Question

this diagram represents a roller coaster. the cart is pulled to the top of the first hill at point q and then relea
which statement correctly describes the carts kinetic energy and gravitational potential energy?
a) at point s, gravitational potential energy and kinetic energy are equal.
b) at point r, both kinetic energy and gravitational potential energy are increasing.
c) at point s, kinetic energy and gravitational potential energy both begin to decrease.
d) at point r, kinetic energy is increasing and gravitational potential energy is decreasing.

Explanation:

• Gravitational potential energy (\(U = mgh\)) depends on height (\(h\)). Kinetic energy (\(K=\frac{1}{2}mv^{2}\)) depends on speed (\(v\)).
• As the cart moves down (from \(Q\) to \(S\)), height \(h\) decreases (so \(U\) decreases) and speed \(v\) increases (so \(K\) increases).
• At point \(R\) (moving down - slope), height \(h\) is decreasing (\(U=mgh\) decreases) and speed \(v\) is increasing (\(K = \frac{1}{2}mv^{2}\) increases).
• At point \(S\) (lowest - point), \(U\) is minimum (since \(h = 0\)) and \(K\) is maximum.

Answer:

D. At point R, kinetic energy is increasing and gravitational potential energy is decreasing.