A bridge whose total weight is 4400 N is 18.4 m long and supported at each end. Find the force exerted at the left end when a 1500 N tractor is located 9.8 m from the left end.

Question

ivancsc1996 · Answer

|dw:1437185904017:dw| We must first analyse the forces acting on the bridge. 
1) There is gravity which is pushing down on the bridge with a force of 4400N.
2) The bridge is carrying a tractor. Since gravity is pushing down on the tractor with a force of 1500N, the bridge must put a force of 1500N up on the wheels of the tractor to keep it at equilibrium. Therefore, through Newton's law of action and reaction, the tractor is puching down on the bridge with a force of 1500N.
3) The left and the right supports are exerting the force $N$ and $n$ up on the bridge respectively.
Now, if we take torques around the right support of the bridge (a choice which eliminates torques made by the right support), we have
$$4400N\frac{18.4m}{2}+1500N9.8m-N18.4m=0$$
Solving for $N$ (do not confuse the force $N$ in the term $N18.4m$ with the units of newtons $N$ in the rest of the equation)
$$N=\frac{4400N\frac{18.4m}{2}+1500N9.8m}{18.4m}$$