How Do Accelerations and Tensions Relate in a Dual Pulley System?

[yitriana]

Problem is written, a diagram of the problem is attached.

Homework Statement

An object of mass m1 on a frictionless horizontal table is
connected to an object of mass m2 through a very light pulley
P1 and a light fixed pulley P2 as shown in Figure P5.34.
(a) If a1 and a2 are the accelerations of m1 and m2, respectively,
what is the relation between these accelerations? Express
(b) the tensions in the strings and (c) the accelerations
a1 and a2 in terms of the masses m1 and m2, and g.

Homework Equations

The Attempt at a Solution

I am confused on how to approach the problem since I don't understand how the pulley 1 affects pulley 2.

 

[turin]

Pulley 1 affects Pulley 2 through tension in the cable between them and contact force of the cable laying across Pulley 2. This contact force leads to friction between the cable and Pulley 2. However, if the contact between the cable and Pulley 2 is frictionless, then the only effect of Pulley 1 on Pulley 2 is the contact force, which you probably simply assume to be balanced by the pivot force.

Bottomline: I don't think that you really want to know how Pulley 1 affects Pulley 2, and, assuming zero friction, this will not help you solve the problem.

 

[merryjman]

I'm sure you know this already, but you've got to use free-body diagrams to figure this one out. In this case, you'll need 3: one for each of the masses and one for pulley 1. The one hint I'll give you is that, since pulley 1 and M2 are connected by a string, they have to have the same acceleration. That doesn't mean M1 has the same acceleration, though.