IP A student sits at rest on a piano stool that can rotate without friction. The

Question

IP A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.3 kgm2 . A second student tosses a 1.5 kg mass with a speed of 2.7 m/s to the student on the stool, who catches it at a distance of 0.40 m from the axis of rotation.

1. Does the kinetic energy of the mass-student-stool system increase, decrease, or stay the same as the mass is caught?

2. Calculate the initial kinetic energy of the system. (in Joules)

3. Calculate the final kinetic energy of the system. (in Joules)

Explanation / Answer

A) there is a loss in the kinetic energy which is shown below

B)Initial energy = 1/2 . 1.5. 2.7^2 = 5.467J

New MI = 4.3+ 1.5 . 0.4^2 = 4.54

Angular momentum start = 1.5. 2.7. 0.4 = 1.62

Ang mom is conserved so new "w" is Ang mom / New MI = 0.3568 rad/s

C)New KE is 1/2 . MI . w^2 = 0.28898 J

This loss is not surprising - there is a huge loss of velocity in this "collision"

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