Question

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.

Answer 1

The amount of work done in lifting the prestressed concrete beam is 21,614,928 ft • lb.

Step-by-step explanation:

To determine the amount of work done in lifting the prestressed concrete beam, we can use the formula:

Work = force x distance

First, we need to convert the weight of the beam from short tons to pounds:

1 short ton = 2000 pounds

So, the weight of the beam is 14 short tons x 2000 pounds/short ton = 28,000 pounds

Next, we can calculate the force exerted by the crane using Newton's second law:

Force = mass x acceleration

Using the given value of g (acceleration due to gravity) as 32.174 ft/s², we can convert the weight of the beam to force:

Force = 28,000 pounds x 32.174 ft/s² = 900,572 ft • lb/s²

Finally, we can calculate the work done by multiplying the force by the distance:

Work = 900,572 ft • lb/s² x 24 ft = 21,614,928 ft • lb

Therefore, the amount of work done in lifting the prestressed concrete beam is 21,614,928 ft • lb.

Answer 2

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

Step-by-step 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