Block against a wall (friction problem)

[3ephemeralwnd]

Homework Statement

A 1.0 kg wood block is pressed against a vertical wood wall by a 12 N force (into the wall, at a 30 degrees angle up from the horizontal). if the block is initially at rest, will it move upward, move downward, or stay at rest?

The attempt at a solution

ive written out the equations for Fnet in the x and y directions;

Fnet(x) = Fn - Fpush(x) , and since Fnet(x) is 0, then Fn = Fpush (x)
so, Fn = Fpush(x) = 12cos30

Fnet(y) = Fstatic friction + Fpush (y) - Fg
= (mu)Fn + 12sin30 - 9.8
and subbing in Fn... i got,
= (mu)12cos30 + 12sin30 - 9.8

but now what? I can't seem to complete the problem without being given the coefficient of static friction.. any suggestions?

 

[tiny-tim]

hi 3ephemeralwnd!

(have a mu: µ and a degree: ° )

(mu)12cos30 + 12sin30 - 9.8

that's right!

(though you haven't actually explained why the friction acts up and not down )

strange question … i guess you now find the value of µ for which the solution changes

 

[3ephemeralwnd]

oh.. that's true! I guess I just assumed that the block was going to move downwards (therefore static friction is pulling upwards on the block). Why is the friction not downwards?

 

[tiny-tim]

oh.. that's true! I guess I just assumed that the block was going to move downwards (therefore static friction is pulling upwards on the block).

And yes it is, because 9.8 is greater than 12sin30° …

but you should still say so! ​

 

[rwisz]

I would suggest calculating the coefficient of static friction using the given information. The coefficient of static friction is a property of the materials in contact and is not dependent on the applied force. Therefore, you can use the equations you have written to solve for the coefficient of static friction. Once you have that value, you can use it to determine if the block will move upward, downward, or stay at rest. If the coefficient of static friction is greater than the calculated value, the block will stay at rest. If it is less than the calculated value, the block will move upward. If it is equal to the calculated value, the block will move downward. It is important to note that the coefficient of static friction can vary depending on factors such as surface roughness and material properties, so the value you calculate may not be exact, but it will give you an estimate of the block's movement.