# Torque and Force

1. Homework Statement

A wrecking ball (weight = 4800 N) is supported by a boom, which may be assumed to be uniform and has a weight of 3600 N. 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 hinge at point P.

2. Homework Equations
$$\Sigma$$$$T$$ = Fr = 0
$$\Sigma$$Fx = -$$T$$cos$$\Theta$$ + Rx = 0
$$\Sigma$$Fy = -Wball - Wboom +$$T$$sin$$\Theta$$+Ry = 0

3. The Attempt at a Solution
$$\Sigma$$$$T$$ = 3600 (L/2) + 4800 L - Ft sin32 L = 0
$$\Sigma$$$$T$$ = 1800 L + 4800 L = Ftsin32L
$$\Sigma$$$$T$$ = 6600 = Ft sin 32
Ft = 12455N

Fx = -Ftcos32 + Rx = 0
Fx = -12455 cos 32= -Rx
Rx = 10562 N

Fy = -4800 - 3600sin48 + Ftsin 32 + Ry = 0
Fy = -4800 -3600sin48 + 12455sin 32 +Ry = 0
Ry = 875N