Question

1. if you take into account air resistance, a penny will stop gaining velocity as it falls. this is called terminal velocity. a penny has a terminal velocity of about 30 mi/hr (13.4 m/s). how much kinetic energy does the penny have at this speed?
2. does the above value violate the conservation of energy? why or why not?

Explanation:

Question 9 (Subfield: Physics)

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (\(KE\)) is \(KE = \frac{1}{2}mv^2\), where \(m\) is mass and \(v\) is velocity. A U.S. penny has a mass \(m \approx 0.0025\) kg (or 2.5 grams). The velocity \(v = 13.4\) m/s.

Step2: Substitute Values into Formula

Substitute \(m = 0.0025\) kg and \(v = 13.4\) m/s into the formula:
\(KE = \frac{1}{2} \times 0.0025 \, \text{kg} \times (13.4 \, \text{m/s})^2\)
First, calculate \((13.4)^2 = 179.56\).
Then, \(\frac{1}{2} \times 0.0025 = 0.00125\).
Multiply: \(0.00125 \times 179.56 = 0.22445\) J.

The law of conservation of energy states that energy cannot be created or destroyed, only transformed. When the penny falls, gravitational potential energy is converted to kinetic energy and work done against air resistance (which becomes thermal energy). The terminal velocity accounts for energy transfer to air resistance, so the kinetic energy value does not violate conservation—energy is conserved as potential energy is converted to kinetic and thermal energy.

Answer:

The kinetic energy of the penny is approximately \(0.22\) J (or \(0.224\) J, depending on precision).

Question 10 (Subfield: Physics)