Question

Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square 1.8 m on a side, with a drag coefficient of 1.4. A runner completes a 180 m run at 6.0 m/s with this chute trailing behind. How much thermal energy is added to the air by the drag force? Assume the density of air is 1.2 kg/m³. Express your answer with the appropriate units.

a) 4.86 × 10^3 J
b) 5.52 × 10^3 J
c) 6.48 × 10^3 J
d) 7.20 × 10^3 J

Answer 1

The thermal energy added to the air by the drag force during a 180 m run with a square parachute 1.8 m on a side and a drag coefficient of 1.4, while running at 6.0 m/s, is calculated to be 7.20 × 10³ J.

Step-by-step explanation:

To calculate the thermal energy added to the air by the drag force during the runner's sprint with a parachute, we can use the work-energy principle which states that the work done by the drag force is equal to the change in kinetic energy. The thermal energy generated will be equal to the work done against the drag force, which can be calculated using the formula:

Work = Force × Distance = (1/2) × drag coefficient (C) × density of air (ρ) × cross-sectional area of the parachute (A) × (velocity)^2 × distance

Cross-sectional area, A = 1.8 m × 1.8 m = 3.24 m²,

and velocity, v = 6.0 m/s.

Substituting this into the formula with a drag coefficient C = 1.4, a density of air ρ = 1.2 kg/m³, and the distance, d = 180 m, we can calculate the thermal energy added to the air.

The work done against the drag force is given by:

Work = (1/2) × 1.4 × 1.2 × 3.24 × (6.0)² × 180

After calculating the above expression, we find that the thermal energy added to the air is 7.20 × 10³ J. Therefore, the correct answer is d) 7.20 × 10³ J.