Static equilibrium of a bar attached to a hinge

[ac7597]

Homework Statement

A bar of width w = 3 m and mass m = 8 kg is attached to a wall by a hinge at P. A steel wire of radius r = 0.51464 mm runs from the end of the bar to the wall, attaching to the wall a distance H = 2 m above the point P.

Fred hangs from the middle of the bar, raising money for a worthy charity. The longer he hangs, the more money will be donated. His mass is M = 53 kg.

Make a table showing the forces acting on the bar in the X-direction and in the Y-direction, and the torques acting on the bar as well.
Use your table to determine the tension T in the wire.

Fred grows hungry. His frat brothers bring him pizza and feed it to him so that he can continue to hang from the bar. Assume that the steel wire is made from type G41400 steel, drawn at 1000 F. How much pizza can he eat before the wire will break?

Relevant Equations

torque= force * radius* sin(theta)

item	Fx	Fy	torque(z)
rod	0	-mg	-mg* (3/2)
Fred	0	-Mg	(-Mg) * (3/2)
hinge	-hx	hy	0
wire	F* cos(theta)	F* sin(theta)	3*F* sin(theta)
total	0	0	0

theta= tan^(-1) (2/3) = 33.7 degree
3*F* sin(theta) = (8*9.8)* (3/2) + (53*9.8) * (3/2)
F= 538.7N
tension is 538.7N

 

[haruspex]

Looks good.
What about the next part?

theta= tan^(-1) (2/3) = 33.7 degree

It is generally unhelpful to find the angle explicitly. You can find the desired trig function from the geometry. In the present case you would have found the sine to be √(4/13). This approach usually results in greater precision.

 

[ac7597]

I was unsure about the answer because the radius of the wire was given as 0.51464 mm. Does this change the tension?

 

[haruspex]

I was unsure about the answer because the radius of the wire was given as 0.51464 mm. Does this change the tension?

It does not change the tension required for stasis. But together with the other information about the wire it determines the maximum tension the wire can withstand.