Sphere/disk rolling down an incline HELP

[asourpatchkid]

Sphere/disk rolling down an incline HELP!

Homework Statement

a ball, or sphere with a radius of R and mass Mis rolling down an incline with a height of H and an angle of $$\Theta$$ how long does it take to get to the bottom

Homework Equations

Conservation of mechanical energy
Kf + Uf = Ki + Ui
K = 1/2 (I/R^2 + M)v^2

The Attempt at a Solution

i solved for the system with conservation of energy

1/2(I/R^2 + M )v^2 + 0 = 0 + Mgh

solved for final velocity of the ball or disc at the bottom of the incline


and got

v = [2gh/1 + ( I/ MR^2)]^0.5



set H=MG$$\Theta$$

and got


v = [2gMG$$\Theta$$/1 + ( I/ MR^2)]^0.5

i am having trouble however seeing how i can solve for time t in terms of all the variables...please help!

 

[physucsc11]

Well using the angle you can solve for the length of the incline in terms of height, and using that length you can find what the acceleration was using the formula
V(final)^2 = V(init)^2 + 2*a*(Xfinal- Xinit), with the velocity and length you found.
Then you can find the time using t = V/a

 

[ogb p]

Hello,

It seems like you have made good progress in solving for the final velocity of the sphere/disk at the bottom of the incline. To find the time it takes for the sphere/disk to roll down the incline, you can use the equation v = d/t, where d is the distance traveled and t is the time. In this case, the distance traveled is the length of the incline, which can be calculated using trigonometry (d = H/sinθ). So, the time it takes for the sphere/disk to roll down the incline can be found by rearranging the equation to t = d/v.

However, keep in mind that this equation assumes that there is no friction present. If there is friction, it will slow down the sphere/disk and affect the time it takes to reach the bottom. In that case, you may need to use more advanced equations that take into account the effects of friction.

Hope this helps! Let me know if you have any other questions.