What is the Force Required to Keep a Block from Slipping Down a Wall in Physics?

[Nx2]

ok, so i got this assignment for the march break and our teacher hit us with this weird question.

You are pushing horizontally on a 3.0kg block of wood, pressing it against the wall. if the coefficient of friction between the block and the wall is μ = 0.60, how much force must you exert on the block to keep it from slipping down the wall?

so, i came to the conclusion that Fg = 29.4N, I am guessing Ff would be opposite to it, but i don't know if it will equal Fg. Also i think that the normal force will be oppsite to the applied force in this question, no? The thing is, i don't know how to solve for any of these values. would i assume that Ff equals Fg then use Ff = μ * FN and solve for FN? would that work?... i don't know...
... Any help would be very much appreciated. Thanks.

- Tu

 

[Andrew Mason]

would i assume that Ff equals Fg then use Ff = μ * FN and solve for FN? would that work?...

That is the solution. But you wouldn't 'assume' Fg = -μ * FN. You know that from Newton's laws of motion since the block does not accelerate: Fg + μFN = ma = 0

AM

 

[Nx2]

im sorry, I am kinda confused... so i would use Fg = -μ * FN?... i don't understand where the negetive came from.

- Tu

 

[HallsofIvy]

Andrew Mason did not mean that you can't use it- his point was the you shouldn't say "assume" for something that MUST be true- if the block doesn't move then there must be no net force. There IS force Fg= -mg (the negative means downward) due to gravity so there must be a force upward of +mg. The only possible upward force is the friction force which is μ*FN: μ*FN= mg= -Fg. The reason for the negative on -Fg is because the two forces oppose: Fg is downward so μ*FN must be upward. If you are worried about the fact that μ*FN is upward, note that "negative times negative is positive" and Fg is itself negative.

 

[Nx2]

ooo... ic... sorry bout that... my teacher never uses negetives, he never told us anythiing bout it... but i read in the textbook that negetive means negetive direction. don't know why he doesn't use it. he always says don't worry about it... well anyways, thanks a lot.

- Tu

 

[Doc Al]

A few comments about this problem:
(1) As Andrew points out, you know the block is in equilibrium so: $mg + F_f = 0$. The weight and friction force point in opposite directions.
(2) The maximum value of static friction force (for a given normal force) is given by $F_f = \mu N$. Although the problem didn't state it, you are supposed to find the least amount of normal force (N) needed to hold the block up. (You are always welcome to push harder!)
(3) You are probably expected to ignore the friction between your hand and the block.

 

[Nx2]

thanks for all the input guys... i appreciate it. makes everything so much clearer.

- Tu