Exam 26: The Special Theory of Relativity

In a nuclear plant, $1017 \mathrm {~J}$ of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

How fast would a rocket ship have to move past Earth to contract to half of its proper length as observed by an Earth-based physicist?

Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific Instruments, including a meter stick. Now that Jill is underway, how long does she measure the Meter stick to be?

A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as Measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea?

A spaceship, traveling at 0.100c away from a stationary space platform, launches a secondary rocket towards the station, with a speed of 0.560c relative to the spaceship. What is the speed of the Secondary rocket relative to the space platform?

Astronaut Rachel leaves Earth in a spaceship at a speed of $0.960 c$ relative to an observer on Earth. Rachel's destination is a star system $14.4$ light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take?

A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of $190 \mathrm {~kg}$ and moves away with a speed $0.280 \mathrm { c }$ , and the second piece moves in the opposite direction with a speed $0.600 \mathrm { c }$ . What is the rest mass of the second piece?

How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m?

Two spaceships approach Earth from opposite directions. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A space barge pushes on a spaceship with a rest mass of $15,000 \mathrm {~kg}$ and accelerates it from a speed of $0.600 c$ to a speed of $0.700 \mathrm { c }$ . How much work does the barge have to do to accomplish this? $( c =$ $3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )

Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from him in opposite directions at 0.70c. At what speed would an Observer in Alpha see the galaxy Gamma moving?

How much energy would be required to accelerate a $77 - \mathrm { kg }$ professor from rest to $90 \%$ the speed of light? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on The ship?

Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star system 12.5 light-years away (one light-year is the distance light travels in one Year). According to Sarah, how far did she travel during the trip?

A spaceship visits a star that is $4.5$ light-years from Earth, and the spaceship travels at one-half the speed of light for the entire trip. (a) How long did the trip take according to an observer on Earth? (b) How long did the trip take according to an observer on the spaceship?

As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes 10.5 y to travel between two planets that are not moving relative to each other. How long does the trip take as measured by Someone on the spaceship?

A $1.00 - \mathrm { kg }$ gold ingot is carried from the bottom of the Eiffel tower to the top, $300 \mathrm {~m}$ above ground level. By what amount does its mass change? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long Did that advance take as measured by the observer on Earth?

According to the equation $E = m c ^ { 2 }$ an object turns into energy when it reaches the speed of light.

An electron has a relativistic momentum of $1.1 \times 10 ^ { - 21 } \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ . What percent of its total energy is its kinetic energy? ( $m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )