As you saw in tutorial, observers measure their own units for time and space dif

Question

As you saw in tutorial, observers measure their own units for time and space differently than the units in a different frame. a. Suppose observer 1 measures a speed v = dx/dt in their frame. Would an observer in a different frame measure the same speed? Explain your reasoning. b. Suppose observer 1 measures a charge density lambda = Q/L in their frame. Would an observer in a different frame measure a greater charge density, lesser charge density, or equal charge density? c. List three other observables for which different observers would measure different values. A game of relativistic soccer is played in space. All players are in rockets that travel at c/4, and all players can kick the ball at c/2 in their frame. A player is travelling straight up, and when they are parallel with the goal they kick the ball straight toward the center of the goal. a. In the player's frame, in which direction relative to the x'-axis should they kick the ball. b In the frame of the goal, the velocity of the ball is purely in the x-direction. How fast is the ball traveling in the goal's frame? c. Suppose all the players sped up to c/2. Would players have to be more accurate or less accurate with their kicks?

Explanation / Answer

a.

No speed v will be different if the observers are themselves moving at relativistic speeds, will be given by Einstein's velocity addition theorem.

b.

This depends on the speed of second observer, The length appears to contract, so the length charge can be longer ,shorter, of same length, if speed of second observer is less, more, equal to observer one.

c.

Clocks slow down on moving at relativistic speeds.

Mass of a paricle moving at relativistic speeds also increases with increase in speed.

Momentum of a moving stick is dependent on frame of refrence.

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