1. A marble rolls down an incline of 30 degrees. If the marble is initally at re

Question

1. A marble rolls down an incline of 30 degrees. If the marble is initally at rest at the top ofthe incline of length 2.0 meters what will the speed of the marble be at the bottom of the incline (a) if the incline is rough enough to prevent any slipping [ it rolls], then (b) if the hill is perfectly smooth [it slides without rolling]? (c) Why does the marble have different speeds when the total energy must be conserved in both cases? [ clear argument is required]


1. A marble rolls down an incline of 30 degrees. If the marble is initally at rest at the top ofthe incline of length 2.0 meters what will the speed of the marble be at the bottom of the incline (a) if the incline is rough enough to prevent any slipping [ it rolls], then (b) if the hill is perfectly smooth [it slides without rolling]? (c) Why does the marble have different speeds when the total energy must be conserved in both cases? [ clear argument is required]

Explanation / Answer

MOI = I = 7/5*M*R^2

at bottom 0.5 * I *W^2 = m g lsin 30.................

a) 0.5*7/5*m *V^2 = m g L sin 30==========>v = sqrt(10 g L sin30/7) = 3.741 m/s

b) o.5 mV^2 = m g L sin 30 =====> V = sqrt(2 g L sin30) = 4.42 m/s

c) b coz of friction some energy is dissipated

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