ume the small block is replaced with a uniform small solid sphere of the same (c

Question

ume the small block is replaced with a uniform small solid sphere of the same (c) Ass sphere's center of mass has an initial speed of vo and the sphere rolls w incline. Assume the sphere is perfectly rigid. mass. The ithout i) Would you expect the sphere to travel the same distance D, a greater distance or a smaller distance as compared to the small block? Briefly explain your reasoning i) If the block's ramp did not have friction, would you expect the sphere to travel the same distance D, a greater distance or a smaller distance as compared to the small block? Briefly explain your reasoning ii) Calculate the distance the sphere moves up the incline.

Explanation / Answer

(1)

in case of pure rolling work done by friction force is zero .

so whole kinetic energy(translational + rotational )will convert into potential energy while a block have only translational kinetic energy. so sphere will go to higher distance up to incline.

(2)

in absense of friction there will not be pure rolling and sphere will lose only transtinal kinetic energy , same as a block. in this case both will go upto same height.

(3)

in case 1

mgh = 0.5mvo2 + 0.5(2/5mR2)vo2/R2

h = (7/10)vo2/g

in case 2

mgh' = 0.5mvo2

h' = vo2/2g

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