physics homework help?

Question

A block of mass 8.00 kg is pushed up against a wall by a force P that makes a 50.0° angle with the horizontal as shown in Figure
P5.46. The coefficient of static friction between the block and the wall is 0.288. Determine the possible values for the magnitude of P that allow the block to remain stationary.
please find N (maximum)
and N (minimum)

http://www.webassign.net/pse/p5-53.gif

Answer 1

We'll need to look at two cases. Case I is when the block is just starting to move up the wall, and Case II is when the block is just starting to move down the wall.

Case I
Draw a free-body diagram.

in the x-direction
Pcos(50)=N

In the y-direction
Psin(50)=mg+uN

combining
Psin(50)=mg+u(Pcos(50))

P=mg/(sin(50)-ucos(50))=9.8*8/(sin(50)-0.288cos(50))=134.96 N

Case II--Mass sliding down.
the only real change with the free body diagram is that the friction force flips and we have the following equations

x-direction
Pcos(50)=N

In the y-direction
Psin(50)=mg-uN

starting to move up the wall, and Case II is when the block is just starting to move down the wall.

in the x-direction
Pcos(50)=N

In the y-direction
Psin(50)=mg+uN

combining
Psin(50)=mg-u(Pcos(50))

solving
P=mg/(sin(50)+ucos(50))=9.8*8/(sin(50)+0.288cos(50))=82.43 N

The normal force is is P cos(50)

so it ranges to 134.96 cos50=86.75 N from 52.98 N