10.6 Collisions of Extended Bodies in Two Dimensions

10.6 Collisions of Extended Bodies in Two Dimensions

  • The bowling pins are sent flying and spinning when hit by a bowling ball.
    • A lot of collisions involve inertia.
    • Cars can spin on ice or a wet surface.
    • Baseball pitchers put spin on the ball.
    • A tennis player can put a lot of top spin on the tennis ball which causes it to dive down onto the court once it crosses the net.
    • We are looking at what happens when objects collide.
  • There is an unbalanced force at the nail.
    • The lever arm is zero so this force doesn't exert any Torque.
    • In the collision, the momentum is conserved.
    • The collision is inelastic.
    • The force at the nail may have a part in the direction of the disk's initial velocity.
  • The pins spin violently when the bowling ball hits them.
    • The surface is not elastic and the unbalanced force at the nail does not exert any Torque.
  • The first question can be answered using the concept of angular momentum.
    • We can solve for the difference between the two.
  • The primed quantities are calculated relative to the pivot point.
    • The disk just before it strikes the stick is the initial inertia of the stick-disk.
  • Before and after the collision, the incoming disk's translational and rotational energy are the same.
  • The first step is to enter the mass and speed of the disk.
  • The final moment of inertia and the final angle of rotation can be found after the collision.
  • The disk has a linear momentum before the collision.
    • The sum of the disk's momentum and the center of mass of the stick is what is left after the collision.
  • The stick's center of mass moves at half the speed of the disk because of the total linear momentum.
  • The collision is inelastic, so the energy after the collision is less.
    • The momentum after the collision is greater than before.
    • The result can be understood if you consider how the nail affects the stick.
    • When the disk strikes the nail, the stick pushes backwards on the nail.
    • The nail's reaction is to push forward on the stick, in the same direction as the disk was initially moving, in order to increase the system's momentum.
  • There are other implications of the above example.
    • The force would be applied to the nail in the forward direction.
    • When the stick is struck at the end farthest from the nail, a backward force is put on the nail, and when it is hit at the end nearest the nail, a forward force is put on the nail.
    • There is no force on the nail when striking it at a certain point.
    • The percussion point is an intermediate point.
  • The handle is pulled away from your hand if you hit a ball with the end of your racquet.
    • The handle is pushed into your palm if you hit a ball much farther down.
    • If you hit the ball at the racquet's percussion point, little or no force is exerted on your hand, and there is less vibration, reducing chances of a tennis elbow.
    • The same thing happens to a baseball bat.
  • A disk hitting a stick is similar to a tennis ball hitting a racquet.
  • Justify your answer.
  • Whether motion is involved or not, energy is always scalar.