Two masses hanging from a pulley (conservation of energy)

[khannon5]

Homework Statement

Two masses are connected by a string that hangs over a frictionless pulley with mass 8kg, radius .25m, and moment of inertia .5mr^2. One mass lays on the ground and has mass 15kg. The other mass is 22.5 kg and is 2.75 m above the ground. Use conservation of energy to determine the speed of the 22.5 kg mass when it hits the ground

Homework Equations

Ke final = pe initial
Ke=.5mv^2 + .5Iw^2

The Attempt at a Solution

I found the pe of the 22.5 mass using pe=mgh. I made that equal the ke equation but I'm not sure whether to combine masses or what to use

 

[PeroK]

The system loses gravitational PE. The first question is to ask where does this energy go?

 

[haruspex]

There are three elements to the system, the two masses and the pulley. Consider the total energy (KE and PE) of each at start and again at the moment of impact.

 

[khannon5]

The system loses gravitational PE. The first question is to ask where does this energy go?

Kinetic energy of each mass and the rotation of the pulley

 

[PeroK]

Kinetic energy of each mass and the rotation of the pulley

Can you write down an energy equation involving all the energies gained and lost?

 

[khannon5]

Can you write down an energy equation involving all the energies gained and lost?

Ke=.5mv^2 of mass 1 + .5mv^2 of mass 2 + .5Iw^2 of pulley

 

[PeroK]

Ke=.5mv^2 of mass 1 + .5mv^2 of mass 2 + .5Iw^2 of pulley

OKay, but there's no PE there.

You're also going to have to find a relationship between the various KE's. So, you need to think about that as well.

 

[khannon5]

OKay, but there's no PE there.

You're also going to have to find a relationship between the various KE's. So, you need to think about that as well.

Would the pe just be the mgh of the weight above the ground?

 

[PeroK]

Would the pe just be the mgh of the weight above the ground?

There are two masses involved.

 

[khannon5]

There are two masses involved.

But why does it have pe if it's on the ground

 

[PeroK]

But why does it have pe if it's on the ground

Does it stay on the ground?

 

[khannon5]

Does it stay on the ground?

No but in the beginning it has no pe

 

[haruspex]

No but in the beginning it has no pe

Right (assuming ground is taken as the reference point for PE). So post the initial energy = final energy equation.