Exam 26: The Special Theory of Relativity

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

The figure shows a right-angled construction frame $A B C$ . When measured at rest, it has dimensions as follows: $A B = 18.9 \mathrm {~m} , A C = 10.0 \mathrm {~m}$ , and $B C = 16.0 \mathrm {~m}$ . This frame is now given a new velocity of $0.420$ c, relative to Earth, in a direction parallel to $A C$ . How long is part $B C$ of this frame with the new velocity as measured by Earth-based engineers?

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space. The satellites collide And somehow manage to stick together. What is the rest mass of the combined object after the Collision?

How many MeV of energy is released during a reaction in which $1.67 \times 10 ^ { - 25 } \mathrm {~kg}$ of material is converted to energy? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.67 \times 10 ^ { - 19 } \mathrm {~J} \right)$

Two stars are at rest relative to each other. In their common rest frame, these stars are 90.0 light-years apart. If they are measured to be 68.7 light-years apart by the navigator of a spaceship Traveling between them, how fast is the spaceship moving relative to these stars?

An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? $( c = 3.00 \times$ $10 ^ { 8 } \mathrm {~m} / \mathrm { s } _ { 1 } e = 1.60 \times 10 ^ { - 19 } \mathrm { C }$ )

The energy released by a certain reaction is enough to totally evaporate $125 \mathrm {~kg}$ of water at its boiling point. How much mass was lost during this reaction? $\left( L _ { F } = 334,000 \mathrm {~J} / \mathrm { kg } \right.$ for water, $c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )

Consider a student whose mass is $70 \mathrm {~kg}$ . If all his mass were converted to electrical energy, for how many years could he keep a $100 - \mathrm { W }$ light bulb burning? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

One of the first atomic bombs released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy by this explosion, given that 1000 tons of TNT produce $4.3 \times 10 ^ { 12 } \mathrm {~J}$ of energy. Incidentally, modern $\mathrm { H }$ -bombs have energy yields 1000 times as much! $( c = 3.0 \times 10^8 \mathrm {~m} / \mathrm { s } )$

One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that

A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction. With what speed does an observer on Earth measure for the light pulse?

If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A muon at rest decays in $2.2 \mu$ s. Moving at $99.00 \%$ the speed of light, it would be seen to "live" for how long?

What is the momentum of a proton when it is moving with a speed of $0.60 c$ ?

The relativistic kinetic energy formula is valid

A pion is an unstable particle that has a mean lifetime of $2.55 \times 10 ^ { - 8 } \mathrm {~s}$ . This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An average pion is traveling at $0.230 \mathrm { c }$ relative to Earth. How far does it travel in its lifetime, relative to Earth?

Calculate the speed at which a $0.723 - \mathrm { kg }$ object has the same momentum as a $1.30 - \mathrm { kg }$ object that is moving $0.515 \mathrm { c }$ .

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. They have identical speeds of 0.600c. The satellites collide and somehow manage to stick together. What Is the rest mass of the combined object after the collision?

At age 21, you set out for a star that is 50 light-years from Earth. How fast would your spaceship have to travel in order to reach that star when you are 61 years old? One light-year is the distance light travels in one year.

Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, with equal speeds relative to Earth. As measured by a passenger in one of the spaceships, the other Spaceship is 96 m long. What is the speed of the spaceships relative to Earth?