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Rigid-Body Equilibrium Problem

by physicsCU
Tags: equilibrium, rigidbody
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physicsCU
#1
Apr26-05, 04:50 PM
P: 202
OK, I am having trouble with parts B and C.

Here is the problem:

A worker sits on a beam attached to a wall at one end, supported by a cable on the other which is itself attached to the wall. Find the tension on the cable and the force on the beam by balancing torque and force.

A uniform steel beam of length L and mass m1 is attached via a hinge to the side of a building. The beam is supported by a steel cable attached to the end of the beam at an angle theta, as shown. Through the hinge, the wall exerts an unknown force, F , on the beam. A workman of mass m2 sits eating lunch a distance d from the building.



Part A. Find T, the tension in the cable. Remember to account for all the forces in the problem.

Part B. Find Fx, the x-component of the force exerted by the wall on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.

Part C. Find Fy, the y-component of force that the wall exerts on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Express your answer in terms of T, theta, m1, m2, and g.

I really have no idea where to go on B or C. But on B, I think the Fx is the normal force from the wall. So I try to use torque_net = 0. But I get d*m2*g - (something). I don't know what that something is.

And C, I have no idea.

Any help is appreciated. Thanks!!!
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Doc Al
#2
Apr26-05, 07:02 PM
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Quote Quote by physicsCU
Part B. Find Fx, the x-component of the force exerted by the wall on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Consider the horizontal forces acting on the beam. (What are they?) They must add to zero.
Part C. Find Fy, the y-component of force that the wall exerts on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Express your answer in terms of T, theta, m1, m2, and g.
Taking the end of the beam as your axis, consider all the forces acting on the beam that create torque about that axis. (What are they?) The net torque must be zero.
inky
#3
Nov22-09, 08:31 PM
P: 101
Take axis at the beam attached the wall.
(Tsin[theta])(l )=m[1]gl/2 +m[2]gd
T=(m[1]g/2sin[theta])+m[2]gd/l sin[theta]

F[x]=Tcos[theta]=(m[1]g+m[2]gl)0.5cot[theta]
F[y]=m[1]g+m[2]g-Tsin[theta])=0.5m[1]g-m[2]g(1-d/l)


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