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

Answer:

19.95 J

Explanation:

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

$h_1=\frac{L}{2}sin\theta$

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

$h_2= \frac{L}{2}sin90$ =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