A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are each release

Question

A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are each released from rest on the incline shown. Knowing that all three objects roll without slipping.  Each has the same outer radius of 10 cm and the same mass of 1 kg.  After rolling for 3 meters, calculate the linear velocity of each rolling object.

A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are each released from rest on the incline shown. Knowing that all three objects roll without slipping. Each has the same outer radius of 10 cm and the same mass of 1 kg. After rolling for 3 meters, calculate the linear velocity of each rolling object.

Explanation / Answer

Here

0.5*i*w^2 + 0.5*m*v^2 = mg*3Sin(10)

0.5*kmv^2 + 0.5*m*v^2 = 0.521mg

0.5*(k+1)v^2 = 0.521g

v = sqrt(10.21/(k+1))

For Sphere

k = 2/5

So

Velocity of sphere = sqrt(10.21/((2/5)+1))

= 2.7 m/sec

For cylinder

k = 1/2

So

Velocity of cylinder = sqrt(10.21/((1/2)+1))

= 2.609 m/sec

For Pile

k = 1

So

Velocity of pipe = sqrt(10.21/((1)+1))

= 2.26 m/sec

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