A tower crane lifts a steel beam 5 meters long and 50 cm in cross section

A tower crane lifts a steel beam 5 meters long and 50 cm in cross section. to a height of 12 meters. What kind of work does the crane do? steel density-7700kg / m3.

L = 5 m.

S = 50 cm2 = 0.005 m2.

g = 10 m / s2.

h = 5 m.

ρ = 7700 kg / m3.

A -?

We express the mechanical work of a tower crane by the formula: A = F * h * cosα.

We will assume that the crane lifts the beam uniformly, therefore, according to 1 Newton’s law, F = m * g.

Since the force of the crane is directed vertically upward and the beam is also lifted vertically ∠α = 0, cos0 = 1.

m = V * ρ.

The volume of the beam V is expressed by the formula: V = S * L, where S is the cross-sectional area, L is the length of the beam.

The formula for crane operation will take the form: A = 0.005 m2 * 5 m * 7700 kg / m3 * 10 m / s2 * 5 m = 9625 J.

Answer: the crane is doing work A = 9625 J.