The next two questions refer to this situation: A uniform ladder of length L and

Question

The next two questions refer to this situation: A uniform ladder of length L and mass m is leaning against a wall at an angle to the horizontal, and a person of mass M is part-way up the ladder, a distance x from the bottom of the ladder, as shown. The top of the ladder has a frictionless roller, so the wall exerts only a normal force of magnitude Nw on the top of the ladder. The extended free-body diagram shows all the forces acting, with their correct directions, but not necessarily their correct magnitudes. The magnitude of the normal force on the ladder from the floor is NF and the magnitude of the friction force oin the ladder from the floor is f. The ladder never slips; it remains stable as the person ascends. 22. As the person ascends the ladder (as x increases), the magnitude of the upward normal force Nf from the floor on the ladder A) increases B) decreases C) remains constant 23. As the person ascends the ladder (as x increases), the magnitude of the net torque tnet on the ladder about the point where the bottom of the ladder touches the floor... A) increases B) decreases C) remains constant and zero D) remains constant and non-zero

Explanation / Answer

If we balance the torque from the very top point,

mgcos(L-x)+MgL/2cos+fLsin=NfLcos

So we can see from this equation that as x increases the quantity on the left decreases, and everything else is constant.

So Nf will decrease.

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