Stars and Galaxies – Relative Motion & Twin Paradox Lab

I have attached the lab, 8 questions. Need it done by the end of the night (Central Time).

  

Message me if you can do it!

Summer 2010
Name: ______________________________

Relative Motion and Twin Paradox

Part I

Bob is on a train that is traveling at 100 miles/hr.

1. Tim stands on the ground. Bob throws a ball at 5 miles/hr in the same direction as the train. What is the speed of the ball according to Tim?

[Type answer here]

2. Now Bob throws the ball at 5 miles/hr in the opposite direction. What does Tim see the speed of the ball to be?

[Type answer here]

3. Tim stands on another train that is moving in the same direction as Bob at 90 miles/hr. How fast is Bob moving according to Tim?

[Type answer here]

4. Now Tim stands on another train that is moving in the opposite direction as Bob at 90 miles/hr. How fast is Bob moving according to Tim?

[Type answer here]

Part II

The twin paradox is an interesting question that arises with the special theory of relativity. Consider the following scenario.

Bob and Tim are twins. Bob blasts away and travels to a distant galaxy with a speed of 3/5c and back. Tim, who stayed behind, has aged 10 years. Because of time dilation, Bob experienced a slowing time, so he will be younger. But Bob claims, since motion is relative, it is Tim who has left him and then returned. So Bob says it is Tim who is younger. Who is right? Let’s look at this paradox.

According to Tim, Bob traveled 10 years at 3/5c to a nearby galaxy and back.

Hint: See Mathematical Insight S2.1 and S2.2 on pages 416 – 417 in the 6th edition (pages 434-435 and 438-439 in the 5th edition)

5. Relative to Tim, how many years did Bob age?

[Type answer here]

6. According to Tim, how far (distance) did Bob go?

[Type answer here]

7. How far does Bob think he traveled?

[Type answer here]

According to Bob, he is the rest frame and Tim blasts away at 3/5c for 4 years.

8. When Bob has aged 4 years, how many years has Tim aged according to Bob?

[Type answer here]

Explanation: Now, as Bob is coming back, there is a change of reference frame. This change of reference frame is the key to understanding the paradox. Since Tim has always stayed in the same inertial frame in this first version (Tim stayed at rest), we must keep Tim in the same inertial frame in the second version too. So Tim must keep moving in the same direction with 3/5c speed. Now, in order for Bob and Tim to meet again, Bob now must change speed and catch up on Tim. He must zoom off with 15/17c speed. So on this trip, Bob is traveling much faster than Tim. Bob would again age much less than Tim. As it turns out, he needs 4 years to catch up on Tim if we assume Tim aged 10 years. So Bob again aged 8 years.

Another way to express this is such: there is no frame of reference UNTIL someone changes their acceleration (because accelerations require a direction). An acceleration is a change in speed and/or direction. Thus, in order for Bob to return to Earth, he must make a U-turn – an acceleration because he changed direction. (Tim remains on Earth the entire time, not moving and therefore not accelerating. This means Tim remained in the same frame of reference. Bob did not.)

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