Question

which object will have the most potential energy?
1 kg book, 0.5 m from the ground
1 kg book, 2 m from the ground
5 kg book, 0.5 m from the ground
5 kg book, 2 m from the ground

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \(U = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g = 9.8\space m/s^{2}\)), and \(h\) is the height.

Step2: Calculate potential energy for each option

• For \(1\space kg\) book, \(0.5\space m\) from the ground: \(U_1=1\times9.8\times0.5 = 4.9\space J\)
• For \(1\space kg\) book, \(2\space m\) from the ground: \(U_2=1\times9.8\times2=19.6\space J\)
• For \(5\space kg\) book, \(0.5\space m\) from the ground: \(U_3 = 5\times9.8\times0.5=24.5\space J\)
• For \(5\space kg\) book, \(2\space m\) from the ground: \(U_4=5\times9.8\times2 = 98\space J\)

Answer:

\(5\space kg\) book, \(2\space m\) from the ground