I need helpwith number 4,5, and 6 please. A person with mass m p = 74 kg stands
ID: 1568089 • Letter: I
Question
I need helpwith number 4,5, and 6 please.
A person with mass mp = 74 kg stands on a spinning platform disk with a radius of R = 2.28 m and mass md = 183 kg. The disk is initially spinning at = 1.8 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.76 m from the center).
1)What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?
the answer was : 860.33
2) What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk?
the answer was : 521.837
3) What is the final angular velocity of the disk?
the answer was : 2.96
4) What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.)
5) What is the centripetal acceleration of the person when she is at R/3?
6) If the person now walks back to the rim of the disk, what is the final angular speed of the disk?
Explanation / Answer
4)
here
initial KE1 = 0.5 * I * w^2
KE1 = 0.5 * 860.33 * 1.8^2
KE1 = 1393.73 J
final KE2 = 0.5 * If * wf^2
KE2 = 0.5 * 521.83 * 2.96^2
KE2 = 2286.03 J
then
delta KE = KE2 - KE1
delta KE = 2286.03 - 1393.73
delta KE = 892.3 J
5)
a = w^2 * r
a = 2.96^2 * 2.28/3
a = 6.65 m/s^2
6)
the final angular speed of the disk is
w = 1.8 rad/s