The crane lifts a steel cylindrical piece 2m long and 10cm in diameter vertically upwards to a height

The crane lifts a steel cylindrical piece 2m long and 10cm in diameter vertically upwards to a height of 5m. what useful work did the crane do?

l = 2 m.

d = 10 cm = 0.1 m.

h = 5 m.

ρ = 7800 kg / m3.

g = 9.8 m / s2.

Apol -?

The useful work of Apol will be determined by the formula: Apol = m * g * h, where m is the mass of the lifted body, g is the acceleration of gravity, h is the height to which the body was lifted.

We express the mass of the part m by the formula: m = V * ρ, where V is the volume of the part, ρ is the density of the material from which the part is made.

Since the part has the shape of a cylinder, then V = P * l * d ^ 2/4.

m = ρ * P * l * d ^ 2/4.

The formula for determining the useful work of Apol will be: Apol = ρ * P * l * d ^ 2 * g * h / 4.

Apol = 7800 kg / m3 * 3.14 * 2 m * (0.1 m) ^ 2 * 9.8 m / s2 * 5 m / 4 = 6000 J.

Answer: the crane is doing useful work Apol = 6000 J.