Mass Pulley Acceleration Problem

[Leeoku]

Homework Statement

A m2 = 4.63 kg mass is connected by a light cord to a m1 = 2.10 kg mass on a smooth surface (see the figure below).The pulley rotates about a frictionless axle and has a moment of inertia of 0.513 kg•m2 and a radius of 0.257 m. Assuming that the cord does not slip on the pulley, find the acceleration of m1.

Homework Equations

Torque = I*alpha = F*D

The Attempt at a Solution

FBD Mass 1
F_net = Tension 2... mass1*a = Tension 2
FBD Mass 2
F_net = mg-T1
T1 = mass2*g- mass2*a

Torque = I*alpha
Torque_1+Torque_2 = I*alpha
Tension_1+Tension_2 = I*alpha/r

and now I am stuck. Correct answer is 3.13 m/s^2

 

[PhanthomJay]

Homework Statement

A m2 = 4.63 kg mass is connected by a light cord to a m1 = 2.10 kg mass on a smooth surface (see the figure below).The pulley rotates about a frictionless axle and has a moment of inertia of 0.513 kg•m2 and a radius of 0.257 m. Assuming that the cord does not slip on the pulley, find the acceleration of m1.

Homework Equations

Torque = I*alpha = F*D

The Attempt at a Solution

FBD Mass 1
F_net = Tension 2... mass1*a = Tension 2
FBD Mass 2
F_net = mg-T1
T1 = mass2*g- mass2*a

Torque = I*alpha
Torque_1+Torque_2 = I*alpha
Tension_1+Tension_2 = I*alpha/r

and now I am stuck. Correct answer is 3.13 m/s^2

You have noted 3 equations with 4 unknowns (alpha, a, T1 and T2).. You need a 4th that relates a and alpha. Also, watch your signage in your second and third equations.

 

[SammyS]

Draw three free body diagrams; one for each mass and one for the pulley.

 

[Leeoku]

cant i just convert the alpha to a/r to get I*a/r^2. but then i don't get how to eliminate the massses.

Tension 2 takes the weight of both so... its (M1+M2)g
Tension one would be Tension 2 - mass2*g

im not sure if my logic is right

 

[jhae2.718]

You just need to solve the system of equations.

 

[SammyS]

cant i just convert the alpha to a/r to get I*a/r^2. but then i don't get how to eliminate the massses.

Tension 2 takes the weight of both so... its (M1+M2)g
Tension one would be Tension 2 - mass2*g

im not sure if my logic is right

No, it's not.

Now, get on with drawing the free body diagrams.

 

[PhanthomJay]

You had 3 of the 4 equations correct in your original post, except for a signage error, and you now have the 4th equation relating a and alpha. So correct your sign error, and, as jhae2.718 notes, solve the equations. Plug in the values of m1 and m2 before solving; they are given, so make life easier for you.