Block held at rest against a vertical wall by a horizontal force

[Magagagag]

Homework Statement

A 5.00-kg block is held at rest against a vertical wall by a horizontal force of 100 N. (a) What is the frictional force exerted by the wall on the block? (b) What is the minimum horizontal force needed to prevent the block from falling if the static coefficient of friction between the wall and the block is 0.400?

Homework Equations

F=ma
F_S=F_Nμ_S

The Attempt at a Solution

(a) Taking the normal force on the block to be 100 N, the frictional force should be 100μ_S or 40.0 N. This answer is wrong. Where am I screwing up? I probably shouldn't need μ_S for this part since it isn't given to me until part (b).
(b) 5.00g-F_S=5.00g-F_N*0.400=0, so F_N=123. N. This answer is correct, but if the block is held at rest by a force of 100 N, then how can that be?

Any help would be much appreciated!

 

[Orodruin]

What forces will be acting vertically on the block apart from the friction?

 

[Magagagag]

The gravitational force will, but how does that play into part (a)?

 

[Orodruin]

What does Newton's laws say about objects at rest?

 

[Magagagag]

What does Newton's laws say about objects at rest?

An object at rest will stay at rest unless acted on by an unbalanced force. In order for it to stay at rest, The friction and gravitational forces must be equal. I still don't see where I went wrong! And if the 123. N force is the minimum required to keep the object at rest, then how does a 100. N force hold it at rest in part (a)!?

 

[Orodruin]

It could have a larger coefficient of friction. Remember that you were not given the hypothetical coefficient of friction until (b). Even if the coefficient of friction had been one in (a), the force would have been the same. That the friction can be a maximum value does not imply that it has that value when the object is at rest. (Consider a block on top of a table, the table could likely provide more normal force but does not since it is a reactive force.)

 

[Magagagag]

It could have a larger coefficient of friction. Remember that you were not given the hypothetical coefficient of friction until (b). Even if the coefficient of friction had been one in (a), the force would have been the same. That the friction can be a maximum value does not imply that it has that value when the object is at rest. (Consider a block on top of a table, the table could likely provide more normal force but does not since it is a reactive force.)

Thank you! I think I get it now.