Please show how tosolve step by step. thank you! 14) A homogeneous cylinder is r

Question

Please show how tosolve step by step. thank you!

14) A homogeneous cylinder is released from rest and rolls withoutslipping down an inclined plane inclined at 18° to thehorizontal. How fast is it moving after it has rolled 2.2 m downthe plane? A) 4.3 m/s
B) 2.6 m/s C) 3.0m/s D) 5.2m/s E) 3.7m/s Please show how tosolve step by step. thank you!

14) A homogeneous cylinder is released from rest and rolls withoutslipping down an inclined plane inclined at 18° to thehorizontal. How fast is it moving after it has rolled 2.2 m downthe plane? A) 4.3 m/s
B) 2.6 m/s C) 3.0m/s D) 5.2m/s E) 3.7m/s

Explanation / Answer

= 18o, d = 2.2 m mass = m, moment of inertia I = mR2/2, energy conservation: mgdsin = mv2/2 + I2/2= mv2/2 + (mR2/2)(v/R)2/2 =0.75mv2 v = (gdsin/0.75) = 3.0 m/s answer: C

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