Relativistic time dilation & length contraction

A person moving parallel to a 2.00 m ruler observes the change in length of this ruler due to relativity to be 0.50 m. What speed are they travelling?

• 0.1c

• 0.43c

• 0.66c

• 0.9c

A train with rest length 100 m is travelling towards a railway platform with length of 50 m. What speed must the train be travelling for train and the platform to be the same length when viewed by an observer standing on the platform?

• 0.64c

• 0.87c

• 0.6c

• 0.9c

At what speed will an electron’s relativistic momentum be exactly 1.5 times its Newtonian momentum?

• 0.5c

• 0.87c

• 0.75c

• 0.6c

Two spacecraft, Castor and Pollux travel in opposite directions as shown. Castor travels at a speed of 0.6c and Pollux travels at a speed of 0.4c. Both are travelling relative to the fixed stars of the galaxy. A radio signal from Castor reaches Pollux 0.0100 s after it was emitted by Castor, measured in the frame of Castor.

According to the navigator of Castor, who is correctly using special relativity, how far did the radio signal travel between leaving Castor and reaching Pollux?

• 1500 km

• 3000 km

• 300 km

• 4500 km

A spacecraft travels at a speed 0.70c relative to the nearest stars. It approaches a space rock that is stationary relative to the nearest stars, as shown. A landing strip on the space rock is 200 m in the rock’s frame of reference.

What is the length of this landing area as measured by instruments on the spacecraft?

• 286 m

• 143 m

• 190 m

• 135 m

A spacecraft travels at a speed 0.70c relative to the nearest stars. It approaches a space rock that is stationary relative to the nearest stars, as shown. A landing strip on the space rock is 200 m in the rock’s frame of reference.

Attached to the spacecraft is a measuring probe. The spacecraft releases the probe so that it will land on the space rock. Near touchdown, the probe is at the same velocity as the space rock. Which one is able to measure the proper length of the landing area?

• The spacecraft at the instant it passes by the landing area on the rock.

• The probe when it is travelling at the same velocity as the space rock.

• The spacecraft because it has far more accurate radar instruments than the probe.

• A radar pulse from the spacecraft because the pulse will momentarily be stationary when it reflects off the landing area.

A spacecraft is fitted with a special clock consisting of two mirrors between which a pulse of light is repeatedly reflected, as shown. The proper length between the two mirrors is 5.0 m. The astronaut in the spaceship measures the clock’s period while the spacecraft is stationary in the inertial frame of our galaxy. She then measures its period from inside the spacecraft while it is moving at a constant velocity of 0.60c, relative to the galaxy’s frame of reference.

Which one of the following statements about the period of the clock, as measured by the astronaut in the moving spacecraft, is true?

• The period is the same as when the spacecraft was stationary in our galaxy’s inertial frame.

• The period is greater than when the spacecraft was stationary in our galaxy’s inertial frame.

• The period depends on the particular details of the clock mechanism.

• The period is smaller than when the spacecraft was stationary in our galaxy’s inertial frame.

A spacecraft is fitted with a special clock consisting of two mirrors between which a pulse of light is repeatedly reflected, as shown. The proper length between the two mirrors is 5.0 m. The astronaut in the spaceship measures the clock’s period while the spacecraft is stationary in the inertial frame of our galaxy. She then measures its period from inside the spacecraft while it is moving at a constant velocity of 0.60c, relative to the galaxy’s frame of reference.

According to an observer in the frame of our galaxy, the distance between the mirrors is closest to:

• 6.25 m

• 4.00 m

• 12.5 m

• 8.0 m

A spacecraft is fitted with a special clock consisting of two mirrors between which a pulse of light is repeatedly reflected, as shown. The proper length between the two mirrors is 5.0 m. The astronaut in the spaceship measures the clock’s period while the spacecraft is stationary in the inertial frame of our galaxy. She then measures its period from inside the spacecraft while it is moving at a constant velocity of 0.60c, relative to the galaxy’s frame of reference. One period of this clock is the time taken for light to travel from A to B (tick) and back to A (tock).

According to an observer in the frame of our galaxy, the period of this clock is closest to:

• 33ns

• 20 ns

• 16 ns

• 42 ns

Tags

NGSS.HS-PS4-1

Which of the following is one of the two key postulates of Einstein’s special theory of relativity, expressed correctly?

• E = mc²

• The laws of physics are the same in all inertial frames of reference.

• All inertial observers obtain the same result when measuring the time and position of an event.

• Nothing can travel faster than the speed of light.