# Help with a simple conversation of energy problem?

• the_quack
In summary, the smaller mass has potential energy to raise to height (h), has kinetic energy just before the larger mass hits the ground, and has rotational energy at angular speed (w = v/r).
the_quack
energy is conserved, no slipping or air resistance or anything.

There is a pulley, on one side is a mass resting on the ground, and on the other side is a larger mass above the ground. If the larger mass is released, what is it's speed when it hits.

okay, here is what I have:

PgM = Pgm + KM + KR + Km
Mgh = mgh + v[ srqt(.5M) + sqrt(.5I)/r + sqrt(.5m) ]

I=
.5mr^2 = .5(7.50kg)(.260m)^2 = 0.2535kg*m^2
h=3
m=18
M=26.5
so
PgM = 779.1 J
Pgm = 529.2 J

My answer is v(M)=49.84m/s, completely illogical, and the book answer is 3.22m/s. What did I do wrong? All the numbers look right, and it appears to make sense, but the answer is way off...

Thanks for any help!

Last edited:
The smaller mass also has kinetic energy just before the larger mass hits the ground.

No conversation about energy is ever simple.

So, you're changing the potential energy of the large mass into:

potential energy for the small mass
energy in the pulley
kinetic energy of the large mass

There's one more thing with energy... if the large mass is moving, and it's attached to the small mass via a string and pulley...

hmm, I added the kinetic energy of the small mass and that only changed it a little...

Do you see any problems with my algebra? Is the formula correct?
PgM = Pgm + KM + KR + Km
Mgh = mgh + v[ srqt(.5M) + sqrt(.5I)/r + sqrt(.5m) ]

Any last-minute tips?

I have to quit pretty soon...

I don't think so, you seem to think that you can just pull out that V and sqrt the other terms. Thats a problem. Also, the V in the energy for the pulley is radial velocity or w(omega) that is not the same velocity as the boxes.

I know, the V in the equations was squared, wasn't it?

And w = v/r

Something to think about. The potential energy of the large mass is going to:

1 - Give the smaller mass potential energy to raise to height (h).
2 - Give the system of masses (M+m) kinetic energy for a speed (v).
3 - Give the pulley rotational energy at angular speed (w = v/r)

You've written that (I assume) as:

PgM = Pgm + KM + Km + KR

If I you write this out without the square-root bits you get:

$$Mgh - mgh = \frac{1}{2} (M + m) v^2 + \frac{1}{2}I \omega ^2$$

Regards,
Sam

Now its over to you to re-arrange and solve for v.

Hope that helps :-)

## What is energy?

Energy is the ability to do work or cause change. It comes in many forms, such as kinetic energy, potential energy, thermal energy, and electrical energy.

## How does energy transfer between objects?

Energy can be transferred between objects through various processes, such as conduction, convection, and radiation. These processes involve the movement of particles or waves.

## How can I calculate the amount of energy in a system?

The total energy in a system can be calculated using the formula E = m x c^2, where E is energy, m is mass, and c is the speed of light. Other forms of energy, such as kinetic and potential energy, can also be calculated using specific equations.

## What are some examples of energy conversions?

Energy can be converted from one form to another. For example, when a person runs, chemical energy stored in their body is converted to kinetic energy. Other examples include converting solar energy to electrical energy through solar panels, and converting thermal energy to mechanical energy in a steam engine.

## Why is understanding energy important?

Energy is a fundamental concept in science and is essential for understanding how the world works. It is also crucial for developing new technologies and finding sustainable solutions for energy use.

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