Homework 15 Due Friday, April 30, 2004

  1. A person riding on the roof of a freight-train car fires a gun pointed forward. Compare the velocity of the bullet with respect to the ground when the train is at rest to that when the train is moving.

    2. The velocity of the bullet wrt the ground is greater when the train is moving.

  2. Suppose, instead, that the person riding on top of the frieght car shines a searchlight beam in the direction in which the train is traveling. Does the light beam travel faster with respect to the ground than it would is she had shone it while standing at rest on the ground? Explain.

    3. The velocity of light is the same for both cases. One of the postualtes of relativity is that every observer measures the same value for the speed of light.

  3. If you were in a rocket ship traveling away from the earth at a speed close to the speed of light, what changes would you note in your pulse? Explain.

    4. None. The pulses measured by all identical observers in their own frames is the same. It's only when you are looking at a person moving away from you that you detect their pulse as slow.

  4. If you were on earth monitoring a person in a rocket ship traveling away from the earth at a speed close to the speed of light, what changes would you note in his pulse? Explain.

    You would see his pulse as slow. This is due to the relativistic Deppler effect which incorporates the Doppler effect and time dilation.

  5. Sally flies past Martin in her spaceship at nearly the speed of light. According to Martin, Sally's clock runs slow. According to Sally, does Martin's clock run slow, fast, or at the normal rate? Explain.

    She sees Martin's clock running slow. Martin thinks that he is stationary and that Sally is receding from him. The relativistic Doppler effect then says that Sally's clock runs slow. According to Sally, she is stationary and Martin is receding from her. So she sees Martin's clock running slowly.

  6. In relativity we find that "moving clocks run slow," but this effect does not occur because the motion alters the way a clock works. Why does it occur? What does it mean to say that "moving clocks run slow"?

     Consider two events that occur in one frame at two different times but at the same point in space. A person moving wrt this frame sees the light arriving from these two events at two different times. But due to the finite speed of light, this second observer see the time between these events as longer than the time measured in the first frame. This is what we mean by "moving clocks run slow.