What is the Frictional Force on the Wooden Crate?

[Saged]

Homework Statement

An older gentleman drags a wooden crate (m = 10 kg) containing his childhood toys out of storage. The 120 N force F that he applies on the crate makes an angle of 30° with the horizontal. The coefficient of kinetic friction μk between the well-polished floor and wooden crate is experimentally determined to be 0.1. What is the frictional force f on the crate? (cos 30° = .866, sin 30° = .5)

Homework Equations

F=ma
mgsin(θ)
f = μN
W=mg

The Attempt at a Solution

I have the solution in front of me, however, it's killing me that I can't solve it.

Any assistance would be fantastic.

 

[azizlwl]

1. Identify all forces..
2. Since no acceleration, no change in uniform motion, net force must be equal to zero.
3. Draw free-body diagram.

 

[CWatters]

I don't think it's safe to assume no acceleration and I don't think you need to.

First off look up the definition of coefficient of friction. Hint: It's a ratio.

As he is pulling up at an angle he is reducing the vertical force between box and floor caused by the weight of the box. Calculate the resulting vertical force. The rest should be easy. If not then look at the definition of coefficient of friction again.

 

[CWatters]

Then for personal interest you could check if the frictional force is more or less than the horizontal component of the force the man is applying. If less then the box is accelerating.

 

[CWatters]

PS: the title says "Inclined Plane Dilemma" but the problem does not appear to mention an inclined plane.

 

[Saged]

I was able to figure it out after hours of studying.

Thanks everyone!