Question

which object has the most gravitational potential energy?
a. an 8 kg book at a height of 3 m
b. an 5 kg book at a height of 3 m
c. a 5 kg book at a height of 2 m
d. a 8 kg book at a height of 2 m

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy \(U = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g = 9.8\space m/s^{2}\)), and \(h\) is the height. Since \(g\) is a constant, we can compare \(m\times h\) values for each option.

Step2: Calculate \(m\times h\) for each option

• Option A: \(m = 8\space kg\), \(h=3\space m\), so \(m\times h=8\times3 = 24\space kg\cdot m\)
• Option B: \(m = 5\space kg\), \(h = 3\space m\), so \(m\times h=5\times3=15\space kg\cdot m\)
• Option C: \(m = 5\space kg\), \(h = 2\space m\), so \(m\times h=5\times2 = 10\space kg\cdot m\)
• Option D: \(m = 8\space kg\), \(h = 2\space m\), so \(m\times h=8\times2=16\space kg\cdot m\)

Answer:

A. An 8 kg book at a height of 3 m