Q: A 0.1 kg ball is released from rest at a height of 1.0 m above a wooden base (where $$U = 0). $$What is the potential energy of the ball-Earth system at this point? (Use $$g = 10\ \mathrm{m/s^2$})$$

$$U = 0.1\ \mathrm{kg} \times 10\ \mathrm{m/s^2$} \times 1.0\ \mathrm{m} = 1.0\ \mathrm{J}$$

Question 1

A 0.1 kg ball is released from rest at a height of 1.0 m above a wooden base (where $$U = 0). $$What is the potential energy of the ball-Earth system at this point? (Use $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$U = 0.1\ \mathrm{kg} 	imes 10\ \mathrm{m/s^2$} 	imes 1.0\ \mathrm{m} = 1.0\ \mathrm{J}$$

Question 2

If the ball is released from rest at position A ($$y = 1.0\ \mathrm{m}$$), what is the total mechanical energy of the ball-Earth system at any point along the frictionless track?

Accepted Answer

$$E = 1.0\ \mathrm{J}$$

Question 3

At position B ($$y = 0.25\ \mathrm{m}$$), what is the kinetic energy of the ball? (Assume $$E_{total} = 1.0\ \mathrm{J}$$ and $$U_B = 0.25\ \mathrm{J})$$

Accepted Answer

$$K = E_{total} - U_B = 1.0\ \mathrm{J} - 0.25\ \mathrm{J} = 0.75\ \mathrm{J}$$

Question 4

Which of the following best describes a 'bound state' in the context of potential energy curves?

Accepted Answer

A state where the total energy is less than the maximum potential energy, so the object cannot escape to infinity.

Question 5

Given the potential energy curve for a ball on a track, at which labeled point (A-E) is the gravitational force on the ball zero?

Accepted Answer

At points where the slope of the potential energy curve is zero (B, C, D).

Question 6

If the ball is released from rest at $$x = 1.0\ \mathrm{m}$$, what is the largest value of $$x it $$can possibly reach, given the potential energy curve with $$E_{total} = 10\ \mathrm{J}$$?

Accepted Answer

$$x = 2.5\ \mathrm{m}$$

Question 7

For the ball-Earth system, which equation correctly relates the force to the potential energy curve?

Accepted Answer

$$F = -\frac{dU}{dx}$$

Question 8

A hydrogen molecule has a potential energy curve with a minimum at $$-8.0 	imes 10$$^{-19}$$\ \mathrm{J}. $$What is the minimum total energy required to break the bond and separate the atoms to infinity?

Accepted Answer

$$0\ \mathrm{J}$$

Question 9

If the total energy of a two-atom system is $$E = -3.0 	imes 10$$^{-19}$$\ \mathrm{J}$$, what is the maximum possible separation between the two hydrogen atoms according to the potential energy curve?

Accepted Answer

$$0.110\ \mathrm{nm}$$

Question 10

If the ball is released from $$x = 1.0\ \mathrm{m}$$, what is the minimum amount of initial kinetic energy it would need in order to just reach point C on the potential energy curve?

Accepted Answer

$$K_{min} = U_C - U_A$$

Question 11

Which of the following statements about the conservation of energy in a frictionless system is correct?

Accepted Answer

The sum of kinetic and potential energy remains constant.

Question 12

At which labeled point on the potential energy curve is the ball most likely to reverse direction?

Accepted Answer

At points where $$K = 0$$, i.e., where $$E_{total} = U (A $$and E).

Question 13

If the slope of the potential energy curve is negative at a certain point, what is the direction of the force acting on the object?

Accepted Answer

The force points to the right (increasing $$x).$$

Question 14

A ball is released from rest at point A and moves to point B. If $$U_A = 1.0\ \mathrm{J}$$ and $$U_B = 0.25\ \mathrm{J}$$, what is the change in kinetic energy?

Accepted Answer

$$\Delta K = U_A - U_B = 0.75\ \mathrm{J}$$

Question 15

Which of the following best describes the relationship between the potential energy curve and the shape of the track for the ball?

Accepted Answer

The potential energy curve matches the vertical profile of the track.

Question 16

If the total energy of a system is equal to the potential energy at a certain point, what can be said about the kinetic energy at that point?

Accepted Answer

The kinetic energy is zero.

Question 17

For a two-atom system, what does it mean if the total energy is less than zero ($$E \u003c 0) on $$the potential energy curve?

Accepted Answer

The atoms are in a bound state and cannot separate to infinity.

Question 18

If the force on an object is zero at a certain point on the potential energy curve, what does this imply about the slope of the curve at that point?

Accepted Answer

The slope of the potential energy curve is zero.

Question 19

A ball is released from rest at $$x = 1.0\ \mathrm{m}$$ with total energy $$E = 10\ \mathrm{J}. At $$which points on the potential energy curve will the ball be bound?

Accepted Answer

Between $$x = 1.0\ \mathrm{m}$$ and $$x = 2.5\ \mathrm{m}$$, where $$U \u003c E.$$

Potential Energy Curves and Energy Conservation in Physics

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