Question

refer to the diagram below to answer the question.
where on the roller coaster does the cart
transfer potential energy into kinetic energy?
from a to b
at point d
from b to c

Explanation:

Step1: Analyze potential - kinetic energy conversion

Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height) and kinetic energy \(K=\frac{1}{2}mv^{2}\) (where \(v\) is velocity). When height \(h\) decreases, potential energy decreases and kinetic energy increases (assuming no non - conservative forces like friction for simplicity).

Step2: Check each interval

• From A to B: The roller - coaster is going up. As height \(h\) increases, potential energy \(U\) increases (since \(U = mgh\) and \(m\), \(g\) are constant), so it's not a potential - to - kinetic conversion.
• At point D: There is no change in height (instantaneous) to cause a significant potential - to - kinetic conversion at a single point (kinetic and potential energy are just values at that point, not a transfer).
• From B to C: The roller - coaster is going down. As height \(h\) decreases (since \(U = mgh\) and \(m\), \(g\) are constant), potential energy \(U\) decreases. According to the conservation of mechanical energy (neglecting non - conservative forces \(E = U+K\)), if \(U\) decreases, \(K\) (kinetic energy) increases. So this is the interval where potential energy is transferred into kinetic energy.

Answer:

From B to C