Energy exchange for a falling body

Practical method

Aim

Investigate the exchange between gravitational potential energy and kinetic energy for a falling body.

Variables

Independent variable: height fallen h
Dependent variable: speed v at the light gate
Control variables: the same falling mass and card; release from rest; the card passes squarely through the gate.

Apparatus

• Mass with a card of known length attached
• Light gate and timer
• Metre rule
• Clamp stand
• Balance
• Vernier calipers

Method

1. Measure the mass and the card length (with calipers).
2. Release the mass from rest at a measured height above the light gate.
3. Record the time the card blocks the beam and calculate v = card length ÷ time.
4. Repeat for heights from 0.20 m to 0.80 m.
5. Calculate mgh and ½mv² for each height, and plot v² against h (gradient 2g).

Sample results

Mass 0.200 kg, card length 25.0 mm.

Analysis

Kinetic energy gained is within about 3% of potential energy lost, and slightly smaller, because some energy is transferred to the surroundings by air resistance. A graph of v² against h has gradient close to 2g = 19.6 m s⁻².

Uncertainty

At 0.800 m the blocking time is 6.4 ms; a timer resolution of 0.1 ms gives 1.6% in v and 3% in ½mv². Using a longer card reduces this.

Errors and improvements

Risk assessment

Common mistakes

• Measuring h to the bottom of the mass rather than to where the card's midpoint passes the gate.
• Squaring the time instead of the speed.
• Expecting exact equality of energies.

Worked analysis

At h = 0.800 m: GPE lost = 0.200 × 9.81 × 0.800 = 1.570 J. v = \(\dfrac{0.0250}{0.0064}\) = 3.91 m s⁻¹, so KE = ½ × 0.200 × 3.91² = 1.53 J. About 97% of the GPE has become KE.

Common misconception

The 'missing' energy is not destroyed; it has been transferred to thermal energy of the air and surroundings by drag.