+-1 points My Notes A 8.90 kg lamp is hung from an 8.00 m long horizontal beam,

Question

+-1 points My Notes A 8.90 kg lamp is hung from an 8.00 m long horizontal beam, as shown in the figure. The left end of the beam is attached to a frictionless hinge on a vertical post that allows the beam to rotate up and down freely. The right end of the beam is supported by a wire that runs to the top of a post. The wire makes a 50 angle with the vertical post. The lamp is hung from the beam, 7.50 m away from the vertical post. If the mass of the beam is negligible, what is the tension in the wire? 50°

Explanation / Answer

Note - clockwise torque is negative, Counter clockwise torque is positive

Now, Torque = force*distance

The angle which the wire makes with beam is calculated as

angle = 180 - (90+50) = 40 degree

so the vertical component of tension is Tsin40.

Now, taking torque about left end (pivot) as zero, we get

-8.90*9.8*7.50 + Tsin40*8 = 0

654.15 = 5.1423T

T = 127.21 N

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