Q: A woman weighing 600 N steps onto a bathroom scale, compressing the spring by 1.0 cm. What is the force constant $$k of $$the spring?

$$k = 6.0 \times 10^4$ \ \text{N/m}$$

Q: A baseball of mass $$m = 0.145 kg is $$thrown upward with $$v_1 = 20.0$ m/s. What is the maximum height y_2$ it reaches? (Use g = 9.80$ m/s^2$)

$$y_2$$ = \frac{$$v_1^2$$}{2g} = 20.4 \ \text{m}$$

Q: A spring is compressed by 0.02 m and has a spring constant $$k = 1000 N/m. $$What is the potential energy stored in the spring?

$$U = \frac{1}{2}k x^2$ = 0.2 \ \text{J}$$

Question 1

A particle moves along the x-axis from $$x_1 to$$ $$x_2$$ under a varying force $$F_x. $$How is the total work done by the force represented on a graph of force versus position?

Accepted Answer

By the area under the curve between $$x_1$$ and $$x_2$$

Question 2

A spring obeys Hooke's law, $$F_x = kx. $$What is the work done to stretch the spring from $$x = 0 to$$ $$x = X$$?

Accepted Answer

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

Question 3

A woman weighing 600 N steps onto a bathroom scale, compressing the spring by 1.0 cm. What is the force constant $$k of $$the spring?

Accepted Answer

$$k = 6.0 	imes 10^4$ \ 	ext{N/m}$$

Question 4

What is the formula for gravitational potential energy of a particle near Earth's surface?

Accepted Answer

$$U_{grav} = mgy$$

Question 5

If a basketball falls from a height, which energy transformation occurs?

Accepted Answer

Potential energy is converted to kinetic energy

Question 6

Which equation expresses the conservation of mechanical energy for a system under gravity?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 7

A baseball of mass $$m = 0.145 kg is $$thrown upward with $$v_1 = 20.0$ m/s. What is the maximum height y_2$ it reaches? (Use g = 9.80$ m/s^2$)

Accepted Answer

$$y_2$$ = \frac{$$v_1^2$$}{2g} = 20.4 \ 	ext{m}$$

Question 8

When only conservative forces (like gravity) act on a system, what happens to the total mechanical energy?

Accepted Answer

It is conserved

Question 9

A spring is stretched from $$x_1 to$$ $$x_2. $$What is the work done on the spring?

Accepted Answer

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

Question 10

A person jumps upward. As they rise, what happens to their kinetic and gravitational potential energy?

Accepted Answer

Kinetic energy decreases, potential energy increases

Question 11

Which of the following best describes the work done by a constant force $$F$$ over a displacement $$s$$?

Accepted Answer

$$W = Fs$$

Question 12

A spring scale compresses by $$x = -0.01 m $$under a force of $$F_x = -600 N. $$What is the correct expression for the spring constant $$k$$?

Accepted Answer

$$k = \frac{F_x}{x}$$

Question 13

If a force varies with position, how can the total work done be calculated?

Accepted Answer

By integrating the force over the displacement

Question 14

Which of the following is NOT a conservative force?

Accepted Answer

Friction

Question 15

A ball is thrown upward and reaches its maximum height. What is true about its kinetic and potential energy at that point?

Accepted Answer

Kinetic energy is zero, potential energy is maximum

Question 16

Which equation correctly relates initial and final mechanical energy for a falling object (neglecting air resistance)?

Accepted Answer

$$\frac{1}{2}mv_i^2$ + mgy_i = \frac{1}{2}mv_f^2$ + mgy_f$$

Question 17

A spring is compressed by 0.02 m and has a spring constant $$k = 1000 N/m. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}k x^2$ = 0.2 \ 	ext{J}$$

Question 18

A person jumps and lands back on the ground. What happens to their total mechanical energy during the jump (ignoring air resistance)?

Accepted Answer

It remains constant throughout

Question 19

Which scenario best illustrates the conversion of kinetic energy to potential energy?

Accepted Answer

A ball thrown upward slowing down as it rises

Work, Energy, and Conservation in College Physics

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