Minimum Force to Prevent Slipping Down Plane

[cryptoguy]

Homework Statement

A block weighing 75 N rests on a plane inclined at 25 degrees. A force F is applied to the object at 40 degrees to the horizontal, pushing it upward on the plane. Coefficient of static friction between block and plane is .363

EDIT: What is the minimum value of F that will prevent the block from slipping down the plane?

Homework Equations

Ff = uFn. F = ma, etc.

The Attempt at a Solution

So the free-body diagram has F and Ff in the same direction (diff angles) and F(parallel to surface) is in the other way.

Ff + Fcos(15) = Fgsin(25) (15 degrees because 45-20 = 15)
.363*75cos(25) + Fcos(15) = 75sin(25)

I solved for F and got 7.3 N while the answer is 8.05 N. Thank you for any hints/help

 

[Feldoh]

If you have a block moving up a plane then it's kinetic friction (which will most likely be <= static friction) for starters... Also the friction force opposes the movement of the object you it should be

Fcos(15) = Fgsin(25) + Ff

 

[cryptoguy]

Wow I forgot to put the actual question down, they're actually asking

What is the minimum value of F that will prevent the block from slipping down the plane?

 

[Doc Al]

Hint: What's the normal force? How does F affect the normal force?

 

[cryptoguy]

got it thank you.