Originally Posted by **topsquark** One of us made a mistake. I get the same answer, but with the m1 and m2 switched.:
(2.7 + 4.6)(.1*9.8*4.6/2.7)
To answer your question, your friction comment is correct. But in order to find the friction force on m2 you have to find an equation for it for m1 (they are 3rd Law pairs.) And remember that the whole system is accelerating, so you can't put a = 0.
Before I will even think of helping you more with this answer, I'm going to need to see your work. This one's too big to just spot-check.
-Dan |

Hello Dan, thank you for your help! I really appreciate it.

As for the mistake, I am perfectly happy to claim it for my own. I did submit it to a grader (this problem is associated with an online MIT course) and the grader accepted the answer as correct, but I'm also perfectly willing to accept that the person who programmed the grader made a mistake. I'm the last person qualified to adjudicate.

In any case, about your answer, I hope I can ask another question about this. Wouldn't the force of friction applied by m2 on m1 just be given by the proportion of the normal force? And wouldn't the normal force have magnitude matching the force of gravity? So the normal force has magnitude m1*g and the frictional force therefore be mu*m1*g, or am I missing something?

You asked to see my work--did you mean for the first question, or for the others? I'll assume you meant for the second question, since I think I've shown you my basic logic for the first question in the paragraph above.

In the second question, I reasoned (apparently incorrectly) this way:

I choose the positive direction parallel to the plane to be up-and-right.

The net of the forces on m1 is m1*a, which is also [gravity's force down the plane]+[friction's force down the plane]+[tension's force up the plane] = -m1*g*sin(theta) + mu*m1*g*cos(theta) + T.

The net of the forces on m2 is -m2*a = [g down] + [f up] + [T up] = -(m1+m2)*g*sin(theta) + mu*m1*g*cos(theta) + T.

I think my logic surrounding m1 is correct and clear, but correct me if I'm wrong, so I'll just focus on the forces on m2. In particular, my reasoning behind [g down] seems to be what's wrong. And in more particular, I would have thought that m1 would exert a downward force on m2 and therefore further contribute to how much gravitational force would push m2 down the plane. Apparently not, but why? It must push m2 down somewhat, right? I mean, if m2 were absent, then m1 would fall down a little even under the force of the tension, right? So anyway, exactly why [g down] =/= -(m1+m2)*g*sin(theta) is so, seems to be what's confusing me here. When I change that to just -m2*g*sin(theta), it yields the right answer.