A device consists of cight balls cach of mass 0.6 kg attached to the ends of low

Question

A device consists of cight balls cach of mass 0.6 kg attached to the ends of low-mass spokes of length 1.4 m, so the radius of rotation of the balls is 0.7 m. The device is mounted in the vertical plane. The axle is held up by supprts that are not showrn, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.12 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 5 m/s, and the wheel is rotating counterclockwise with angular speed 0.08 radians/s. (a) Which of the following statements are true about the device and the clay, for angular momentu relative to the axle of the device? he angular momentum of the fallin clay is zero because the clay is moving in a straight line. The angular momentum of the device i clay just after the collision is equal to the angular momentum of the device·clayjust before the collision Just before the collision the angular momentum of the wheel is The angular momentum of the device is the sum of the angular momenta of all eight balls. The angular momentum of the device is the same betore and after the collision. b) Just before the impact, what is the angular momentum of the combined system of device plus clay a outt e center As us a is to e rcht.·is uo ard z s out of he screen to a rod kg mis (c) Just after the impact, what is the angular mornentum of the combined system of device plus clay about the center C? (d))ust after the impact, what is the angular velocity of the device? radians/s

Explanation / Answer

(A) The angular momentum of the device + clay just after the collision is equalto the angular momentum of the device+clay just beofre the collision.

And The angular momentum of device is the sume of angular momenta of all eight balls.

(b) Li = Iw + m v r sin45

= (8 x 0.6 x 0.7^2)(0.08) + (0.12 x 0.7 x - 5 x sin45)

= - 0.109 kg m^2/ s

angular momentum is 0.109 kg m^2/s in clockwise direction.

(c) it will be same = 0.109 kg m^2/ s clockwise

Or - 0.109 kg m^2 /s

(d) Lf = (8 x 0.6 x 0.7^2 + 0.12 x 0.7^2) w = - 0.109

w = -0.045 rad/s

Or 0.045 rad/s clockwise

(e) linear momentum decrease becaise the exle exerts up upward force.

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

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