Question

1. which of the following best describes the energy in the system?

a. the gravitational potential energy increases because gravity decreases as the cart moves up
the hill.
b. energy enters the system when the cart is pulled from point a to b. this is the only time energy
enters the system.
c. the gravitational potential energy is zero at point a and e. it increases and decreases as the
cart moves between those points because energy leaves the system and enters back in.
d. none of the above answers are correct. gravitational potential energy does not affect the
movement of the cart.
in a roller coaster system, the cart is constantly being attracted towards the surface of the earth.
examine the image.

Explanation:

• Option A: Gravitational potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height). As the cart moves up the hill, \(h\) increases, and \(U\) increases because \(U\propto h\) (assuming \(m\) and \(g\) are constant near the Earth's surface). Gravity (\(g\)) does not decrease significantly for the height changes in a roller - coaster, so this option is incorrect.
• Option B: When the cart is pulled from \(A\) to \(B\), work is done on the cart (energy enters the system). But as the cart moves down from \(B\) to \(D\), gravitational potential energy is converted into kinetic energy. However, due to non - conservative forces (like friction), energy is constantly leaving the system (as heat and sound). So, energy is not only entering the system when moving from \(A\) to \(B\), and this option is incorrect.
• Option C: Gravitational potential energy is a relative quantity. We can choose a reference level (e.g., \(h = 0\) at \(A\) or \(E\)), but in reality, \(U = mgh\). If we assume \(h = 0\) at \(A\) and \(E\), when the cart moves up (e.g., from \(A\) to \(B\)), \(U\) increases (work is done against gravity), and when it moves down (e.g., from \(B\) to \(D\)), \(U\) decreases (gravity does work on the cart). But energy does not "leave and enter back" in the way described. Energy is lost due to non - conservative forces (like friction) as the cart moves, so this option is incorrect.
• Option D: Since options A, B, and C are incorrect, this option is correct. Gravitational potential energy does affect the movement of the cart (e.g., converting to kinetic energy when the cart moves down a slope). But the descriptions in A, B, and C are wrong.

Answer:

D. None of the above answers are correct. Gravitational potential energy does not affect the movement of the cart.