How to find coefficient of friction of a body sliding down the slope?

[Callmelucky]

Homework Statement

Body starts to slide down the 60degree incline plane and after 20 meters reaches speed of 4 m/s. What is the coefficient of friction?

Relevant Equations

acceleration due to gravity under angle ->Fg=mgsin60, Normal force -> Fn=mgcos60, Ffriction = mi(coefficient of friction)*Fn

So basically I need to find the coefficient of friction given the listed information.
What bothers me is that I am getting two different accelerations for two different approaches. When I calculate acceleration using Fg=mgsin60 I do it this way: Fg=mgsin60 -> ma=mgsin60 ->a=gsin60 -> a=8.66. But when I use formula $v^2=2as$ I get a=0.4.

After I got a using Fg=mgsin60 I use Ftr=Fn*mi -> ma=mgcos60*mi -> $\frac{a}{gcos60}=mi$ -> mi(fr coef)= 1.73. Which makes no sense, since body is moving and coef of friction can't be greater or equal to 1 if body is moving.

And using a I got from $v^2=2as$ -> $\frac{a}{gcos60}=mi$ -> mi= 0.08 and that makes sense, BUT the solution in the textbook is 1.65, so I am really confused. I suppose it's mistake in textbook, but why am I getting two different soltions for a?

So yeah, if you could please explain I would be very grateful,
thank you.

 

[haruspex]

Fg=mgsin60 -> ma=mgsin60

That assumes no friction. Try including the frictional force in the equation.

 

[kuruman]

. . . and coef of friction can't be greater or equal to 1 if body is moving.

Why?

 

[phinds]

how to find coefficient of friction of a body sliding down the slop?​

Just FYI, most slop has a VERY low coefficient of friction.

 

[MatinSAR]

You want to find coefficient of friction. But you have forgotten the firiction force in your answer!

Try to add a X-Y coordinate system and find component of each force in $x$ and $y$ direction. Then apply $\vec F_{net}=m\vec a$ ! You should know that the mentioned vector equation equivalent to three component equations! So you can find equations you have mentioned in post #1 without forgetting the firiction force.

 

[Callmelucky]

@MatinSAR, @haruspex. I got it, thank you.
@kuruman, I had no idea that mi can be >=1, there was a question in the textbook if mi can be >= 1 and the answer at the end was that it can not. I never checked that, just accepted it as a fact, but after checking I realized that it obviously can be, thank you for telling me.

 

[haruspex]

@MatinSAR, @haruspex. I got it, thank you.
@kuruman, I had no idea that mi can be >=1, there was a question in the textbook if mi can be >= 1 and the answer at the end was that it can not. I never checked that, just accepted it as a fact, but after checking I realized that it obviously can be, thank you for telling me.

What text book?

 

[Callmelucky]

What text book?

it's actually a workbook by Nada Brkovic, there is a question(273) if the friction coefficient can be greater than 1, and, somehow I concluded that it can not be greater than 1 if the body is moving. The best thing is that it is not a proper question, it's more like a side question along with 3 main questions and it is not actually answered at the end of the textbook. I don't know why I thought that it was answered and that the answer was that coef of friction can't be >=1.