What is the energy of the air resistance exerted on his parachute?

Question

A parachuter jumped from the top of a building 850 m high with a velocity of 5 m/s. He landed with a velocity pf 2 m/s.

Answer 1

The mass has to be known in order to arrive at a number

Answer 2

To calculate the energy of the air resistance exerted on the parachute, we need to first calculate the work done by the air resistance on the parachuter. The work done by a force is given by the formula:

Work = Force x Distance x cos(theta)

where theta is the angle between the force and the displacement. In this case, the force is the air resistance, and the displacement is the distance traveled by the parachuter.

The work done by the air resistance is equal to the change in the kinetic energy of the parachuter, since the work-energy theorem states that the work done on an object is equal to its change in kinetic energy.

The initial kinetic energy of the parachuter is:

KE_initial = (1/2) x m x v_initial^2 = (1/2) x m x (5 m/s)^2 = 12.5 m x kg x s^-2

The final kinetic energy of the parachuter is:

KE_final = (1/2) x m x v_final^2 = (1/2) x m x (2 m/s)^2 = 2 m x kg x s^-2

The change in kinetic energy is:

Delta KE = KE_final - KE_initial = 2 m x kg x s^-2 - 12.5 m x kg x s^-2 = -10.5 m x kg x s^-2

Since the work done by the air resistance is equal to the change in kinetic energy, we can write:

Work_air_resistance = -10.5 m x kg x s^-2

The negative sign indicates that the air resistance is acting opposite to the direction of motion of the parachuter, i.e., it is a dissipative force that removes energy from the system.

Now, we can use the work-energy theorem again to calculate the energy of the air resistance:

Work_air_resistance = Force_air_resistance x Distance = Energy_air_resistance

Rearranging the equation, we get:

Energy_air_resistance = Work_air_resistance / Distance

The distance travelled by the parachuter is the height of the building since he jumped from the top and landed on the ground:

Distance = 850 m

Therefore, the energy of the air resistance is:

Energy_air_resistance = Work_air_resistance / Distance = (-10.5 m x kg x s^-2) / (850 m) = -0.0124 m x kg x s^-2



The energy of the air resistance exerted on the parachute is approximately -0.0124 joules. The negative sign indicates that the air resistance removed energy from the system, i.e., it did negative work on the parachuter.