Q.

A sphere of radius r and mass m has a linear velocity v0 m/s directed to the left and no angular velocity as it is placed on a horizontal platform moving to the right witha constant velocity 10 m/s. If after sliding on the platform the sphere is to have no linear velocity relative to the ground as it starts rolling on the platform without sliding.The coefficient of kinetic friction between the sphere and the platform is μk. Determine the required value of v0 in m/s.

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Detailed Solution

Angular Impulse-Angular Momentum : fRΔt=IcmωLinear Impulse-Linear Momentum : −fΔt=m0−v0Pure Rolling : ωr=v1⇒ mv0R=25mR2ω⇒ ω=5v02R ⇒ v1=5v02⇒ v0=2v15 ⇒ v0=2×105=4m/s
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A sphere of radius r and mass m has a linear velocity v0 m/s directed to the left and no angular velocity as it is placed on a horizontal platform moving to the right witha constant velocity 10 m/s. If after sliding on the platform the sphere is to have no linear velocity relative to the ground as it starts rolling on the platform without sliding.The coefficient of kinetic friction between the sphere and the platform is μk. Determine the required value of v0 in m/s.