Exam 27: Relativity

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

If the kinetic energy of a proton is 80% of its total energy, what is the speed of the proton?

As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes $10.5 \mathrm { y }$ 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?

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?

How many MeV of energy is released during a reaction in which 1.67 × 10^-25 kg of material is converted to energy? (c = 3.0 × 10⁸ m/s, 1 eV = 1.67 × 10^-19 J)

Which of the following are basic postulates of special relativity? (There could be more than one correct choice.)

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

Two spaceships are traveling through space at speeds of 0.600c and 0.900c, respectively, with respect to Earth. If they are headed directly toward each other, what is their approach speed (in terms of the speed of light) as measured by the captain of either ship?

In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is $0.543 c$ to the right (both as measured in the lab rest frame), how fast are the particles moving with respect to each other?

A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s)

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?

A starship is constructed to be 100 m long in the factory. It is launched and as it coasts by Earth, it is measured to be shortened to 5.48 m long. (a) How fast, in terms of the speed of light, is it moving past Earth? (b) What length does the ship's crew measure for the ship?

A 1.0-kg aluminum ingot is heated from 0°C to 100°C. By what amount does its mass change? The specific heat of aluminum is 900 J/kg ∙ K. (c = 3.0 × 10⁸ m/s)

You are moving past the Earth at 0.990c and notice your heart beating 88 beats per minute. (a) If a doctor on Earth measures your heart rate as you zip past, what will the measured rate be? (b) If you had been moving 99.99% the speed of light, what rate would you have observed your heart beats?

A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to the ship. Relative to Earth, what is the speed of this missile?

When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer?

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

If the kinetic energy of a particle is 3.00 times its rest energy, the speed of the particle is closest to which of the following values?

If an electron in the lab has a kinetic energy equal to twice its rest energy, what is its speed in the lab?

A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top, 300 m above ground level. By what amount does its mass change? (c = 3.00 × 10⁸ m/s)