Q: A box of mass $$m$$ slides up a rough ramp with angle $$\theta$$ and coefficient of kinetic friction $$\mu_k. If $$its initial speed is $$v_0$$, what is the height $$h it $$reaches before stopping?

$$h = \frac{v_0$^2}{2g(\sin\theta + \mu_k \cos\theta)}$$

Question 1

Which of the following best describes the total energy $$E of a $$system as shown in the first image?

Accepted Answer

The sum of all forms of energy present within the system, including kinetic, gravitational potential, elastic potential, thermal, and chemical energies.

Question 2

A book is lifted at constant speed by a hand, as shown in the third image. What is the work done by the hand in lifting the book a vertical distance $$\Delta y$$?

Accepted Answer

$$W = mg\Delta y$$

Question 3

In the fourth image, a hiker reaches the top of a hill by two different paths. What does this illustrate about gravitational potential energy?

Accepted Answer

Gravitational potential energy depends only on the change in height, not the path taken.

Question 4

Refer to the fifth image. Rank the gravitational potential energies of the four balls (1-4) from largest to smallest, assuming the ground is the reference level ($$U_g = 0 at $$the ground).

Accepted Answer

3 \u003e 2 \u003e 4 = 1

Question 5

A spring is compressed by a distance $$x$$ from its equilibrium position. According to the sixth and seventh images, what is the elastic potential energy stored in the spring?

Accepted Answer

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

Question 6

If a spring with spring constant $$k is $$stretched twice as far from equilibrium, how does the elastic potential energy change?

Accepted Answer

It increases by a factor of 4.

Question 7

Which of the following statements about thermal energy, as illustrated in the eighth image, is correct?

Accepted Answer

Hot objects have atoms with higher kinetic and elastic potential energy than cold objects.

Question 8

A box is dragged across a floor, leaving a visible trail in a thermograph (ninth image). What does this trail represent?

Accepted Answer

An increase in thermal energy due to friction between the box and the floor.

Question 9

According to the tenth image, what happens at the microscopic level when two surfaces slide past each other and friction acts?

Accepted Answer

Elastic potential energy in molecular bonds is converted into thermal energy.

Question 10

A person pushes a box at constant speed across a rough floor (eleventh image). What is the relationship between the work done by the person and the change in thermal energy?

Accepted Answer

The work done by the person equals the increase in thermal energy: $$\Delta E_{th} = f_k \Delta x$$

Question 11

A 2000 kg elevator falls at 4.00 m/s and is stopped by a spring that compresses 2.00 m, while a 17,000 N friction force acts (twelfth image). Which equation would you use to solve for the required spring constant $$k$$?

Accepted Answer

$$\frac{1}{2}mv_1$^2 + $$mgh_1$$ = \frac{1}{2}kx^2$ + $$mgh_2$$ + f\Delta x$$

Question 12

Which of the following is the correct statement of the law of conservation of energy for a system with no external work and no chemical energy changes?

Accepted Answer

$$K_f + U_f + \Delta E_{th} = K_i + U_i$$

Question 13

A 1.00 kg ball is dropped from a height of 100 m. What is the change in gravitational potential energy as it falls 50.0 m? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$\Delta U_g = -490 J$$

Question 14

A block with initial kinetic energy of 4.0 J comes to rest after sliding 1.0 m due to friction. If the block had 8.0 J of kinetic energy, how far would it slide before stopping?

Accepted Answer

2.0 m

Question 15

Which of the following is true about potential energy in a system?

Accepted Answer

Potential energy is associated with interactions between objects in a system, not with a single isolated object.

Question 16

A 145 g ball is thrown upward with an initial velocity of 10.0 m/s. Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

5.10 m

Question 17

A box of mass $$m$$ slides up a rough ramp with angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. If $$its initial speed is $$v_0$$, what is the height $$h it $$reaches before stopping?

Accepted Answer

$$h = \frac{v_0$^2}{2g(\sin	heta + \mu_k \cos	heta)}$$

Potential and Thermal Energy, Conservation of Energy – Study Notes

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