Tension in support cable. Help

[Kelschul]

Tension in support cable. Help!

A wrecking ball (weight = 4500 N) is supported by a boom, which may be assumed to be uniform and has a weight of 3610 N. As the drawing shows, a support cable runs from the top of the boom to the tractor. The angle between the support cable and the horizontal is 32°, and the angle between the boom and the horizontal is 48°. Find (a) the tension in the support cable and (b) the magnitude of the force exerted on the lower end of the boom by the hinge at point P.



I know I have to sum the torque about the hinge to solve for T, but I can't seem to get it right.

I also do not know how to do part b.

 

[cristo]

Could you perhaps show the diagram?

 

[m2003]

Hello,

I understand that you are having trouble solving for the tension in the support cable and the force exerted on the lower end of the boom. Let me try to help you with these calculations.

First, let's draw a free body diagram of the boom and the wrecking ball. We have the weight of the wrecking ball (4500 N) acting downwards at its center of mass, and the weight of the boom (3610 N) acting downwards at its center of mass. We also have the support cable pulling upwards at an angle of 32° from the horizontal, and the force exerted by the hinge at point P pushing upwards at an angle of 48° from the horizontal. These forces form a parallelogram, with the diagonal representing the resultant force acting on the lower end of the boom.

Now, let's sum the forces in the horizontal and vertical directions separately. In the horizontal direction, we have the horizontal component of the support cable (Tcos32°) and the horizontal component of the force exerted by the hinge (Fcos48°). These two forces must balance out the horizontal component of the weight of the wrecking ball (4500 Nsin90° = 0) and the horizontal component of the weight of the boom (3610 Nsin90° = 0). Therefore, we can write the following equation:

Tcos32° + Fcos48° = 0

In the vertical direction, we have the vertical component of the support cable (Tsin32°) and the vertical component of the force exerted by the hinge (Fsin48°). These two forces must balance out the vertical component of the weight of the wrecking ball (4500 Ncos90° = 4500 N) and the vertical component of the weight of the boom (3610 Ncos90° = 3610 N). Therefore, we can write the following equation:

Tsin32° + Fsin48° = 4500 N + 3610 N

Now, we can solve these two equations simultaneously to find the values of T and F. Once we have the value of T, we can use it to calculate the tension in the support cable, and the value of F can be used to find the magnitude of the force exerted by the hinge at point P.

I hope this explanation helps you to solve the problem. If you are still having trouble, please let me know and I would be