Math Exploration 7.3: Potential Energy to Kinetic Energy

Worked Example:

If an 80 kg runner’s velocity changes from 2 m/s to 1 m/s when she runs up a hill, and the total of her kinetic and potential energy is a constant, what is the change in her potential energy?

• Given: m = 80 kg, v_initial = 2 m/s, v_final = 1 m/s
• Find: change in PE
• Concepts: E_final = E_initial and E = PE + KE and KE = ½ mv²
• If the total energy stays the same, however much the KE changes by, the PE must change by the exact same amount
• Solution: The runner’s change in KE is [½ (80)(2)² – ½ (80)(1)²] = 160 – 40 = 120 J, so her PE also changes by 120 J