Exam 26: Space and Time

You and Al are both floating freely in your spaceships.Suppose Al is moving away from you at 85 km/hr.You throw a ball in his direction at a speed of 75 km/hr.According to Al,which of the following is going on?

In relativity,two people share the same reference frame only if what is true?

Process of Science: Devise an experiment you could conduct (using any technology you can dream up-it doesn't have to already exist)to test a prediction of special relativity.

The predictions of special relativity can sound implausible at first.What observational evidence do scientists have that the theory is correct?

Suppose you measure the density (mass per volume)of an object moving by you at very high speed.How will its density compare to the density it would have at rest in your reference frame?

You can see a clock in a spaceship moving past you at 90% of the speed of light.According to you,how much time would pass while the clock in the spaceship ticked through one minute?

According to Gwen back on Earth,about how long does it take Jackie to reach Vega?

Suppose a supersonic airplane flies at a speed of 1,650 km/hr from Nairobi,Kenya,to Quito,Ecuador;note that this is the same speed that Earth rotates,but in the opposite direction.Describe how this flight would look to an observer on the Moon.

You are racing away from Earth in a super space ship in which you can continually increase your speed by firing engines that never quit.Which of the following best explains how people on Earth will perceive your speed?

A clever student decides to spend time cruising around the local solar neighborhood at a speed of 0.95c (95 percent of the speed of light).How much time will pass on her spacecraft during a period in which 70 years pass on Earth?

Sue is traveling toward you at 90 km/hr.She throws a baseball that,according to her,is going at 90 km/hr in the opposite direction.What do you see the ball doing?

The lifetime of a π⁺ meson normally is 18 nanoseconds.In a large particle accelerator,scientists can create π⁺ mesons moving at speeds very close to the speed of light.What do the scientists observe when they measure the lifetime of a π⁺ meson that is created at very high speed?

How would the passengers on the spaceship view our clocks?

Which of the following is not a prediction made by the theory of relativity?

Recall that a π⁺ meson produced at rest has a lifetime of 18 billionths of a second.Thus,in its own reference frame,a π⁺ meson will always "think" it is at rest and therefore decay after 18 billionths of a second (1.8 × 10⁻⁸ s).Suppose a π⁺ meson is produced in a particle accelerator traveling at 0.998c. a.According to scientists in the lab,how long will the π⁺ meson last compared to its normal lifetime of 18 billionths of a second (e.g. ,shorter,the same,or longer)? b.Recall that the time dilation formula is: $t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}}$ 0 where t is the time in the laboratory and is the time for the moving particle.Use the time dilation formula to calculate how long scientists will see the π⁺ meson last before it decays.

Process of Science: The theory of special relativity is one of the most tested theories in physics and has now been completely proven beyond all doubt.

You take a trip to a star located 1,000 light-years away and return.You travel at an average speed of 0.99c. HINT: The time dilation formula is: $t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}}$ -About how long will the trip take,according to you?

Kim is in a spaceship moving past you at half the speed of light.Which of the following correctly describes how you will perceive each other's time?

What do we mean by time dilation in relativity?

A sprinter named Ben has challenged a beam of light to a race in the 100-meter dash.The race is held in a stadium full of spectators.At the start signal,a laser beam is turned on at the start line,pointed down the track.At the same instant,Ben bursts out of the starting blocks at 99% of the speed of light (0.99c).According to the spectators watching in the stands,what happens? (Assume they could somehow watch a slow-motion replay to see what occurred. )