What is the velocity of mass2 after dropping 3cm in a tension/friction problem?

[hadoken22]

Hello. I've been doing this problem and cannot seem to get the correct answer. I'd really appreciate some help. In the problem, mass1(250g) rests on an inclined plane that is 30 degrees above the horizontal, and whose coefficient for kenetic friction is .1. M1 is attached to a frictionless pulley at the top of the plane, with a string. Hanging off of the pulley is mass2(250g), attached to the string. When mass2 has dropped 3cm, what is its velocity?

This is what I have done so far. I summed up the forces on m1 and m2 separately:
#1 sumFym1=Fnormal-m1gcos30=0 (NOTE:I am using the inclined plane as my reference/x-axis, rather than the ground.)
#2 sumFxm1=T-Ffriction-m1gsin30=m1a
#3 sumFym2=T-m2g=-m2a
Fn=m1gcos30
Ffriction=.1Fn=.1m1gcos30
I substituted this value for Ffriction and then tried solving the system of equations by subtracting #3 from #2. The tension canceled out and I solved for acceleration. I got a=2.107cm/s^2. Using v^2=V0^2+2as, the velocity turned out to be 11.24cm/sec . My textbook says the answer is supposed to be 83m/s. I am doing something wrong, but cannot figure out what. Any help would be appreciated.

Thanks!

 

[Doc Al]

Originally posted by hadoken22
I got a=2.107cm/s^2. Using v^2=V0^2+2as, the velocity turned out to be 11.24cm/sec . My textbook says the answer is supposed to be 83m/s.

Your equations look correct, but your answer for "a" seems way off. Did you mix up units? (cm vs. m, for example) (The book's answer seems off as well.)

 

[hadoken22]

Hi. You were absolutely right! After converting to SI units, I repeated the problem and got acceleration to be 1.163m/s^2. The velocity turned out to be .835m/s^2. Thanks for the help. I really appreciate it!