A uniform drawbridge must be held at a 37.0 angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 4.50×104 , is 14.0 long, and pivots about a hinge at its lower end. A cable is connected 3.50 from the hinge, as measured along the bridge, and pulls horizontally on the bridge to hold it in place.

Tension in the cable?

Magnitude of the force the hinge exerts on the bridge.

Direction of the force the hinge exerts on the bridge.

If the cable suddenly breaks, what is the initial angular acceleration of the bridge?

Question

A uniform drawbridge must be held at a 37.0 angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 4.50×104 , is 14.0 long, and pivots about a hinge at its lower end. A cable is connected 3.50 from the hinge, as measured along the bridge, and pulls horizontally on the bridge to hold it in place. 


 Tension in the cable? 

 Magnitude of the force the hinge exerts on the bridge. 

 Direction of the force the hinge exerts on the bridge. 

 If the cable suddenly breaks, what is the initial angular acceleration of the bridge?

anonymous · Answer

My tension was 49258.633, though I am not sure if that is correct

anonymous · Answer

or 20035.291

anonymous · Answer

Complicated problem. General approach is to identify the forces, horizontal and vertical, setting them to zero when no acceleration. Similarly, identify the torques around the hinge and set them to zero when no acceleration. When cable breaks, there will be net torque giving an angular acceleration (alpha) determined by the torque divided by the moment of inertia (I) of the bridge [which is the moment around the center of mass plus M(L/2)^2]. Good luck.