Static/kinetic friction problem

[Hiche]

Homework Statement

A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined 17° above the horizontal. (a) If the coefficient of static friction is 0.45, what minimum force magnitude is required from the rope to start the crate moving? (b) If μk = 0.39, what is the magnitude of the initial acceleration (m/s^2) of the crate?

Homework Equations

Equations of static and kinetic friction; Newton's Second Law.

The Attempt at a Solution

I managed to answer the first question and it was true. The value is 277.66 N. The second part, I have a problem with:

So, after the crate starts moving, a kinetic friction is present. F(kinetic) = μk * N, where N = mg - F(min)sin@ (previous part). The answer is 228.23. Then according to Newton's law, Fcos@ - f(kinetic) = ma. We compute a and the answer is 0.54. But the website is saying perpetually that the answer is wrong. What did I do wrong?

 

[dacruick]

I didn't read over your math carefully at all but you seem to have a good grasp of what youre doing. If its a website that is saying the answer is wrong, always make sure you're using the correct amount of significant digits. Also, you didn't put the units in your answer, maybe they want units too.

 

[Hiche]

They provide the units so it can't be that. And they are asking for only two or three digits after the decimal point. I showed it to some people and they reached slightly different answers, such as 0.73 which is also wrong. It's pretty vexing.

 

[Doc Al]

We compute a and the answer is 0.54. But the website is saying perpetually that the answer is wrong. What did I do wrong?

Redo your arithmetic retaining more intermediate digits. The value I get is a little different than yours, just enough to mess up an online system.

 

[Hiche]

I reached a value of 0.502 somehow; wrong. I don't know. I guess I'll have to try more. Maybe I have something mixed up in my method.

Thanks for the replies.

 

[Hiche]

This is still bugging me. I tried more values after the decimal point, but nothing. I'm sorry to have brought this back up, but I really need the answer.

 

[Doc Al]

This is still bugging me. I tried more values after the decimal point, but nothing. I'm sorry to have brought this back up, but I really need the answer.

It's not a question of more decimal points in your answer, but along the way to getting your answer. I don't know how many sig figs your system requires, but at least the first two digits are required. I recall getting an answer close to yours, but different in the second digit.

(I have no idea if that's the issue with your system, but my guess is that's what's wrong. You gave two answers: 0.54 and 0.502. Rounded to two places, the answer I got didn't match either.)