# Can someone help me with this static friction problem?

1. ### shaggyace

11
1. The problem statement, all variables and given/known data

A 45-kg crate is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to 24 degrees , the crate begins to slide downward. What is the coefficient of static friction between the crate and the ramp?

2. Relevant equations

$\Sigma$F=ma

fs=$\mu$sN

3. The attempt at a solution

I started by drawing a free body diagram. My weight came out to be -441 N. I have the angle of my weight at 24 degrees. The normal force at mgcos24, for which I got 187N. mgsin24 came out to be 399N which is also the static friction force. Then I just substituted into the static friction equation and my coefficient of static friction came out to be 2.13. I entered this into the homework problem which we do online and it is wrong. Did I miss a step? What did I do wrong?

157

3. ### emailanmol

297
The applied formula is right.The math is wrong.

the weight u calculated using m as 450 and g as 9.8 (all in SI units) is right as 441 N.

As u said normal force is mgcos24.
and mgsin24 as component of weight parallel to inclined plane.

However, the calculated values are not right.

Hint(for angles less than 45 degrees cos x is always greater the sin x.

However, here your mgcos24 is less than mgsin24)

Last edited: Mar 12, 2012
4. ### shaggyace

11
Wow, thanks a lot Calc class, lol.