mgh} = \frac{(0.5 	imes 746) 	imes 60}{30 	imes 9.8 	imes 0.9} \approx 84$$

Question 11

A spring with $$k = 100\ \mathrm{N/m} is $$compressed by $$x = 0.2\ \mathrm{m}. $$What is the work done ON the spring?

Accepted Answer

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 100 	imes 0.04 = 2\ \mathrm{J}$$

Question 12

A $$2\ \mathrm{kg}$$ block is pulled by a $$10\ \mathrm{N}$$ force at $$60^\circ$$ above the horizontal for $$4\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$W = 10 	imes 4 	imes \cos 60^\circ = 40 	imes 0.5 = 20\ \mathrm{J}$$

Question 13

A $$5\ \mathrm{kg}$$ block slides $$2\ \mathrm{m} on a $$rough surface ($$\mu_k = 0.3) $$after being released from rest. What is the work done by friction?

Accepted Answer

$$W_f = -\mu_k m g d = -0.3 	imes 5 	imes 9.8 	imes 2 = -29.4\ \mathrm{J}$$

Question 14

A $$10\ \mathrm{kg}$$ box is pulled $$6\ \mathrm{m} by a$$ $$50\ \mathrm{N}$$ force at $$45^\circ$$ above the horizontal. What is the work done by the vertical component of the force?

Accepted Answer

$$W = 0$$

Question 15

A block of mass $$m is $$attached to a spring ($$k) $$and compressed by $$d. $$What is the speed of the block when the spring returns to its unstretched length, assuming a frictionless surface?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} d$$

Question 16

A $$3\ \mathrm{kg}$$ block is accelerated from rest by a net force that varies with distance as shown in a force vs. position graph. How can you determine the work done by the force?

Accepted Answer

By calculating the area under the force vs. position graph.

Question 17

A $$2\ \mathrm{kg}$$ block moves at $$6\ \mathrm{m/s}$$ and compresses a spring ($$k = 100\ \mathrm{N/m}) $$until it comes to rest. How much is the spring compressed?

Accepted Answer

$$d = \sqrt{\frac{m v^2$}{k}} = \sqrt{\frac{2 	imes 36}{100}} = \sqrt{0.72} \approx 0.85\ \mathrm{m}$$

Question 18

Which of the following is true about the sign of work?

Accepted Answer

Work is negative if the force is opposite to the displacement.

CH6-Work and Kinetic Energy: Concepts, Calculations - EXAM 2

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