How to Find the Speeds of Suspended Objects Over a Pulley?

[elizabethg]

I need help on a problem, I tried using many equations, what do I do?...

A m1=13.5kg object and a m2=12.5kg object are suspended, joined by a cord that passes over a pulley with a radius of 10 cm and a mass of 3 kg. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest 3 m apart. Treating the pulley as a uniform disk, determine the speeds of the two objects as they pass each other.

I used the equation to find acceleration...

a=((m1-m2)g)/(m1+m2+.5mR^2) The .5mR^2 is the moment of Inertia

After I found the acceleration I found the velocity...

v=(2a(x/2))^(1/2)

Please Help

 

[kakarukeys]

My first thought:
Use conservation of energy to work for you
Here the kinetic energy of both masses + potential energy of both masses + rotational energy of the pulley is conserved.

 

[wais]

It looks like you are on the right track with using the equations for moment of inertia and acceleration to solve this problem. However, it's important to double check your calculations and make sure you are using the correct values for all variables.

To find the moment of inertia for the pulley, you can use the equation I = 1/2MR^2, where M is the mass of the pulley and R is the radius. In this case, the mass of the pulley is given as 3 kg and the radius is 10 cm (or 0.1 m), so the moment of inertia for the pulley would be I = 1/2(3)(0.1)^2 = 0.015 kgm^2.

Once you have the correct moment of inertia, you can use the equation for acceleration that you mentioned, a = ((m1-m2)g)/(m1+m2+.5mR^2), to find the acceleration of the system. Just make sure to substitute in the correct values for m1, m2, g, and the moment of inertia that you calculated.

Then, to find the velocity of the objects, you can use the equation v = (2as)^1/2, where a is the acceleration you calculated and s is the distance between the objects (in this case, 3 m).

I hope this helps and good luck with your problem! Remember to always double check your calculations and make sure you are using the correct equations and values.