Rotational Motion FInding the total ENergy

AI Thread Summary
The discussion focuses on calculating the final velocity of a ball rolling off a table and down a ramp, using principles of energy conservation. The initial gravitational potential energy and kinetic energy are computed, with values provided for each type of energy. Participants confirm that energy conservation applies, allowing the sum of initial energies to equal the sum of final energies. There is a mention of the need to incorporate rotational kinetic energy using the moment of inertia and the relationship between linear and angular velocity. The final calculated velocity is approximately 3.85 m/s, indicating the calculations are on the right track.
Schu
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Particulars:
ball has a radius of 2.5 cm a mass of .125 and is rolling across a table with a speed of .547 m/s, this table is 1.04 m off the ground. It rolls to the edge and down a ramp How fast will it be rolling across the floor?

First I found the Gravitational Potential Energy: Ep=mgh
Initial of 1.2753 FInal = 0

THen the Linear Kinetic ENergy : 1/2 mv^2
Initial .0187005625 FInal .0625v^2

Elastic Potential Energy: .5k(delta)x^2
0 0

Rotational Kinetic Energy: 1/5mv^2
initial .007480225 FInal .025v^2

Now I need to bring them all togther and solve the final velocity.

Is the Sum of the inital energy's = to the SUM of the final energy's?
If that's true then 1.30148075 = .0875v^2
so v = 3.85 m/s
Is that at all right?? :confused:
 
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I need help ASAP

Is anyone out there?

I would appreciate the help :confused:
 
Looks ok to me. (I got 3.86 m/s, by rounding off)
 
rotational KE

I didn't check your arithmetic, but I have some comments.
Schu said:
Rotational Kinetic Energy: 1/5mv^2
The rotational KE is {KE}_{rot} = 1/2 I \omega^2.

You will also need the "rolling condition": V = \omega R.
Is the Sum of the inital energy's = to the SUM of the final energy's?
Yes, if you assume energy is conserved, which seems reasonable for this problem.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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