Rotational kinetic energy of falling mass

In summary, you are trying to solve for the potential energy of a weight that is attached to a rotating disk. You found that the potential energy is larger on Mars than on Earth because of the difference in 'g'.
  • #1
kyin01
47
0

Homework Statement


1-14.png

Engineers are designing a system by which a falling mass {m} imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum ( View Figure ). There is no appreciable friction in the axle of the drum, and everything starts from rest.

That is top part of the problem


Homework Equations


mgh = rotational + translation kinetic energy


The Attempt at a Solution



I've tried various methods mainly using energy conservation laws, but I can't get it right. the problem didn't give I or R so I've been using .200J as the total rotational energy.

Any hits on how I should be going on this problem?

thanks
 
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  • #2
The presentation of your problem is headache inducing. Can you maybe just include the diagram, and the problem statement and leave off the irrelevant blank graphic parts. Just type out what the question is. You also left out any description of how you attempted to use those conservation laws. There is a relation between the velocity of the descending weight and the rotational velocity of the disk. v=omega*r. Did you use that? No way to know, is there?
 
Last edited:
  • #3
that was all that's given in the problem. The question is under Part A.
 
  • #4
You don't need I or R. The question is to compare the operation of the thing on Earth and on Mars. The only difference is 'g'. If you don't know something leave it as a letter. Now, write down one of these conservation laws.
 
  • #5
In this situation there are no non conservative forces so

Kinetic energy = potential energy.

So in our situation we have
(Point 1 to be taken at before the system is released and point 2 to be taken just before it hits the ground)

mgh= .200 (which is the rotational kinetic energy that was given to us)

so in mars, just replace 9.8 with the given 3.71 (mass is the same) and solve for h. But when I tried that, they told me it's wrong.
I got h to be .003594m
 
  • #6
Absolutely right. But how did you get that silly answer? If m*(9.8m/s^2)*h_earth=m*(3.7m/s^2)*h_mars, then h_mars must be LARGER than h_earth. Can you post the details of how you did it?
 
  • #7
ah, I got it. Forgot to take account linear kinetic energy also

so the system is actually

Potential energy = Kinetic rotational + kinetic linear

thanks.
 

1. What is rotational kinetic energy?

Rotational kinetic energy is a form of energy that an object possesses due to its rotation around an axis. It is dependent on an object's moment of inertia, which is a measure of how difficult it is to change an object's rotational motion.

2. How is rotational kinetic energy different from linear kinetic energy?

Rotational kinetic energy is different from linear kinetic energy in that it is associated with an object's rotation around an axis, while linear kinetic energy is associated with an object's motion in a straight line. Rotational kinetic energy also depends on an object's moment of inertia, while linear kinetic energy depends on an object's mass and velocity.

3. How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is: KE = 1/2 * I * ω^2, where KE is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

4. Does the mass of an object affect its rotational kinetic energy?

Yes, the mass of an object does impact its rotational kinetic energy. The moment of inertia, which is a key component in the calculation of rotational kinetic energy, is directly proportional to the mass of an object. This means that a heavier object will have a larger moment of inertia and therefore a higher rotational kinetic energy.

5. How does the height of a falling object affect its rotational kinetic energy?

The height of a falling object does not directly affect its rotational kinetic energy. However, the potential energy of the object due to its height will be converted into both linear and rotational kinetic energy as the object falls. The amount of each type of energy will depend on the object's moment of inertia and how it rotates as it falls.

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