- #1

Epictetus

- 5

- 0

This is what I've solved:

I(disk)= 1/2mr^2 = I + md(parallel)^2 = 1/2 mr^2 + mr^2 = I = 3/2 mr^2

Energy

Kinetic energy ---> Potential energy

mgh = 1/2 I(omega)^2

mgh = 1/2 (3/2 mr^2) (omega)^2

Omega = square root [4mgh/3mr^2]

Solving for the velocity by mulitplying by radius r:

V= 2/r times sq. root [gh/3] times r = 2 sq.root [gh/3]

Since it's a ramp, I used dsin theta for the hypotenuse and used a kinematic equation

dsin theta = (v initial + v /2) t

Solving for t (time)

t= dsin theta / (2 sq. ro. [gh/3] ) / 2

t = d sin theta / sq. r. [gh/3]

The time for the sphere was also calculated the same way so no need for me to put it up here. My questios are: How am I supposed to find the time difference if there are no definate values for theta, and h. I would have to set up the final answers and subtract them from each other but that wouldn't get me any where. Also, is it valid to set d from the kinematic formula to equal d sin theta?

Please help! Thanks.