Question

Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 7 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3

Answer 1

Answer:

work done is equal to 384279168 lb-ft

Step-by-step explanation:

The cylinder has a circular base of 7 ft.

The height of the cylinder is 200 ft

The weight density of water in the cylinder is 62.4 lb/ft^3

First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.

The volume of a cylinder is given as $\pi r^{2} h$

where, r is the radius,

and h is the height of the cylinder.

the volume of the cylinder = $3.142* 7^{2}*200$ = 30791.6 ft^3

Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...

weight of water = 62.4 x 30791.6 = 1921395.84 lb

We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...

The work done in pumping the water out of the container will be

==> (weight of water) x (height of cylinder) = 1921395.84 x 200

==> work done is equal to 384279168 lb-ft

Answer 2

The required work done will be "384279168 lb-ft".

Work done:

Whenever a force pushes anything across distances, work is performed. This same energy transmitted, as well as work done, maybe determined by calculating the force through the kilometers moved throughout the direction of the applied force.

According to the question,

Circular base of cylinder = 7 ft

Height of cylinder = 200 ft

Weight density of water = 62.4 lb/ft³

The Volume of cylinder be:

= πr²h

By substituting the values,

= $3.142\times (7)^2\times 200$

= $3.142\times 49\times 200$

= $30791.6$ ft³

Now,

The weight of water be:

= $62.4\times 30791.6$

= $1921395.84$ lb

hence,

The work done be:

= Water's weight × Cylinder's height

= $1921395.84\times 200$

= $384279168$ lb-ft

Thus the above answer is right.

Find out more information about work done here:

https://brainly.com/question/25573309