Q: A 25 g pebble is launched straight up at $$16\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the pebble? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v^2$}{2g} = \frac{(16)^2$}{2 \times 9.8} \approx 13.1\ \mathrm{m}$$

Q: A glider compresses a spring by $$2.7\ \mathrm{cm}$$ and comes to rest. If the spring constant is $$k = 150\ \mathrm{N/m}$$, what was the initial kinetic energy of the glider?

$$K = \frac{1}{2} k x^2$ = \frac{1}{2} \times 150 \times (0.027)^2$ \approx 0.055\ \mathrm{J}$$

Q: A steel ball of mass $$0.15\ \mathrm{kg} is $$attached to a $$0.78\ \mathrm{m}$$ string and released from rest at an angle of $$30^\circ$$ from vertical. What is its speed at the lowest point? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 0.78 \times (1 - \cos 30^\circ)} \approx 1.7\ \mathrm{m/s}$$

Question 1

Two boxes, A and B, are connected by a compressed spring and then released on a frictionless surface. Which statement best describes the energy transformation in the system after release?

Accepted Answer

The spring's potential energy is converted into kinetic energy of both boxes.

Question 2

A ball of mass $$m is $$thrown vertically upward and reaches a maximum height $$h$$ above the ground. What is the gravitational potential energy of the ball at its highest point, assuming $$y=0 at $$ground level?

Accepted Answer

$$Ug = mgh$$

Question 3

Which of the following is true about the work done by the normal force on an object sliding down a frictionless curved surface?

Accepted Answer

The normal force does no work because it is always perpendicular to the displacement.

Question 4

A 25 g pebble is launched straight up at $$16\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the pebble? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(16)^2$}{2 	imes 9.8} \approx 13.1\ \mathrm{m}$$

Question 5

Which of the following best describes the effect of friction on the mechanical energy of a system?

Accepted Answer

Friction transforms mechanical energy into thermal energy, reducing the system's mechanical energy.

Question 6

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and compressed by a distance $$x$$ from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_{sp} = \frac{1}{2} k x^2$

Question 7

A sled and rider (total mass $$m) $$start at the top of a frictionless hill with speed $$v_0$$ and height $$h. $$What is their speed $$v at $$the bottom of the hill?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh}$$

Question 8

Which statement about potential energy is correct?

Accepted Answer

Potential energy is associated with interactions between objects, not with individual objects.

Question 9

A glider compresses a spring by $$2.7\ \mathrm{cm}$$ and comes to rest. If the spring constant is $$k = 150\ \mathrm{N/m}$$, what was the initial kinetic energy of the glider?

Accepted Answer

$$K = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 150 	imes (0.027)^2$ \approx 0.055\ \mathrm{J}$$

Question 10

Which of the following is a characteristic of conservative forces?

Accepted Answer

The work done by conservative forces is independent of the path taken.

Question 11

A steel ball of mass $$0.15\ \mathrm{kg} is $$attached to a $$0.78\ \mathrm{m}$$ string and released from rest at an angle of $$30^\circ$$ from vertical. What is its speed at the lowest point? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 0.78 	imes (1 - \cos 30^\circ)} \approx 1.7\ \mathrm{m/s}$$

Question 12

In an energy diagram, what does a local minimum in the potential energy curve represent?

Accepted Answer

A point of stable equilibrium.

Question 13

If a particle is placed at a position where the total energy $$E is $$less than the potential energy $$U(x)$$, what will happen?

Accepted Answer

The particle cannot reach that position.

Question 14

Which equation correctly relates the change in gravitational potential energy to the work done by gravity for a ball moving vertically?

Accepted Answer

$$\Delta U_g = -W_{g}$$

Question 15

A block slides up a rough incline and comes to rest. Which statement best describes the energy transformation?

Accepted Answer

Mechanical energy is transformed into thermal energy due to friction.

Question 16

Which of the following is NOT a conservative force?

Accepted Answer

Friction

Question 17

Given the potential energy function $$U(x)$$, how can you find the force $$F(x)$$ acting on a particle?

Accepted Answer

$$F(x) = -\frac{dU}{dx}$$

Question 18

A mass oscillates on a spring with equilibrium position $$x_0. $$What is the form of the elastic potential energy as a function of position $$x$$?

Accepted Answer

$$U_{sp} = \frac{1}{2} k (x - x_0$)^2$

Question 19

Which statement about the conservation of energy in an isolated system is correct?

Accepted Answer

The total energy, including kinetic, potential, and thermal energy, remains constant.

Interactions and Potential Energy: The Energy Principle and Conservation

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