Homework 16 Due Monday, May 3, 2004

  1. A spear 10 meters long is thrown at a relativistic speed through a pipe that is 10 meters long. Both these dimensions are measured when each is at rest. When the spear passes through the pipe, which of the following statements best describes what is observed by an observer in the rest frame of the pipe?

    This observer see the pipe as having a length of 10 m and the spear as beeing length contracted. He sees the spear as measuring less than 10 m. He sees the pipe covering the spear at some point.

  2. A spear 10 meters long is thrown at a relativistic speed through a pipe that is 10 meters long. Both these dimensions are measured when each is at rest. When the spear passes through the pipe, which of the following statements best describes what is observed by an observer moving in the direction of the spear at half the velocity of the spear (the velocity is measured wrt to pipe)?

    Consider this observer to be at rest. Then the spear is moving to the right towards this observer at v/2 and the pipe is moving to the left towards the observer at v/2. Both the pipe and the spear are length contracted. Both shrink equally so the pipe just covers the spear at some point in time.

  3. A spear 10 meters long is thrown at a relativistic speed through a pipe that is 10 meters long. Both these dimensions are measured when each is at rest. When the spear passes through the pipe, which of the following statements best describes what is observed by an observer moving with the spear?

    This observer measures the spear as 10 m and the pipe as length contracted. He says that the pipe shrinks so that the spear extends from both ends at some point in time.

  4. If you see a person traveling though space at half the speed of light, you will also see her clocks running

    Time is dilated by a factor of 1/square root of (1 - v2/c2). For v=c/2 this factor is 1/.86. Therefore the rate of clock ticking is .86 that of proper time. You see the time in the moving space ship as slower, but not slowed to half speed.