Q: A box is pulled across a frictionless surface with a force $$F at an $$angle $$\theta to $$the direction of displacement $$\Delta x. $$What is the final kinetic energy of the box after moving a distance $$\Delta x$$?

$$K_f = K_i + F \cos \theta \Delta x$$

Question 1

Einstein's famous equation $$E = mc^2$ shows the equivalence of mass and energy. Which of the following statements best explains why Newton did not consider mass and energy to be equivalent in his theories?

Accepted Answer

The speed of light $$c is $$extremely large, so adding energy to a particle with mass does not noticeably change its total energy, making mass and energy appear independent in Newtonian mechanics.

Question 2

A proton and a quantum of light (photon) interact to produce an electron and an anti-electron. Which conservation law is always obeyed in this process?

Accepted Answer

Conservation of energy

Question 3

Which of the following best describes the physics definition of work?

Accepted Answer

Work is the change in an object's energy caused by external forces as it moves between two locations.

Question 4

Obelix carries a heavy stone horizontally across a flat field. According to the physics definition, is he doing any work against gravity?

Accepted Answer

No, because the displacement is perpendicular to the gravitational force.

Question 5

A box is pulled across a frictionless surface with a force $$F at an $$angle $$	heta to $$the direction of displacement $$\Delta x. $$What is the final kinetic energy of the box after moving a distance $$\Delta x$$?

Accepted Answer

$$K_f = K_i + F \cos 	heta \Delta x$$

Question 6

A car of mass $$m$$ traveling at initial speed $$v_i$$ comes to a stop due to friction. If the coefficient of friction is $$\mu$$ and the stopping distance is $$d$$, which equation correctly relates these quantities?

Accepted Answer

$$\frac{1}{2} m v_i^2$ = \mu m g d$$

Question 7

A ball is thrown vertically upward with initial velocity $$v_i. $$Using the work-energy theorem, what is the maximum height $$h it $$reaches?

Accepted Answer

$$h = \frac{v_i^2$}{2g}$$

Question 8

A spring with spring constant $$k is $$compressed by a distance $$x$$ from equilibrium. What is the work done by the spring as it returns to equilibrium?

Accepted Answer

$$W = -\frac{1}{2} k x^2$

Question 9

A spring launcher is used to fire a ball of mass $$m$$ vertically upward. The spring has constant $$k$$ and is compressed by $$x. $$What is the velocity $$v of $$the ball as it leaves the launcher (ignoring friction and air resistance)?

Accepted Answer

$$v = \sqrt{\frac{k x^2$}{m}}$$

Question 10

Which of the following scenarios involves negative work being done?

Accepted Answer

Friction slows down a moving car.

Question 11

A box is pulled with a force $$F$$ over a distance $$\Delta x on a $$surface with friction force $$f. $$What is the net work done on the box?

Accepted Answer

$$W_{net} = F \Delta x - f \Delta x$$

Question 12

If a spring is stretched from $$x_i to$$ $$x_f$$, what is the work done by the external force?

Accepted Answer

$$W_{ext} = \frac{1}{2} k x_f^2$ - \frac{1}{2} k x_i^2$

Question 13

A ball of mass $$m is $$thrown upward with velocity $$v_i$$ and comes to rest at height $$h. $$What is the work done by gravity during this motion?

Accepted Answer

$$W_{gravity} = -mgh$$

Question 14

Which of the following is a correct statement about energy conservation in the presence of friction?

Accepted Answer

Total energy is conserved, but mechanical energy can be transformed into heat.

Question 15

A spring with constant $$k is $$used to launch a ball of mass $$m$$ vertically. If the spring is compressed by $$x$$, what is the maximum height $$h$$ the ball reaches (ignoring air resistance)?

Accepted Answer

$$h = \frac{k x^2$}{2 m g}$$

Question 16

Which equation represents the work-energy theorem for an object of mass $$m$$ moving with initial velocity $$v_i$$ and final velocity $$v_f$$?

Accepted Answer

$$W = \frac{1}{2} m v_f^2$ - \frac{1}{2} m v_i^2$

Question 17

A spring with constant $$k is $$stretched by $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 18

A person pulls a box with a force $$F at an $$angle $$	heta to $$the horizontal over a distance $$d. If$$ $$	heta = 90^\circ$$, what is the work done by the force?

Accepted Answer

$$W = 0$$

Work and Kinetic Energy (Physics 211, Module 10)

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