Block on an incline and frictional force

[Carrie]

Homework Statement

A 4.00-kg block rests on a 30.0 degree incline. If the coefficient of static friction between the block and the incline is 0.700, with what magnitude force must a horizontal force act on the block to start it moving up the incline?

Homework Equations

F=ma

Ffriction=μs*Fnormal

The Attempt at a Solution

I attached the force body diagram I did.

Fy
Fn - mgsin(30) = 0
Fn = mgsin(30)[/B]


Fx
Ffr - FA = 0
Ffr = FA
μ*N = FA
mgsin(30) + .7*mgcos(30)) = FA
(4)(9.8)sin(30)+.7*(4)(9.8)cos(30) = FA
FA = 43.36 N

However, the answer is 84.1 N. I'm pretty rusty with this stuff. Thank you!

 

[sometimes=1]

a horizontal force

Consider what does it means to be "horizontal" here.

 

[gneill]

Hi Carrie, Welcome to Physics Forums.

Note that the problem stated that the applied force is horizontal. You've drawn it as parallel to the face of the slope. This will make a difference

Edit: D'oh! sometimes=1 beat me to it!

 

[Carrie]

Hello and thank you!

I'm sorry, I realize what you mean by me drawing the force diagram incorrectly, but I'm still confused as to what that changes.

 

[gneill]

Hello and thank you!

I'm sorry, I realize what you mean by me drawing the force diagram incorrectly, but I'm still confused as to what that changes.

Some part of the applied force pushes the block upslope, but another component will act to press the block into the slope. What other force will be affected by this?

 

[Carrie]

The frictional force, right?

 

[gneill]

The frictional force, right?

Yup.

 

[Carrie]

I thought that's what I represented when I said:

Ffr - FA = 0

 

[gneill]

That's not a valid equation. FA (which is horizontal) and the friction force (which acts along the slope) do not act along the same direction.

The force due to friction is obtained from the normal force and the friction coefficient. The normal force is made up of two contributions: one due to a component of the block's gravitational weight, the other due to a component of the force FA.

So FA increases the total normal force, and hence increases the friction too.

 

[Carrie]

Thank you!