A device consists of eight balls each of mass 0.5 kg attached to the ends of low
ID: 1468269 • Letter: A
Question
A device consists of eight balls each of mass 0.5 kg attached to the ends of low-mass spokes of length 1.2 m, so the radius of rotation of the balls is 0.6 m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.13 kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45 degrees to the horizontal. Just before the impact the clay has a speed 7 m/s, and the wheel is rotating counterclockwise with angular speed 0.21 radians/s.
(a) Which of the following statements are true about the device and the clay, for angular momentum relative to the axle of the device?
(0,0,.386)
(f) Qualitatively, what happens to the total kinetic energy of the combined system? Why?
Explanation / Answer
here,
mass of each ball , m = 0.5 kg
radius , r = 0.6 m
mass of the clay , mc = 0.13 kg
theta = 45 degree
initial speed ofclay , uc = 7 m/s
initial speed of device , w0 = 0.21 rad/s
(a)
using conservation of momentum
The angular momentum of the device + clay just after the collision is equal to the angular momentum of the device + clay just before the collision
(b)
the angular momentum of the combined system of device plus clay about the center C ,
L = (MI of device) *w0 + m*v*r( cos(45))
L = 8 * 0.5 * 0.6^2 *0.21 - 0.13 * 7 * 0.6 * cos(45)
L = - 0.0836 kg.m^2/s z
(c)
using conservation of momentum
the angular momentum of the combined system of device plus clay about the center C is same as before the impact i.e - 0.0836 kg.m^2/s
(d)
just after the impact angular speed of the device ,
w = L /MInew
w = 0.0836 /( 8 * 0.6^2 + 0.6 * 0.13)
w = 0.028 rad/s
the angular speed just after the impact is 0.028 m/s
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.