Question

torque and static equilibrium question

4. Tension in Drawbridge Chain A single chain is used to raise the draw bridge in a castle. In this problem we will examine the chain tension when the drawbridge is stationary at an angle of 45° with respect to the horizontal. Assume that the chain is also at 45° with respect to horizontal, and the chain is perpendicular to the drawbridge. The length of the drawbridge is 4 m and its mass is 500 kg All torques should be calculated about an axis passing through the hinge, represented by the small circle where the drawbridge contacts the castle wall (a) Find the net torque on the drawbridge when it is stationary Explain your answer. (b) Assuming that the drawbridge has a uniform mass distribution, calculate the clockwise torque on the drawbridge, due to the gravitational force on the draw bridge (c) Find the tension in the chain.

I have the answers but please show ALL work neatly. (a) zero (b) 6930 Nm (c) 1733 N

Answer 1

a ) net torque =must be zero  because if there were any  torque left it must be rotating about hinge but it is in the stationary position so net torque must be zero.

b) torque tue to gravity =  mg*L/2*cos45 = 500*9.8*4/2*1/sqrt(2) =6929.64646 = 6930 N.m

c) net torque =mg*L/2*cos45- T*L = 0

T= mg*1/2*cos45 = 500*9.8*1/2*1/sqrt(2) =1732.41161 = 1733 N

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