After class one day, two physics students get into an argument about rotational

Question

After class one day, two physics students get into an argument about rotational dynamics. Jack thinks the nickel in his pocket would beat Jill's silver ring in a race down an incline, but Jill is convinced her ring would win. To settle their argument, Jack and Jill climb up a 20m hill inclined at 30 degrees to the horizontal. Both objects are released from rest at the top of the hill and roll without slipping all the way to the bottom. What is the translational speed of each object when it reaches the bottom? How long does each onject take to get from the release point to the bottom of the hill? Include a drawing in your solution.

Explanation / Answer

Here

For the Nickel

Gravitational Poteteial Energy = Linear Kinetic Energy

mgh = 0.5*m*v^2

gh = 0.5*v^2

9.8*20 = 0.5*v^2

v = 19.789 m/sec

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For Ring

Gravitational POtetneial Energy = Rotational Kinetic Energy + Linear Kinetic Energy

mgh = 0.5*I*w^2 + 0.5*m*v^2

As For Ring I = mr^2 and w = v/r

Therefore

mgh = 0.5*m*v^2 + 0.5*m*v^2

mgh = mv^2

v = sqrt(gr)

So As Punt the Value of Radius of Silver ring to get Answer

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