A uniform horizontal beam with a length of 8.00 m and a weight of 200n is attached to a wall by a pin connection ( allows rotation). Its far end is supported by a cable that makes an angle of 53 degrees with the horizontal. If a 600n person stands on the beam at 2.00 m from the wall , find the tension in the cable
Answers
Given A uniform horizontal beam with a length of 8.00 m and a weight of 200 n is attached to a wall by a pin connection ( allows rotation). Its far end is supported by a cable that makes an angle of 53 degrees with the horizontal. If a 600 n person stands on the beam at 2.00 m from the wall , find the tension in the cable
Now the force acting on the beam are the gravitational force of earth and weight attached to a wall is 200 N which acts at centre. Also force of person standing is 600 N and force exerted is r and tension is T , also torque due to r is zero because it acts at the pivot point. So r = 0
Torque due to tension in the rope is sin 53 x 8.00 x T.
Torque due to force is 2.0 m x 600 N
The weight of beam acts in the centre since the beam is uniform.
So we have
sin 53 x 8.00 x T - 2 m x 600 N - 4 x 200 N = 0
8 .00 x 0.8 x T = 1200 + 800
0.64 T = 2000 N-m
T = 2000 / 0.64
T = 312.5 N