A device consists of eight balls each of mass 0.5 kg attached to the ends of low

Question

A device consists of eight balls each of mass 0.5 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 5 m/s, and the wheel is rotating counterclockwise with angular speed 0.07 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 falling clay is zero because the clay is moving in a straight line. 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 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 is the same before and after the collision. (b) Just before the impact, what is the angular momentum of the combined system of device plus clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen, toward you.) (c) Just after the impact, what is the angular momentum of the combined system of device plus clay about the center (d) Just after the impact, what is the angular velocity of the device? (e) Qualitatively, what happens to the total linear momentum of the combined system? Why? Some of the linear momentum is changed into angular momentum. There is no change because linear momentum is always conserved. Some of the linear momentum is changed into energy. The downward linear momentum decreases because the axle exerts an upward force. (f) Qualitatively, what happens to the total kinetic energy of the combined system? Why? Some of the kinetic energy is changed into angular momentum. 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.

Explanation / Answer

a)

True: The angular momentum of the device and clay system just after the collision is equal to the angular momentum of the device and clay system just before the collision

True: The angular momentum of the device is the sum of the angular momenta of all eight balls.

b)

Clay: Translational angular momentum is prsin(). p is <0, -0.65, 0>. rsin() Since the clay is falling down on the ball, it would cause it to rotate in the clockwise direction. Therefore, the angular momentum of the clay is into the page or in the -z direction. So, we get <0, 0, -0.735>

we take the angular momentum of 1 ball and multiply by 8. One ball attached by a massless rod has a moment of inertia of mr2. In this case, m=0.5kg and r=1.6m. So I=1.28. =.07, so the angular momentum of one ball is 0.0896. Multiply by eight balls and we have 2.646. Since the device rotates in the counterclockwise direction, it has angular momentum out of the page or in the +z direction. Therefore, the angular momentum is <0, 0, 0.7168>.

e)

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

f)

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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