Question

1. define

a. potential energy
b. kinetic energy

part 1: this graph shows a ball rolling from a to g.
graph of a balls path from a to g with points a, b, c, d, e, f, g

2.
a. which letter shows the ball when it has maximum kinetic energy?
b. which letter shows the ball when it has the least potential energy?
c. which letter shows the ball when it has the least kinetic energy?
d. which letter shows the ball when it has the maximum potential energy?

Explanation:

1. a. Potential Energy:

Potential Energy (PE) is the energy an object possesses due to its position or state. In the context of the ball, it's related to the height (gravitational potential energy, \( PE = mgh \), where \( m \) is mass, \( g \) is gravity, \( h \) is height). At higher positions (like A or G), the ball has more PE.

1. b. Kinetic Energy:

Kinetic Energy (KE) is the energy of motion, given by \( KE=\frac{1}{2}mv^{2} \) ( \( m \) = mass, \( v \) = velocity). For the ball, KE is highest at the lowest points (where speed is highest) and lowest at the highest points (where speed is lowest, or zero at rest).

2. a. Maximum Kinetic Energy:

Kinetic Energy depends on speed ( \( KE=\frac{1}{2}mv^{2} \) ). The ball moves fastest at the lowest point (since potential energy converts to kinetic energy as it falls). Point D is the lowest, so speed (and KE) is maximum here.

2. b. Least Potential Energy:

Potential Energy (gravitational) depends on height ( \( PE = mgh \) ). The lowest height means the least PE. Point D is the lowest, so it has the least PE.

2. c. Least Kinetic Energy:

Kinetic Energy is lowest when speed is lowest (or zero). At the highest points, the ball’s speed is minimal (it slows down or stops momentarily to change direction). Point A (or G) is the highest, but A is the start (initial position, speed ~0). So A has the least KE (since speed is lowest here).

2. d. Maximum Potential Energy:

Potential Energy (gravitational) is highest at the greatest height ( \( PE = mgh \) ). Point A is the highest point on the track, so it has the maximum height, hence maximum PE.

Answer:

1.

a. Potential Energy: Energy due to position/state (e.g., height for gravity).
b. Kinetic Energy: Energy of motion ( \( KE=\frac{1}{2}mv^{2} \) ).

2.

a. Maximum Kinetic Energy: D (lowest point, highest speed).
b. Least Potential Energy: D (lowest height).
c. Least Kinetic Energy: A (highest point, lowest speed).
d. Maximum Potential Energy: A (highest point, maximum height).