A 76 kg man walks along a 50 kg horizontal plank which is 2.5 m long. The plank is attached to a hinge mounted to one wall, and the far end is supported by a vertical wire which is attached to an anchor in the ceiling. The wire can just barely support the man's full weight without snapping.
What is the force provided by the hinge on the wall when the man is at this maximum distance?
What is the force provided by the hinge on the wall when the man is at this maximum distance?
-
The wire's maximum tension is (76 x 9.8) = 744.8N. This is also the man's weight.
The plank will alone put a force on the wire of 1/2 (50 x 9.8) = 245N.
Therefore the maximum tension the man can cause to occur in the wire is (744.8 - 245) = 499.8N.
2.5mx(499.8/744.8) = 1.678 metres from the wall, and 0.822m. from the wire.
The force provided up by the hinge will be 245 + (0.822 x 744.8)/2.5 = 244.9, = 489.9N.
The plank will alone put a force on the wire of 1/2 (50 x 9.8) = 245N.
Therefore the maximum tension the man can cause to occur in the wire is (744.8 - 245) = 499.8N.
2.5mx(499.8/744.8) = 1.678 metres from the wall, and 0.822m. from the wire.
The force provided up by the hinge will be 245 + (0.822 x 744.8)/2.5 = 244.9, = 489.9N.