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← 07ps-11 Block Clock

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Showing Revision 1 created 10/27/2012 by Amara Bot.

  1. This next problem, we're going to construct a basic timing device
  2. using a block bouncing back and forth between two springs.
  3. Imagine that we have two springs here, each with a spring constant K,
  4. one attached to this wall over here and one attached to this wall over here.
  5. In the middle, we have a block that's freedom-bounce
  6. between the two of these over this friction less surface here.
  7. The separation between the two springs' equilibrium distance is 3 mm as shown here.
  8. Now, right in the middle of the 3 mm here is a little switch which connects to a timer over here,
  9. and every time the block moves over the switch in either direction,
  10. it sends a signal to the timer telling it that one second has passed.
  11. As an extra point of clarification, this switch is 1.5 m from either spring.
  12. I want you to tell me what does this initial velocity V₀ have to be
  13. such that every time the block passes over the switch here, a second has actually passed.
  14. In other words, we want to choose V₀ such that the time it takes the block
  15. to push up against the spring and bounce back to this same spot again will be one second exactly.
  16. You can put your answer over here in meters per second.
  17. Now there's one thing in particular that might trip you off with this problem.
  18. If you imagine that this block was attached to this spring,
  19. then the block would push against the spring in one-fourth of a period,
  20. return to the equilibrium position in half a period extend outwards in three-fourths of a period,
  21. and finally return to the equilibrium position once again after an entire period.
  22. But keep in mind that the block is not actually attached to the spring,
  23. This point, where the block extends outward
  24. and is pulled backwards by the spring actually never happens.
  25. In fact, the block loses contact with the spring at this point right here
  26. when it has maximum velocity at the equilibrium position.
  27. Keep that in mind when you're solving a problem. Good luck!