The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as  L' = L sqrt 1 - (v2/c2)   1 −  v2 c2 ,  where L is the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 71 percent of the speed of light?

A spaceship leaves the solar system at v = (3/5)c and is headed towards a planet that is 20 c • years away (c is the speed of light). Assume the following: the Sun and the planet are mutually at rest and their clocks have been synchronized such that both read zero when the spaceship leaves. What should the clock on the planet read at the moment when the spaceship arrives?

Our universe has properties that are determined by thevalues of the fundamental physical constants, and it would be a muchdifferent place if the charge of the electron, the mass of the proton, orthe speed of light was substantially different from its actual value. Forinstance, the speed of light is so great that the effects of relativity usuallygo unnoticed in everyday events. Let’s imagine an alternate universewhere the speed of light is 1,000,000 times less than it is in ouruniverse to see what would happen. If the airplane of Passage Problem 37.71 has a rest mass of 20,000 kg, what is its relativistic mass when the plane is moving at 180 m/s ? (a) 8000 kg; (b) 12,000 kg; (c) 16,000 kg; (d) 25,000 kg; (e) 33,300 kg.

Our universe has properties that are determined by thevalues of the fundamental physical constants, and it would be a muchdifferent place if the charge of the electron, the mass of the proton, orthe speed of light was substantially different from its actual value. Forinstance, the speed of light is so great that the effects of relativity usuallygo unnoticed in everyday events. Let’s imagine an alternate universewhere the speed of light is 1,000,000 times less than it is in ouruniverse to see what would happen. In our universe, the rest energy of an electron is approximately 8.2 * 10-14 J. What would it be in the alternate universe? (a) 8.2 * 10-8 J; (b) 8.2 * 10-26 J; (c) 8.2 * 10-2 J; (d) 0.82 J.

A particle has a lifetime, as measured in its own reference frame, of 2.86 µs. It propagates at a speed of 0.933c. How far does it go before disintegrating? Express your answer in meters and keep three significant digits.

A beam of particles travels by at 2.0*10^8. At this speed you measure them to live 5.00* 10^6  sec, before decaying. What is the particle's life time at rest?

A particle accelerator is three kilometers long and accelerates electrons ( mass of electron = 9.11 × 10−31kg) to a speed of 0.9999999997c, which is very close to the speed of light.  Find the magnitude of the relativistic momentum of the electrons. Compar-ing it with the nonrelativistic value, is it bigger, smaller? By what factor?

In our inertial reference frame, we see a particle accelerating with a velocity   dx/dt = ( 1 - e-gt )1/2 in units where c = 1 (speed of light)  When we watch the particle's trajectory from t=0 to t=T, how much time passes in the particle's non inertial frame? Now express the answer such that T and the time have units of seconds instead of meters What's the 4-velocity in units c=1?

a) Given a = (7, −6, 4) and b = (3, 8, −1), find a ·b and a ×b.b) A (100 m) long spaceship is travelling at 90% the speed of light. How long is the spaceship as measuredby a stationary observer?

The length of a moving spaceship is 29.8 m according to an astronaut on the spaceship. If the spaceship is contracted by 16.3 cm according to an Earth observer, what is the speed of the spaceship? (answer in c, speed of light)