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Melchoire
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The mass m3 is tied to m2 with an idealized string and m2 rests on m1. There is a rough
interface between m2 and m1 with a coefficient of friction μ. The mass m1 rests on a frictionless
surface. The pulley is “ideal,” that is, massless and frictionless. All three masses move together
as if m1 and m2 were solidly attached.
(a) Draw free body diagrams for the three masses showing all forces and directions of acceleration.
Find expressions for the following in terms of g, m1, m2 and m3:
(b) the acceleration of each mass.
(c) the tensions T2 and T3.
(d) the smallest value of the coefficient of friction μ to permit the above motion
http://img407.imageshack.us/img407/9299/m1m2m3.jpg
I drew the free body diagrams that wasn't really complicated. But I'm stuck on all the rest. For 'b' I wrote out Newtons second law for each mass where 'a' was equal in all but that didn't get me anywhere. When I think about it I know that the larger the masses of m1 and m2 the slower the acceleration of system. But I don't know how to get that in my equations.
Any help would be appreciated. =]
interface between m2 and m1 with a coefficient of friction μ. The mass m1 rests on a frictionless
surface. The pulley is “ideal,” that is, massless and frictionless. All three masses move together
as if m1 and m2 were solidly attached.
(a) Draw free body diagrams for the three masses showing all forces and directions of acceleration.
Find expressions for the following in terms of g, m1, m2 and m3:
(b) the acceleration of each mass.
(c) the tensions T2 and T3.
(d) the smallest value of the coefficient of friction μ to permit the above motion
http://img407.imageshack.us/img407/9299/m1m2m3.jpg
I drew the free body diagrams that wasn't really complicated. But I'm stuck on all the rest. For 'b' I wrote out Newtons second law for each mass where 'a' was equal in all but that didn't get me anywhere. When I think about it I know that the larger the masses of m1 and m2 the slower the acceleration of system. But I don't know how to get that in my equations.
Any help would be appreciated. =]
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