Q: A box is pulled 5 meters across a floor by a force of 10 N at an angle of $$60^\circ to $$the direction of motion. What is the work done by the force?

$$W = 10 \times 5 \times \cos 60^\circ = 25 J$$

Q: A 2 kg object initially at rest is acted upon by a net force that does 18 J of work. What is its final speed?

$$v = \sqrt{\frac{2 \times 18}{2}} = \sqrt{18} \approx 4.24 m/s$$

Q: A spring with $$k = 200 N/m is $$stretched from $$x_0 = 0$ m to x_f = 0.1$ m. What is the work done by the spring?

$$W_s = \frac{1}{2} \times 200 \times (0.1)^2$ = 1 J$$

Q: A 3 kg block slides down a frictionless incline, starting from rest at a height of 2 m. What is its speed at the bottom? (Use $$g = 9.8 m/s$^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} \approx 6.26 m/s$$

Q: A spring is compressed by 0.2 m from its equilibrium position. If $$k = 50 N/m$$, what is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 50 \times (0.2)^2$ = 1 J$$

Question 1

Which of the following best describes the physical meaning of work in the context of energy in a system?

Accepted Answer

Work is the process by which energy is transferred to or from a system by means of a force acting through a distance.

Question 2

Given a constant force $$\vec{F}$$ applied at an angle $$	heta to $$the direction of displacement $$\vec{d}$$, which equation correctly calculates the work done?

Accepted Answer

$$W = Fd \cos	heta$$

Question 3

A box is pulled 5 meters across a floor by a force of 10 N at an angle of $$60^\circ to $$the direction of motion. What is the work done by the force?

Accepted Answer

$$W = 10 	imes 5 	imes \cos 60^\circ = 25 J$$

Question 4

Which of the following is the correct expression for kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$

Question 5

If the net work done on an object is positive, what happens to its kinetic energy?

Accepted Answer

It increases.

Question 6

A 2 kg object initially at rest is acted upon by a net force that does 18 J of work. What is its final speed?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 18}{2}} = \sqrt{18} \approx 4.24 m/s$$

Question 7

Which statement about the work done by a spring is correct according to Hooke's Law?

Accepted Answer

The work done by a spring is proportional to the square of the displacement, $$x^2.$$

Question 8

What is the correct formula for the work done by a spring when stretched from $$x_0 to$$ $$x_f$$?

Accepted Answer

$$W_s = \frac{1}{2}k x_f^2$ - \frac{1}{2}k x_0$^2$$

Question 9

A spring with $$k = 200 N/m is $$stretched from $$x_0 = 0$ m to x_f = 0.1$ m. What is the work done by the spring?

Accepted Answer

$$W_s = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1 J$$

Question 10

Which of the following best describes the spring constant $$k$$?

Accepted Answer

It is the force required to stretch a spring by 1 meter.

Question 11

What are the SI units of the spring constant $$k$$?

Accepted Answer

$$\mathrm{N/m}$$

Question 12

If a force is applied perpendicular to the direction of displacement, what is the work done?

Accepted Answer

Zero

Question 13

Which equation represents the work-energy theorem?

Accepted Answer

$$W_{	ext{tot}} = \Delta K$$

Question 14

A 3 kg block slides down a frictionless incline, starting from rest at a height of 2 m. What is its speed at the bottom? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} \approx 6.26 m/s$$

Question 15

Which of the following statements about energy conservation is correct?

Accepted Answer

The total energy of an isolated system remains constant if only conservative forces act.

Question 16

A spring is compressed by 0.2 m from its equilibrium position. If $$k = 50 N/m$$, what is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 50 	imes (0.2)^2$ = 1 J$$

Question 17

Which of the following is true about the direction of the spring force according to Hooke's Law?

Accepted Answer

The spring force always acts opposite to the displacement from equilibrium.

Question 18

If the force applied to an object varies with position, how is the work calculated?

Accepted Answer

$$W = \int_{x_0$}^{x_f} F(x) dx$$

Question 19

A student claims that the work done by a spring is always positive. Which scenario disproves this claim?

Accepted Answer

When the spring returns to equilibrium from a stretched position, the work done by the spring is negative.

Work, Energy, and Springs: Fundamental Concepts in Physics

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