A drawbridge is set up as in this figure. The mass of the actual bridge is 1000

Question

A drawbridge is set up as in this figure. The mass of the actual bridge is 1000 kg, and it is 30 m long. The counterweight, located 3 m from the left end of the bridge, has a mass of 500 kg. The pivot point of the bridge is 10 meters from the left end. The cable, a 50 m long and 5-cm diameter steel cable that runs through a system of pullies as shown, is connected to the bridge at a point 5m from the right end.

What is the tension in the cable if the bridge is elevated 20ݺ from the horizontal?

What force is on the bridge at the pivot point?

By what amount does the cable stretch from its original length?

(Let g=10 m/s2.)

Can Anybody take a picture of their work? I have a test tommorow and am having trouble following the sequence people are going in to derive their answer. Thanks!

Explanation / Answer

T*25*sin20+500*10*7*cos20=1000*10*5*cos20

T=1648.49

F+T-1000*10-500*10=0

F=13351.5

e=T*L/Ae=(1648.49*50)/(3.14*0.05^2*200*10^9)=0.052 mm

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