Question

energy exam
in the roller coaster diagram above, at which point would the potential energy of the cart be at its lowest?
a
b
c
d

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity (\(g= 9.8\space m/s^{2}\) near the Earth's surface), and \(h\) is the height of the object above a reference level.

Step2: Analyze the height at each point

• At point \(a\), the roller - coaster cart is at a relatively high height.
• At point \(b\), the height is lower than \(a\) but higher than \(c\).
• At point \(c\), the height \(h\) (in the formula \(U = mgh\)) is the lowest among the four points \(a\), \(b\), \(c\), and \(d\). Since \(m\) (mass of the cart) and \(g\) (acceleration due to gravity) are constant for the cart, when \(h\) is the smallest, the potential energy \(U\) is the smallest.
• At point \(d\), the height is higher than \(c\) but lower than \(a\).

Answer:

C. c