A sandwich board advertising sign is constructed as shown in Figure 9.35. The sign’s mass is 8.00 kg. (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?

Problem 14PE

Solution 14 PE

Step1 of 6:

In this question, we need to find the tension in the chain

In part (b) we need to find the force exerted by each side on the hinge

Data given

Mass of sign

Let us consider the given figure

Step 2 of 6:

From the figure above, we understand, there are three forces acting on the system

Weight is acting downward

Normal for left leg and normal force for right are acting above from the ground

The tension and hinge exerts internal forces, which cancel each other

Thus we have net force on the system as using equilibrium conditions

Step 3 of 6:

The normal forces are equal, due to symmetry

Hence we have normal force as

We have

And

Substituting values we get

Now we shall consider a free body diagram for one side figure to find the tension in the chain and force due to hinge on one side

We have

From the figure we have

We have for one side

The forces

Since we the system is in equilibrium, it should satisfy equilibrium conditions

and

Thus we get the equations as

And