Why is my frictional force calculation wrong for a crate on a 40° incline?

[lalahelp]

Homework Statement

A crate of potatoes of mass 13.0 kg is on a ramp with angle of incline 40° to the horizontal. The coefficients of friction are μs = 0.78 and μk = 0.43. Find the frictional force (magnitude) on the crate if the crate is at rest.

Homework Equations

F=ma
Ff=μmgcosα

The Attempt at a Solution

Ff=.78*13*9.81*cos40
=76.2 N


Why is my answer wrong?

 

[Doc Al]

You assumed that the static friction would be equal to its maximum possible value (μN). Instead, solve for the value of static friction considering that the crate is in equilibrium.

 

[lalahelp]

What equation would I use to do that?

 

[Doc Al]

what equation would i use to do that?

The net force is zero.

 

[lalahelp]

I don't understand it still

 

[Doc Al]

I don't understand it still

What forces act on the crate?

 

[lalahelp]

the mass and friction

 

[Doc Al]

the mass and friction

The weight, the friction, and the normal force. What direction does each act?

 

[lalahelp]

the weights acts straight down, friction to the right, and normal force up

 

[Doc Al]

the weights acts straight down, friction to the right, and normal force up

Consider force components parallel to the incline and apply ΣF = 0.

 

[lalahelp]

Ok thank you I got it !