A construction crane lifts a prestressed concrete beam weighing 14 short tons from the ground to the top of piers that are 24 ft above the ground. Determine the amount of work done considering the beam. Take the value of g as 32.174 ft/s2.

The amount of work done is 2.16 x 10⁷ Foot-pound

Explanation:

Given:

Mass of concrete beam, M = 14 tons

But 1 ton = 2000 lb

So, mass of concrete beam, M = 14 x 2000 lb = 28000 lb

Acceleration due to gravity, g = 32.174 ft/s²

Displacement of the concrete beam, d = 24 ft

Force applied by the construction crane on the concrete beam is equal to the

force experience by the concrete beam due to Earth's gravity, i. e.,

F = M x g ... (1)

Word done by the object is equal to the product of displacement and force acting on the object, i. e.,

W = F x d

Here d is displacement.

Substitute equation (1) in the above equation.

W = M x g x d

Substitute the suitable values in the above equation.

W = 28000 x 32.174 x 24

W = 2.16 x 10⁷ Foot-pound