Consider a marble of mass m rolling down a ramp set up on a table. The marble st

Question

Consider a marble of mass m rolling down a ramp set up on a table. The marble starts out up the ramp, at height h above the table top. It is released from rest and allowed to roll down the ramp.

What is the kinetic energy of the marble at the top of ramp?

What is the potential energy of the marble at the top of the ramp (assume U=0 at the bottom of the ramp)?

(in terms of the mass of the marble m, the height of the ramp h, and the acceleration due to gravity

Ignoring the rotation of the marble, what is the kinetic energy of the marble when it reaches the bottom of the ramp?

( in terms of the mass of the marble m, and the speed of the marble at the bottom of the ramp,

v.)

Putting parts A, B, and C together, solve for the speed of the marble at the bottom of the ramp? ( in terms of the height of the ramp h and the acceleration due to gravity)

Explanation / Answer

kinetic energy of the marble at the top of ramp = 0

the potential energy of the marble at the top of the ramp = mgh

the kinetic energy of the marble when it reaches the bottom of the ramp = 0.5mv^2

0.5mv^2 = mgh

=> v = sqrt(2gh)

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