How Does a Moving Pulley Affect Acceleration and Tension in a Mechanics Problem?

[BigCheese234]

Homework Statement

A mass 4m lying on a rough horizontal table is connected by a string,
passing over a pulley, to another mass 3 m hanging freely. The pulley (regarded
as a disk) has mass 4 m and rotates freely about a polar axis parallel to the
edge of the table. The coefficient of kinetic friction between the mass and the
table is μ=3/8. Assuming that the string does not slip on the pulley, Find the
common acceleration of the masses and show that the ratio of the tensions in
the string on either side of the pulley is T1 : T2 = 13 : 15. (You may assume
that the moment of inertia of a disk of radius r and mass m about a polar axis
through the disk is I =1/2 M r^2)

[D] Attempt
acceleration

4mg-t=4a
t-3mg=3A

1g=7a
10=7a
a=10/7
a=1.428
Tension 2:
4m(g)=4m(10)=40m

3/8=T2/40 , 120/8 = T2 , T2=15m

Tension 1:
3(10)=30
am i on the right track?
Thanks for the help have a big exam and this is a common question , having problems with it because the pulley is moving and don't know how it effects the acceleration .solution would be fantastic !:shy:

 

[Villyer]

The force of gravity on the hanging mass will not only accelerate the system of masses, but also cause the pulley to rotate.

 

[BigCheese234]

Thanks for your help ! so the pulley does not effect the common acceleration? does the pulley due to its mass have any bearing on the tension of the hanging mass?

 

[Villyer]

It does effect the acceleration of the mass system because as the mass drops, energy is transferred into the pulley as well, instead of remaining in the system.