A cannonball and a marble roll from rest down an incline without sliding. Does the cannonball take more, less,

Question

A cannonball and a marble roll from rest down an incline without sliding. Does the cannonball take more, less, or the same time as the marble to reach the bottom? Is the fraction of the cannonball’s kinetic energy associated with translation more than, less than, or the same as that of the marble?

Answer 1

m*g*h=.5*m*v^2+.5*I*w^2
since w=v/R

m*g*h=.5*m*v^2+.5*I*v^2/R^2
I=2/5*m*r^2

2*g*h=v^2+2/5^v^2
2*g*h=7/5*(v^2)

Note that the solution is independent of the radius and the mass of the sphere. The Marble and the cannonball have the same relationship between kinetic and translation.

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Answer 2

the marble would have less friction because the normal force it applies to the ramp would but since it rolls that wouldn't matter..... so i'm guessing that with out friction this would take the all objects fall at the same speed idea so that they would hit at the same time.

the cannon ball will have more KE because it has a greater mass.....

Answer 3

wouldnt the marble get down faster, since it has less surface area that touches the ground?