please answer in detail showing all work... The Dreaded Statics Problem Two ladd

Question

please answer in detail showing all work...

The Dreaded Statics Problem Two ladders. 4m and 3m long and 40kg and 30kg mass respectively, are hinged together and tied together by a horizontal rope of length 2.5m so the hinge makes a 90 degree angle as shown in the above figure. Each ladder's center of mass is at its midpoint, and the rope connects their centers of mass. The floor is friction loss, and assume Earth s gravity. What is the normal upward force from the floor acting on the left ladder, in Newtons? On the right ladder, in Newtons? What is the tension T in the rope, in Newtons? What is the magnitude of the force that each ladder exerts on the other at the hinge, in Newtons? If a weight of 90N is suspended from the hinge, what is the new tension T of the rope, in Newtons?

Explanation / Answer

Draw the picture. Recognize you have a 3-4-5 triangle with all angles known. Your angles don't add to 180, but ill assume you made a typo. Ill use your angles anyway.
(a) asks for the reaction foces. We know all of the external forces acting on the rope-ladder system except these. We can easily find these by taking a moment about one of them, and then the other (Taking a moment about one will make the distance = 0, this the torque, or moment, = 0)

Let A = point of contact on 3m ladder and B = poit of contact on 4m ladder.

I'm assuming you know how to take a moment, and how to convert mass to weight.

Also realize the rope is attached midway.Therefore, we can use trig to find the distance of the Force due to gravity from the reaction points (the perpendicular distance.)

Moment about B

0 = 393N(2mcos37) + 294N(5m - 1.5mcos57) + 5m A
A = 371.5m

All forces added = 0

B = 686N - 371.5N
B = 315N

b) Since the rope attaches the midpoints of the ladders, the triangle it forms at the top is similar with (1/2) proportions to the entire ladder triangle, and therefore is horizontal.

Isolate one side of the ladder-system and take a moment about the hinge. Free body diagrams are your friend.

You have the force at the reaction point and the tension in the rop as forces.

c) Sum of the forces on the isolated ladder add to 0. You will need to break forces into components.

d) Find the new force at one of the reaction points and repeat step B.

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