Two masses hanging from a pulley (conservation of energy)

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1. Mar 6, 2015

khannon5

1. The problem statement, all variables and given/known data
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

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

3. 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

2. Mar 6, 2015

PeroK

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

3. Mar 6, 2015

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.

4. Mar 6, 2015

khannon5

Kinetic energy of each mass and the rotation of the pulley

5. Mar 6, 2015

PeroK

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

6. Mar 6, 2015

khannon5

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

7. Mar 6, 2015

PeroK

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.

8. Mar 6, 2015

khannon5

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

9. Mar 6, 2015

PeroK

There are two masses involved.

10. Mar 6, 2015

khannon5

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

11. Mar 6, 2015

PeroK

Does it stay on the ground?

12. Mar 6, 2015

khannon5

No but in the beginning it has no pe

13. Mar 6, 2015

haruspex

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