Calculating Force on a Table Attached to Hinges

[Kissinor]

A 100 Newton table surface (table without the legs) is attached to hinges in a wall. a chair hold the table surface in a horizontal position . The chain (chain forms a hypoteneus with the table surface and the wall) is attached to position in the table surface 0.25m from the end of the table surface. The other end ( the end attached to the hinges in the wall) is 0.50m below the other end of the chain that is attached to wall. The distance between the table back and of the table surface attached to hinges in the wall and the hanging front end of the table is 1.0 m ( in other words the table surface is 1.0 m long.

description: ( we can easily imagine the whole situation as a right angle triangle where point a is the 90 degree side of the triangle where the table surface is attached in the wall.Point B is the other end of the table surface, point c positioned above a where the support chain is attached to the wall above point A which is on the same line but 0.50m below)


a) find the force that the chain exerts on the table surface.

b) How much force is acting on the table surface at the point where the hinges are attached. Give both the magnitude and direction of this force.

I Know that there are three forces acting on the table , the first I identified was the positioned where the chain is attached to the table ( tensional force acts upwards) . I assumed that another force is acting at the end of the table ( the part 0.5m away from the point at which table is attached to the table. The other is from the point where the hinges are.

I am stucked . Do I find the tensional force in the string by decomposing the mass 0.5 meters from the hanging end of the table and then find the mass and threat it as a hanging mass ? which means Ftens(tensional force) = Bla bla bla Newtons over the sine of the angle between table surface and the chain which is 34 degrees? I am stuck . Can anybody kindly help with both questions?

 

[Doc Al]

The forces on the table are:

(a) its weight, which acts downward through the center of mass
(b) the tension force from the chain (which acts at an angle)
(c) the force the wall exerts on the table; picture it as having components $F_x$ and $F_y$.​

Since the table is in equilibrium, you know that:

(1) The net torque about any point must be zero
(2) The vertical forces must add to zero
(3) The horizontal forces must add to zero​

Use fact (1) to find the tension in the chain. Hint: use the hinges as your axis in calculating torques.

Then use facts (2) and (3) to solve for the components of the force that the wall exerts.

 

[Kissinor]

Thanks Doc Al. My question now is what formula am I going to use for the 2 problems ?

 

[Doc Al]

Translate each of the three equilibrium conditions I gave (labeled 1, 2, & 3) into equations. Try it.