Free Printable Spacetime & Lorentz Transformations

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Spacetime & Lorentz Transformations

Total questions: 20

Worksheet time: 12mins

Name

Class

Date

There are two clocks one is stationary on the earth the other is traveling close to the speed of light around the earth. If we put the clocks back together after the second clock makes it back from its trip, the times are compared. What do you expect to occur?

More time elapsed on the stationary clock

More time elapsed on the traveling clock

No time has changed between them

We do not usually observe relativistic effects in our daily lives because

we are moving at speeds much less than c.

we are much larger than atoms.

we are much heavier than elementary particles.

we are much lighter than stars.

If you travel at the speed of light a second can be observed to last forever.

True

False

One of the most startling consequences of time dilation is that a moving clock ______________ relative to a stationary observer.

Speeds up

Slows down

The relativistic expression for length contraction of an object moving at velocity v is

$L=L_0\sqrt{1-\frac{v^2}{c^2}}$

$L=\frac{L_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$L\ =\ L_0\sqrt{1-\frac{c^2}{v^2}}$

$L=\frac{L_0}{\sqrt{1-\frac{c^2}{v^2}}}$

A particle with a lifetime of 2.0 × 10^–6 s moves through the laboratory with a speed of 0.9 c. Its lifetime, as measured by an observer in the laboratory, is

2.0 × 10^–6 s

3.2 × 10^–6 s

4.6 × 10^–6 s

5.4 × 10^–6 s

6.3 × 106–6 s

A train has a rest length of 100 m. Traveling at a very high velocity, it goes through a tunnel of length 80 m. Observers located at both ends of the tunnel note that at one instant the train appears to exactly fit within the tunnel.

What is the velocity of the train expressed in units of c?

0.333 c

0.50 c

0.60 c

0.80 c

0.866c

How fast does a rocket have to move relative to an observer for its length to be contracted to 95% of its original length?

0.2 c

0.3 c

0.4 c

0.5 c

A Klingon spaceship is approaching Earth at approximately 0.8 c measured relative to Earth. The spaceship directs a laser beam forward directly through your physics classroom window.

You measure the speed of this light to be:

1.8 c

1.0 c

0.9 c

0.8 c

0.2 c

10.

What does the relativity of simultaneity say?

Two events may occur at the same time in one reference frame, but not another.

If two events occur at the same time in one reference frame, they will occur at the same time in all reference frames.

11.

An object moving at a relativistic speed past a stationary observer appears to

have length expanded and have a faster clock

have length contracted and have a slower clock

have length contracted and have a faster clock

have length expanded and have a slower clock

12.

If you were to travel at a speed close to the speed of light, you would notice which of the following?

Your mass has increased.

Your pulse rate has decreased.

Your ship has contracted

You would notice none of these effects because you are in an inertial frame.

13.

The animation depicts a...

Galilean Transformation

Lorentz Transformation

14.

The animation depicts a...

Galilean Transformation

Lorentz Transformation

15.

Given the info in the diagram, find the coordinates of the spacetime event at the dot relative to the rest frame.

$(x,\ ct)=(5,\ 7.2)$

$(x,\ ct)=(3,\ 6)$

$(x,\ ct)=(6,\ 3)$

$(x,\ ct)=(6.3,\ 2.9)$

16.

The half-life of a muon is 2.2 µs. How fast is it moving relative to an observer who says its half-life is 4.4 µs?

0.87 c

0.75 c

0.97 c

0.72 c

17.

A clock moves along the x-axis in your reference frame at a speed of 0.80c and reads zero as it passes the origin. What time does it read as it passes the 180 meter mark on this axis?

2.22 micro-seconds

0.90 micro-seconds

0.45 micro-seconds

18.

A 520 m long (measured when the spaceship is stationary) spaceship passes by the Earth. What length would the people on Earth say the spaceship was as it passed the Earth at 0.87c?

256 m

1056 m

452 m

67 m

19.

A stationary observer on Earth observes spaceships A and B moving in the same direction toward the Earth. Spaceship A has speed 0.5c and spaceship B has speed 0.80c.

Determine the velocity of spaceship A as measured by an observer at rest in spaceship B.

0.5c

0.3c

1.3c

20.

Two spaceships approach each other, each moving with the same speed as measured by a stationary observer on the Earth. Their relative speed is 0.70c.

Determine the speed of each spaceship as measured by the stationary observer on Earth.

Both move at a speed of 0.41c in Earth's frame.

Both move at a speed of 0.7c in Earth's frame.

Both move at a speed of 1.4c in Earth's frame.

Both move at a speed of 0.29c in Earth's frame.

100 %

Spacetime & Lorentz Transformations

Total questions: 20

Worksheet time: 12mins

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