A uniform hollow ball (like a soccer ball) is released fromrest at the top of a

Question

A uniform hollow ball (like a soccer ball) is released fromrest at the top of a hill of height H.
Find its forward linear speed (in terms of H)at the base of this hill if there is no friction on the hill. Find its forward linear speed (in terms of H)at the base of this hill if the hill is rough enough so that theball rolls without slipping. A uniform hollow ball (like a soccer ball) is released fromrest at the top of a hill of height H.
Find its forward linear speed (in terms of H)at the base of this hill if there is no friction on the hill. Find its forward linear speed (in terms of H)at the base of this hill if the hill is rough enough so that theball rolls without slipping. Find its forward linear speed (in terms of H)at the base of this hill if there is no friction on the hill. Find its forward linear speed (in terms of H)at the base of this hill if the hill is rough enough so that theball rolls without slipping. Find its forward linear speed (in terms of H)at the base of this hill if the hill is rough enough so that theball rolls without slipping.

Explanation / Answer

(a) From law of conservation of energy     1/2 mv2 = mgh    then v = 2gh (b) From law of conservation of energy mgh = 1/2 mv2 + 1/2 I2          = 1/2mv2 + 1/2 (2/3 mR2 ) (v/R) 2         = 1/2 mv2 + 3mv2 = 5/3 mv2 therefore    v = 3gh/5

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