Problem 3: Six objects are released from rest at the same point on a ramp at a h

Question

Problem 3: Six objects are released from rest at the same point on a ramp at a height of 2 meters from the bottom. The objects are moving exactly vertically when they are launched from the ramp at the same point. All of the ramps are the same shape. All of the spheres roll without slipping, and the blocks slide without friction. The shapes and masses of the objects are given in the drawing for each case. Rank the maximum height of the objects after they become airborne at point T. (For convienence Ic solid sphere 2/5MR2, hollow sphere - 2/3MR2) A m= 1 kg B ,n = 2 kg C m=1kg Hollow sphere Solid sphere Hollow sphere D m=2kg E ,n = 2 kg F ,n =1kg Block Block Solid sphere

Explanation / Answer

Rank : E=F > C=D > A=B

First of all, mass will have no effect. Now we have to compare between block, hollow and solid spheres. The spheres will gain some rotaional kinetic energy when they will roll down. So their translational KE will be less. Since hollow sphere has more moment of inertia , its rotaional KE will be more, translational KE will be least. The translation KE at bottom determines what height will the objects rise. It is most for blocks, then solid shperes , and then hollow spheres.

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