Q: A box is pulled across a horizontal surface by a force of $$50\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal for a distance of $$10\ \mathrm{m}. $$What is the work done by the force on the box?

$$W = 50 \times 10 \times \cos(30^\circ) = 433\ \mathrm{J}$$

Q: A $$0.145\ \mathrm{kg}$$ baseball is thrown straight up with an initial speed of $$20.0\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball?

$$h = \frac{v^2$}{2g} = \frac{(20.0)^2$}{2 \times 9.8} = 20.41\ \mathrm{m}$$

Q: A $$5,000\ \mathrm{N}$$ tractor pulls a sled at an angle of $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}. $$What is the horizontal component of the force?

$$F_x = 5,000 \times \cos(36.9^\circ) = 3,980\ \mathrm{N}$$

Q: A $$0.40\ \mathrm{kg}$$ ball moving at $$30\ \mathrm{m/s} to $$the left hits a wall and rebounds at $$20\ \mathrm{m/s} to $$the right. What is the impulse delivered to the ball by the wall?

$$J = m(v_f - v_i) = 0.40 \times (20 - (-30)) = 20\ \mathrm{kg} \cdot \mathrm{m/s}$$

Q: A $$1,500\ \mathrm{kg}$$ sled is pulled by a tractor with a $$3,500\ \mathrm{N}$$ force at $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}. $$What is the work done by the tractor?

$$W = 3,500 \times 20 \times \cos(36.9^\circ) = 55,980\ \mathrm{J}$$

Question 1

A box is pulled across a horizontal surface by a force of $$50\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal for a distance of $$10\ \mathrm{m}. $$What is the work done by the force on the box?

Accepted Answer

$$W = 50 	imes 10 	imes \cos(30^\circ) = 433\ \mathrm{J}$$

Question 2

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and its SI unit is the joule ($$1\ \mathrm{J} = 1\ \mathrm{N} \cdot \mathrm{m}).$$

Question 3

A $$0.145\ \mathrm{kg}$$ baseball is thrown straight up with an initial speed of $$20.0\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(20.0)^2$}{2 	imes 9.8} = 20.41\ \mathrm{m}$$

Question 4

A $$5,000\ \mathrm{N}$$ tractor pulls a sled at an angle of $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}. $$What is the horizontal component of the force?

Accepted Answer

$$F_x = 5,000 	imes \cos(36.9^\circ) = 3,980\ \mathrm{N}$$

Question 5

Which scenario results in zero work being done by a force?

Accepted Answer

The force is perpendicular to the displacement.

Question 6

A $$0.40\ \mathrm{kg}$$ ball moving at $$30\ \mathrm{m/s} to $$the left hits a wall and rebounds at $$20\ \mathrm{m/s} to $$the right. What is the impulse delivered to the ball by the wall?

Accepted Answer

$$J = m(v_f - v_i) = 0.40 	imes (20 - (-30)) = 20\ \mathrm{kg} \cdot \mathrm{m/s}$$

Question 7

A $$0.100\ \mathrm{kg}$$ glider is attached to a spring with force constant $$200\ \mathrm{N/m}$$ and moves at $$1.50\ \mathrm{m/s} to $$the right. What is the maximum compression of the spring if there is no friction?

Accepted Answer

$$\frac{1}{2}mv^2$ = \frac{1}{2}kx^2$ \Rightarrow x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{0.100 	imes (1.50)^2$}{200}} = 0.075\ \mathrm{m}$$

Question 8

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

Accepted Answer

The net work done on a particle equals its change in kinetic energy: $$W_{net} = \Delta K = K_f - K_i$$

Question 9

A spring with force constant $$k is $$stretched from $$x_1 to$$ $$x_2. $$What is the work done by the spring?

Accepted Answer

$$W = \frac{1}{2}k(x_2$^2 - x_1$^2)$$

Question 10

A $$1,500\ \mathrm{kg}$$ sled is pulled by a tractor with a $$3,500\ \mathrm{N}$$ force at $$36.9^\circ$$ above the horizontal for $$20\ \mathrm{m}. $$What is the work done by the tractor?

Accepted Answer

$$W = 3,500 	imes 20 	imes \cos(36.9^\circ) = 55,980\ \mathrm{J}$$

Question 11

Which of the following is the correct expression for instantaneous power delivered by a force $$\vec{F}$$ acting on a particle with velocity $$\vec{v}$$?

Accepted Answer

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

Question 12

A $$0.50\ \mathrm{kg}$$ ball moving at $$4.0\ \mathrm{m/s}$$ and a $$0.50\ \mathrm{kg}$$ ball moving at $$2.0\ \mathrm{m/s}$$ are both stopped by your hand. Which requires more work to stop and why?

Accepted Answer

The $$4.0\ \mathrm{m/s}$$ ball requires more work because its kinetic energy is greater: $$K = \frac{1}{2}mv^2$

Question 13

In a completely inelastic collision, two bodies stick together after colliding. Which quantity is always conserved?

Accepted Answer

Momentum

Question 14

A $$0.100\ \mathrm{kg}$$ glider attached to a spring ($$k = 200\ \mathrm{N/m}) $$moves at $$1.50\ \mathrm{m/s} to $$the right. If there is kinetic friction with coefficient $$\mu_k = 0.10$$, what is the maximum compression of the spring?

Accepted Answer

$$x = \sqrt{\frac{mv^2$}{k} - \frac{2\mu_k mgx}{k}}$$

Question 15

A $$0.145\ \mathrm{kg}$$ baseball is thrown straight up with an initial speed of $$20.0\ \mathrm{m/s}. $$What is its kinetic energy at the highest point?

Accepted Answer

$$K = 0$$

Question 16

Which of the following is the correct definition of impulse?

Accepted Answer

Impulse is the product of the net force and the time interval: $$J = F_{net} \Delta t$$

Question 17

A $$2m$$ iceboat and a $$m$$ iceboat are both pushed by identical constant forces from rest over the same distance. Which boat has greater momentum at the finish line?

Accepted Answer

The $$2m$$ boat has greater momentum because it takes longer to reach the finish line, accumulating more impulse.

Question 18

Which of the following is true about the relationship between work and kinetic energy?

Accepted Answer

The total work done on an object equals the change in its kinetic energy.

Work, Energy, Power, Impulse, and Momentum: Study Notes

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