Inclined plane with friction, find kinetic energy.

[dttah]

I need someone to double check it, because this was an exam given by my teacher and I am trying to solve it, but I do not have any results so I would like to know if I did it correctly or not. Thank you!

Homework Statement

Two blocks m1 = 50kg and m2= 100kg are attached to a rope as shown in figure. Pulley is massless. The angle of the inclined plane is pi/6 and the coefficient of kinetic friction is 0.250. Find the variation of kinetic energy if the body m1 goes up 20meters.

Homework Equations

F = ma
kinetic energy = 1/2 mv^2
kinetic friction = mu*normal force.

The Attempt at a Solution

See attachment
or: http://i40.tinypic.com/6hklm8.jpg for better quality.

Thanks for any help.

 

[Delphi51]

Welcome to PF! Thanks for taking time to show your whole solution so clearly.

Over on the right side, where you first have "a =", it appears you are missing a "-m₂g" in the numerator. Also, the "μ*m₁*cos(30)" should have a factor of g as well. I end up with a negative acceleration (m₂ goes down) of about 4.

 

[dttah]

Aw, how could I fall in such a stupid typos mistakes ! :(.
Thanks a lot, that's appreciated. Forgetting about the "numbers" is the reasoning correct ( I mean the use of the formulas) or is there anything wrong? Thanks a lot!

 

[Delphi51]

Yes, it all looks good! Nice use of variables right up to the calculation stage.

 

[dttah]

Alright! Thanks a lot, I am grateful and I appreciate your help. Thanks again :)

 

[Delphi51]

Most welcome.