A large wooden turntable in the shape of a flat uniform disk has a radius of 2.0

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00 m and a total mass of 120 kg . The turntable is initially rotating at 3.00 rad/s about a vertical axis through its center. Suddenly, a 70.0-kg parachutist makes a soft landing on the turntable at a point near the outer edge.

a- Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.)

b- Compute the kinetic energy of the system before and after the parachutist lands.Why are these kinetic energies not equal?

Explanation / Answer

Let the final angular speed is W2

then from the law of conservation of angular momentum

I1 W1 = I2 W2

I1 W1 = (0.5 mR^2 + Mr^2) W2

I = 0.5 MR^2 , M is mass R is raidus

so

0.5 * 120 * 2^2 * 3 = ( 0.5 * 120 * 2^2 + 70 * 2^2) * wf

wf = 1.384 rad/s. thus the final angular speed is 1.384 rad/s

-----------------------------------------------------

b)KE = 0.5 I W^2

for the kinetic energy before the landing ,

kinetic energy = 0.5 * 0.5 * 120 * 2^2 * 3*3

kinetic energy = 1080 J

after ,

for the kinetic energ after the landing

kinetic energy = 0.5 * ( 0.5 * 120 * 2^2 + 70 * 2^2) * 1.384 ^2

kinetic energy = 498.01 J

as kinetic energy is lost due to collision, Energies are separated and lost in the form of heat and sound is produced

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.