Static equilibrium and a ladder

[vu10758]

A ladder leans against a frictionlee wall. If the bottom of the ladder is pushed closer to the wall (so theta increases) which of the following change? Why or why not? Assume the ladder is in static equilibrium.

a) Normal force exerted by the ground

b) Normal force exerted by the wall

c) Friction force exerted by the ground

The correct answer is that the a will not change but b and c will change.


This is my reasoning...

The normal force exerted by the ground will not change. All it does is to balance out the force of gravity. If the ladder falls, it will be rotated about the point at the bottom of the ladder touching the ground. Therefore, it doesn't contribute to torque.

The normal force exerted by the wall will change if the ladder is pushed closer to the wall. The normal force is trying to resist gravity as well as the clockwise torque. It provides a counter clockwise torque to prevent the ladder from falling. As theta increases, this normal force will decrease.

The friction force exerted by the ground will be affected. It prevents the ladder from falling. It needs to balance the normal force from the wall in order to prevent the ladder from falling counterclockwise.

Is my reasoning correct? I think I am missing something, but I am not sure.

 

[PhanthomJay]

A ladder leans against a frictionlee wall. If the bottom of the ladder is pushed closer to the wall (so theta increases) which of the following change? Why or why not? Assume the ladder is in static equilibrium.

a) Normal force exerted by the ground

b) Normal force exerted by the wall

c) Friction force exerted by the ground

The correct answer is that the a will not change but b and c will change.


This is my reasoning...

The normal force exerted by the ground will not change. All it does is to balance out the force of gravity. That is correct. Since the wall is frictionless, all of the weight of the ladder , and person and equipment on the ladder, must be supported vertically by the ground. So no matter what the angle, this value remains the same, as per Newton first law, F_net_y = 0. If the ladder falls, it will be rotated about the point at the bottom of the ladder touching the ground. Therefore, it doesn't contribute to torque.This statement is not necessary, the value of the vertical force by the ground is the same regardless of any torque.

The normal (perpendicular to the wall)force exerted by the wall will change if the ladder is pushed closer to the wall. The normal force is trying to resist the clockwise torque of gravity as well as the clockwise torque. It provides a counter clockwise torque to prevent the ladder from falling. As theta increases, this normal force will decrease.yes, correct

The friction force exerted by the ground will be affected. It prevents the ladder from slipping and falling. It needs to balance the normal force from the wall in order to prevent the ladder from falling counterclockwise.It needs to balance the normal force from the wall in order to prevent the ladder from slipping. I ought to know, since I fell off the darn thing last week when my angle theta was too flat. The lateral force on the ground exceeded the available static friction force, and the ladder slipped, and I came straight vertically down, with my feet still implanted on the same rung. No, I didn't get hurt, thanks.

See mark up in red above.

 

[kyle8921]

Your reasoning is correct. The normal force exerted by the ground will not change because it is only balancing out the force of gravity, as you mentioned. However, the normal force exerted by the wall and the friction force exerted by the ground will both change.

As the ladder is pushed closer to the wall, the normal force exerted by the wall will decrease because the angle between the ladder and the wall is increasing, meaning there is less of a perpendicular component of the ladder's weight pushing against the wall. This decrease in normal force will also affect the friction force exerted by the ground, as it needs to balance out the normal force from the wall in order to prevent the ladder from falling.

In summary, as the ladder is pushed closer to the wall, the normal force exerted by the wall will decrease, and the friction force exerted by the ground will also decrease in order to maintain static equilibrium. Both of these changes are necessary to prevent the ladder from falling.