A ball weighing 500 g is thrown vertically downwards from a height of 15 m above the surface

A ball weighing 500 g is thrown vertically downwards from a height of 15 m above the surface of the earth at a speed of 10 m / s. The ball fell to the ground at a speed of 16 m / s. Determine the absolute amount of work done by the air resistance force when the ball moves.

h = 15 m.

g = 10 m / s2.

m = 500 g = 0.5 kg.

V0 = 10 m / s.

V = 16 m / s.

A -?

We express the work of the resistance force by the formula: A = Fcopr * h.

When the ball moves, 2 forces act on it: the force of gravity m * g, directed vertically downward, and the resistance force Fcopr, directed in the opposite direction of the movement of the ball, that is, up.

m * a = m * g – Fc.

Fcopr = m * g – m * a = m * (g – a).

The acceleration of the ball a during movement is expressed by the formula: a = (V ^ 2 – V0 ^ 2) / 2 * h.

a = ((16 m / s) ^ 2 – (10 m / s) ^ 2) / 2 * 15 m = 5.2 m / s2.

A = m * (g – a) * h.

A = 0.5 kg * (10 m / s2 – 5.2 m / s2) * 15 m = 36 J.

Answer: when the ball moves, the resistance force performs work A = 36 J.