A ladder of length 20.0 m is carried by a fire truck. The ladder has a weight of

Question

A ladder of length 20.0 m is carried by a fire truck. The ladder has a weight of 3200 N and its center of gravity is at its center. The ladder is pivoted at one end (A) about a pin (Figure 1) ; you can ignore the friction torque at the pin. The ladder is raised into position by a force applied by a hydraulic piston at C. Point C is a distance 8.0 mfrom A, and the force F  exerted by the piston makes an angle of = 40 with the ladder.

Part A

What magnitude must F  have to just lift the ladder off the support bracket at B?

Express your answer using two significant figures.

Explanation / Answer

length of the ladder, L=20 m

weight of the ladder, w=3200 N

the distance between point A and C is, r=8m

angle, theta=40 degrees

use,

at equilibrium,

F*r*sin(theta)=w*L/2

F*8*sin(40)=3200*(20/2)

===> force, F=6222.9 N

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