Q: A $$2\,\mathrm{kg}$$ block is moving at $$3\,\mathrm{m/s}. $$What is its kinetic energy?

$$K = 0.5 \times 2 \times 3^2$ = 9\,\mathrm{J}$$

Q: A pendulum of length $$l$$ and mass $$m is $$moved from its lowest point to an angle $$\theta_f by a $$horizontal force. What is the work done by the force?

$$W = mgl (1 - \cos \theta_f)$$

Question 1

A person pushes a box across a horizontal floor with a constant force $$F at an $$angle $$	heta to $$the direction of displacement $$d. $$Which equation correctly gives the work done by the person on the box?

Accepted Answer

$$W = F \cos 	heta \, d$$

Question 2

A block of mass $$m$$ slides on a frictionless surface and is attached to a spring with spring constant $$k. If $$the block is displaced a distance $$x$$ from equilibrium, what is the work done by the spring force?

Accepted Answer

$$W = \frac{1}{2}kx^2$

Question 3

A car of mass $$1000\,\mathrm{kg}$$ accelerates from $$0 to$$ $$20\,\mathrm{m/s} in$$ $$5\,\mathrm{s}$$ under a constant force. What is the average power delivered by the engine during this time?

Accepted Answer

$$P = 40,000\,\mathrm{W}$$

Question 4

A block of mass $$m is $$released from rest at height $$H$$ above the ground. Using the work-energy theorem, what is its velocity $$v_f$$ just before it hits the ground?

Accepted Answer

$$v_f = \sqrt{2gH}$$

Question 5

A $$1500\,\mathrm{kg}$$ car traveling at $$25\,\mathrm{m/s} on a $$dry road ($$\mu_k = 0.7) $$applies its brakes and skids to a stop. What is the stopping distance?

Accepted Answer

$$d = \frac{v^2$}{\mu_k g}$$

Question 6

Which of the following statements about work is TRUE?

Accepted Answer

Work can be positive, negative, or zero depending on the direction of force and displacement.

Question 7

A block moves at constant velocity up an inclined plane. Which statement is correct about the net work done on the block?

Accepted Answer

The net work is zero because the block's velocity is constant.

Question 8

A force $$\vec{F}$$ acts on a particle moving along a curved path from $$\vec{r}_a to$$ $$\vec{r}_b. $$How is the work done by the force calculated?

Accepted Answer

$$W = \int_{r_a}^{r_b} \vec{F} \cdot d\vec{r}$$

Question 9

Which of the following is the correct statement of the work-energy theorem?

Accepted Answer

$$W_{total} = K_{final} - K_{initial}$$

Question 10

A block attached to a spring (spring constant $$k) is $$pulled from $$x=0 to$$ $$x=x_f. $$What is the work done by the spring force?

Accepted Answer

$$W = -\frac{1}{2}kx_f^2$

Question 11

Which of the following forces is considered a conservative force?

Accepted Answer

Spring restoring force

Question 12

A $$2\,\mathrm{kg}$$ block is moving at $$3\,\mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = 0.5 	imes 2 	imes 3^2$ = 9\,\mathrm{J}$$

Question 13

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

Accepted Answer

A person holds a book stationary above their head.

Question 14

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

Accepted Answer

$$W = Fd \cos 90^\circ = 0$$

Question 15

A block of mass $$m$$ slides on a surface with kinetic friction coefficient $$\mu_k$$ and initial velocity $$v_0. $$What is the distance $$d it $$travels before stopping?

Accepted Answer

$$d = \frac{v_0$^2}{\mu_k g}$$

Question 16

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 17

A pendulum of length $$l$$ and mass $$m is $$moved from its lowest point to an angle $$	heta_f by a $$horizontal force. What is the work done by the force?

Accepted Answer

$$W = mgl (1 - \cos 	heta_f)$$

Question 18

Which of the following is NOT a correct unit for work or energy?

Accepted Answer

Watt (W)

Question 19

A force $$F$$ acts on a body causing a displacement $$d at an $$angle $$	heta to $$the force. If $$	heta = 180^\circ$$, what is the work done?

Accepted Answer

$$W = -Fd$$

Work and Kinetic Energy: Principles, Calculations, and Applications

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