Grade 12 Physics - mass on an inclined plane (different question)

[an_mui]

A block weighing 80N rests on a plane inclined at 20 degrees to the horizontal. The coefficient of static friction is 0.25, while the coefficient of kinetic friction is 0.15.

a) What is the minimum force F, parallel to the plane that will prevent the block from slipping down the plane?
b) What is the minimum force F that will start the blocking moving up the plane?
c) What force F is required to move the block up the plane at constant velocity?

a) I am confused about the difference between question a and b? I don't know how to determine the minimum force that will prevent the block from slipping down the plane.

b) my equations

x-direction: Fapplied - Ffriction - mgsin theta = 0
y-direction: N - mgcos theta = 0
Ffriction = usN
Ff = us (mg cos theta)
Fapplied = us (mg cos theta) + mgsin theta
Fapplied = 18.79 + 27.36 = 46.15 N

N = mgcos theta

c)

Ffriction = ukN
Ff = uk (mgcos theta)
Fapplied = uk(mg cos theta) + mg sin theta
Fapplied = 10.4 + 27.36 = 37.76N

Please correct me if i made any mistakes

 

[an_mui]

actually for a:

the answer i got is:

F = mg (sin theta - ucos theta)
but other people got different answers... could someone please help me out?

 

[Fermat]

Your answers for a) and b) are correct.
For c), check your value for the kinetic friction. It should be about 11.3.

The difference between a) and b) is in the direction that the friction acts.

Friction always opposes motion, or tendency to move.

If the block is moving in one direction, then friction is acting in the other direction.

If the block is static, then in what direction would it move if there were no friction ?
The actual friction would then act in the opposite direction to that motion.