A device consists of eight balls each of mass 0.4 kg attached to the ends of low

Question

A device consists of eight balls each of mass 0.4 kg attached to the ends of low-mass spokes of length 1.6 m, so the radius of rotation of the balls is 0.8 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 8 m/s, and the wheel is rotating counterclockwise with angular speed 0.17 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?

The angular momentum of the device is the sum of the angular momenta of all eight balls. Just before the collision the angular momentum of the wheel is 0. 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. The angular momentum of the falling clay is zero because the clay is moving in a straight line. The angular momentum of the device is the same before and after the collision.

Some of the linear momentum is changed into angular momentum.

Some of the linear momentum is changed into energy.    

The downward linear momentum decreases because the axle exerts an upward force.

There is no change because linear momentum is always conserved.

(f) Qualitatively, what happens to the total kinetic energy of the combined system? Why?

The total kinetic energy decreases because there is an increase of thermal energy in this inelastic collision.

Some of the kinetic energy is changed into linear momentum.    

There is no change because kinetic energy is always conserved.

Some of the kinetic energy is changed into angular momentum.

Explanation / Answer

(A) the angular momentum of rge device +clay just after the collision is equal to the angular momentum of device + clay just after the collision.

(B) Li = (Ii wi) - ( m v r cos45)

= (8 x 0.4 x 0.8^2)(0.17) - (0.13 x 8 x 0.8 x cos45)

= - 0.24 kg m^2 /s

(C) Lf = - 0.24

(D) - 0.24 = (8 x 0.4 x 0.8^2 + 0.13 x 0.8^2) w

w = - 0.113 rad/s

(e) The downward linear momentum decreases because the axle exerts an upward force.

(f) the total kinetic energy decreases because there is an increase of thermal energy in this inelastic collision.

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