Classical Mechanics: 12N Block on Wall - Will it Move?

[Bostonpancake0]

A 1kg wooden block is being pressed against a wooden wall by 12N. If the block is initially at rest will it move upward, downward or remain at rest?



Picture of problem is in link below along with my working out. co-effecient of static friction of wood on wood is 0.50. I have also made static friction and force upward in the y component positive (same direction) and fore of gravity downwards.

 

[Bostonpancake0]

answer in book says at rest

 

[PeterO]

A 1kg wooden block is being pressed against a wooden wall by 12N. If the block is initially at rest will it move upward, downward or remain at rest?



Picture of problem is in link below along with my working out. co-effecient of static friction of wood on wood is 0.50. I have also made static friction and force upward in the y component positive (same direction) and fore of gravity downwards.

Don't forget that μR is the maximum available friction - it could always be less.

If the mass was to move up, friction would be acting down.

I would calculate what what happens in the absence of friction, then see if friction can prevent that happening.

 

[Bostonpancake0]

in the absence of friction block moves down as Fg is greater than force of press in the vertical component. And i assumed that static frcition would play a role and oppose the direction of motion thus would act upwards (similar to that on an incline plane). so adding Fg, static friction and vertical upward force should give me a net force of zero right? if the object was to remain at rest, as stated in answers.

 

[PeterO]

in the absence of friction block moves down as Fg is greater than force of press in the vertical component. And i assumed that static frcition would play a role and oppose the direction of motion thus would act upwards (similar to that on an incline plane). so adding Fg, static friction and vertical upward force should give me a net force of zero right? if the object was to remain at rest, as stated in answers.

Zero net force would be nice.

What size would the force of friction have to be to give a net force of zero?

What is the maximum size the friction force can be?

Does that mean it IS possible for friction to prevent motion?

Remember, friction will not drive the block in either direction, it can only prevent the block from moving.