Question

1. using what you know about the formulas for potential and kinetic energy, explain how height and mass affects gravitational potential energy.

then, compare two scenarios:
a 2.5 kg ball dropped from 10.7 meters high
a 3.7 kg ball dropped from 7.5 meters high
which has more potential energy and why? (show your work for the math)

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 the potential energy for the first ball

For the \(2.5\space kg\) ball dropped from \(10.7\space m\):
\(U_1=m_1gh_1\)
Substitute \(m_1 = 2.5\space kg\), \(g = 9.8\space m/s^{2}\), and \(h_1=10.7\space m\)
\(U_1=2.5\times9.8\times10.7\)
\(U_1 = 24.5\times10.7\)
\(U_1=262.15\space J\)

Step3: Calculate the potential energy for the second ball

For the \(3.7\space kg\) ball dropped from \(7.5\space m\):
\(U_2=m_2gh_2\)
Substitute \(m_2 = 3.7\space kg\), \(g = 9.8\space m/s^{2}\), and \(h_2 = 7.5\space m\)
\(U_2=3.7\times9.8\times7.5\)
\(U_2=36.26\times7.5\)
\(U_2 = 271.95\space J\)

Answer:

The \(3.7\space kg\) ball dropped from \(7.5\space m\) has more potential energy. \(U_1 = 262.15\space J\) and \(U_2=271.95\space J\), and \(271.95> 262.15\)