2. Jane (55. o kg) and Tarzan (95.0 kg) are standing on opposite edges (4.00 m a

Question

2. Jane (55. o kg) and Tarzan (95.0 kg) are standing on opposite edges (4.00 m apart) of a merry-go- round and Cheetah (Tarzan's 25.0 kg pet chimpanzee) is sitting at the edge of the The merry-go- round. The merry-go-round by itself has a moment of inertia of 225 kgm2 and a diameter of 4.00 m The merry-go-round is rotating at a rate of 0.510 rev/s just before Tarzan gave Jane a lustful wink (which Jane misinterpreted) and they walked toward each other. They met near the center of the merry-go-round such that their centers of mass were each only 10.0 cm from the axis of rotation. What is the new rotational speed of the merry-go-round?rev/s What was the rotational kinetic energy of the system before Tarzan and Jane walked toward each other?J What was the kinetic energy of the system when they met near the center of the merry-go-round? where the energy came from. Tarzan then makes a boneheaded move and touches Jane in an inappropriate way. Jane slaps Tarzan, screams, and jumps (radially) backward so she is 1.00 m from the rotation axis. This startles Cheetah (even though he's used to Tarzan's stupid antics) and the chimp jumps (radially) off of the merry-go-round. What is the new (post-scream) rotational speed of the merry-go-round? J Are the energies different? If so, explain rev/s

Explanation / Answer

initial moment of inertia of system,

Ii = (225) + (55 x 4^2) + (95 x 4^2) + (25 x 4^2)

Ii = 225 + 880 + 1520 + 400

Ii = 3025 kg m^2

wi =0.510 rev/s

final moment of inertia. If = (225) + ((55 + 95)(0.10^2)) + 400

= 626.5 kg m^2

Applying angular momentum conservation for the system,

Ii wi = If wf

wf = 2.46 rev/s ..........Ans

Ki = Ii wi^2 /2  

{ wi = 0.510 rev/s = 0.510 x 2pi rad/s = 3.20 rad/s }

Ki = 15531 J .......Ans

Kf = If wf^2 / 2

( wf = 2.46 x 2pi = 15.5 rad/s )

Kf = 74838 J ......Ans

yes. Energy are different. Energy comes from work done by Jane and tarzan while walking on merry - go o round.

If = 225 + (95 x 0.10^2 ) + (55 x 1^2) = 280.95 kg m^2

angular momentum conservation,

3025 x 0.510 = 280.95 wf

wf = 5.50 rev/s ........Ans

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