A marble and a cube are placed at the top of a ramp. Startingfrom rest at the sa

Question

A marble and a cube are placed at the top of a ramp. Startingfrom rest at the same height, the marble rolls and the cube slides(no kinetic friction) down the ramp. Determine the ratio of thecenter-of-mass speed of the cube to the center-of-mass speed of themarble at the bottom of the ramp. How do you figure for the cube? A marble and a cube are placed at the top of a ramp. Startingfrom rest at the same height, the marble rolls and the cube slides(no kinetic friction) down the ramp. Determine the ratio of thecenter-of-mass speed of the cube to the center-of-mass speed of themarble at the bottom of the ramp. How do you figure for the cube?

Explanation / Answer

A marble and a cube are placed at the top of a ramp. Startingfrom rest at the same height, the marble rolls and the cube slides(no kinetic friction) down the ramp. Determine the ratio of thecenter-of-mass speed of the cube to the center-of-mass speed of themarble at the bottom of the ramp.
speed of center of mass ofcube=2gh=2glsin
where l is the length of the inclination and is the angle ofinclination.
speed of center of mass ofmarble=2gh/(1+K2/R2)=2glsin/(1+K2/R2)

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