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Problem 59

Calculate the Schwarzschild radius of a black hole with the mass of a) the Sun. b) a proton. How does this result compare with the size scale 1015 m usually associated with a proton?

Problem 63

Using relativistic expressions, compare the momentum of two electrons, one moving at 2.00108 m/s and the other moving at 2.00103 m/s. What is the percentage difference between classical momentum values and these values?

Problem 64

Rocket A passes Earth at a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A?

Problem 67

The explosive yield of the atomic bomb dropped on Hiroshima near the end of World War II was approximately 15.0 kilotons of TNT. One kiloton is about 4.181012 J of energy. Find the amount of mass that was converted into energy in this bomb.

Problem 68

At what speed will the length of a meter stick look 90.0 cm?

Problem 69

What is the relative speed between two objects approaching each other head on, if each is traveling at speed of 0.600c as measured by an observer on Earth?

Problem 71

You shouldn't invoke time dilation due to your relative motion with respect to the rest of the world as an excuse for being late to class. While it is true that relative to those at rest in the classroom, your time runs more slowly, the difference is likely to be negligible. Suppose over the weekend you drove from your college in the Midwest to New York City and back, a round trip of 2200. miles, driving for 20.0 hours each direction. By what amount, at most, would your watch differ from your professor's watch?

Problem 72

A spaceship is traveling at two-thirds of the speed of light directly toward a stationary asteroid. If the spaceship turns on it headlights, what will be the speed of the light traveling from the spaceship to the asteroid as observed by a) someone on the spaceship? b) someone on the asteroid?

Problem 73

Two stationary space stations are separated by a distance of 100. light- years, as measured by someone on one of the space stations. A spaceship traveling at 0.950c relative to the space stations passes by one of the space stations heading directly toward the other one. How long will it take to reach the other space station, as measured by someone on the spaceship? How much time will have passed for a traveler on the spaceship as it travels from one space station to the other, as measured by someone on one of the space stations? Round the answers to the nearest year.

Problem 74

An electron is accelerated from rest through a potential of 1.0106 V. What is its final speed?

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