Question

A uniform 2.50m ladder of mass 7.30kg is leaning against a vertical wall while making an angle of 51.0degree with the floor. A worker pushes the ladder up against the wall until it is vertical.

A)How much work did this person do against gravity?
____J

Answer 1

19.95 J

Step-by-step explanation:

The center of mass of the ladder is initially at a height of:

`h_1=(L)/(2)sin\theta`

The center of mass of the ladder ends at a height of:

`h_2= (L)/(2)sin90` =L/2

So, the work done is equal to the change in potential energy which is:

W = PE =
`mg(h_2-h_1)`

now
`h_2-h_1= 1-sin\theta`

therefore

W = [mgL/2]×[1 - sin(theta)]

W = [(7.30)(9.81)(2.50)/2]×[1-sin(51°)]

solving this we get

W = 19.95 J