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Mass m1=40kg, is sitting on a frictionless floor while m2=10kg sits on top of it. Between each mass, the coefficient of static friction is .6, and the kinetic coefficient is .4. M2 is pulled by a force of 100N to the left. What are the accelerations of each mass?

I solved it and got answers that do make sense, I'm just looking for a second opinion as to whether I did it right or not. Here's my work...

F(kinetic)=.4(10kg)(9.8)=39.2N

F(static)=.6(10kg)(9.8)=58.8N

The force pulling mass 2 is of 100N, which is >58.8N of friction, so the mass will move.

m1=ƩF=ma

F(friction m2)=ma

-39.2N=40kg(a)

a=-.98m/s^2

m2=ƩF=ma

100N-39.2N=10kg(a)

A=-6.08m/s^2.

Since m1 is moving along with m2, I added the -.98 to the -6.08 to get the total acceleration of mass 2 to be -7.06m/s^2. Yet I feel like I must use static friction for something other than proving that the mass will move. However, it could be in there just to throw us students off. Did I do this correctly, or is there another route to take to a correct answer?

All help is appreciated!

-TW