Can someone help me with this static friction problem?

[shaggyace]

Homework Statement

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?

Homework Equations

$\Sigma$F=ma

fs=$\mu$sN

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?

 

[tal444]

Your values for mgcos24 and mgsin24 are incorrect. Your calculator appears to be in radian mode.

 

[emailanmol]

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)

 

[shaggyace]

Wow, thanks a lot Calc class, lol.
Got the answer, thanks for your help guys

 

[asteriatic]

As a scientist, it is important to carefully analyze the problem and double check your calculations. It seems that you have made a mistake in your calculation for the normal force. The correct value should be 408 N, which would result in a coefficient of static friction of approximately 0.49. It is also important to check the units of your answer to make sure they are consistent with the expected units for a coefficient of friction. In this case, the units should be unitless. I would recommend checking your calculations and trying again to see if you get the correct answer. If you continue to have trouble, it may be helpful to seek assistance from a classmate, teacher, or tutor.