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group Small Group Activity

30 min.

Mass is not Conserved

energy conservation mass conservation collision

Groups are asked to analyze the following standard problem:

Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?

assignment Homework

Hockey

Consider the frictionless motion of a hockey puck of mass \(m\) on a perfectly circular bowl-shaped ice rink with radius \(a\). The central region of the bowl (\(r < 0.8a\)) is perfectly flat and the sides of the ice bowl smoothly rise to a height \(h\) at \(r = a\).

  1. Draw a sketch of the potential energy for this system. Set the zero of potential energy at the top of the sides of the bowl.
  2. Situation 1: the puck is initially moving radially outward from the exact center of the rink. What minimum velocity does the puck need to escape the rink?
  3. Situation 2: a stationary puck, at a distance \(\frac{a}{2}\) from the center of the rink, is hit in such a way that it's initial velocity \(\vec v_0\) is perpendicular to its position vector as measured from the center of the rink. What is the total energy of the puck immediately after it is struck?
  4. In situation 2, what is the angular momentum of the puck immediately after it is struck?
  5. Draw a sketch of the effective potential for situation 2.
  6. In situation 2, for what minimum value of \(\vec v_0\) does the puck just escape the rink?

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