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 mm on a side, with a drag coefficient of 1.4. A runner completes a 240 mm run at 6.0 m/s with this chute trailing behind.

Required:
How much thermal energy is added to the air by the drag force?

Answer 1

by the drag force, 2.4004512 × 10⁻⁵ J is added to the air.

Step-by-step explanation:

Given the data in the question;

drag coefficient of Cd = 1.4

speed v = 6.0 m/s

One model expands to a square 1.8 mm on a side

Area A = 1.8 × 1.8 = 3.24 mm² = 3.24 × 10⁻⁶ m²

distance travelled s = 240 mm = 0.24 m

we know that; density of air e = 1.225 kg/m³

Now,

Dragging force F
`_D` = ( Cd × e × v² × A ) / 2

thermal energy = F
`_D` × s

so

thermal energy = ( 1.4 × 1.225 × (6)² × (3.24 × 10⁻⁶) × 0.24 ) / 2

thermal energy = ( 4.8009024 × 10⁻⁵ ) / 2

thermal energy = 2.4004512 × 10⁻⁵ J

Therefore, by the drag force, 2.4004512 × 10⁻⁵ J is added to the air.