HPS 0410 Einstein for Everyone Spring 2015

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# Assignment 3: E = mc2

For submission

1. (a) What is the momentum of a body with a given mass and velocity?

(b) What happens in classical physics to a body when its momentum is increased?

(c) What happens in relativistic physics to a slowly moving body when its momentum in increased?

(d) What happens in relativistic physics to a very rapidly moving body when its momentum is increased?

2. How does your answer to 1. relate to the impossibility of accelerating bodies through the speed of light in relativity theory?

3. How does your answer to 1. relate to the famous equation Energy = mass x c2?

For discussion in the recitation.

A. When a golfclub strikes a golfball, the ball is accelerated to a higher velocity than that of the club head. Classically, with a heavy club head and a perfectly elastic golfball, the ball can be impelled to twice the speed of the club head. Might a sufficiently robustly constructed club and ball, wielded with sufficient speed, be able to accelerate the ball past the speed of light?

What kinematical effects in special relativity block this means of accelerating something past the speed of light?

What dynamical effects in special relativity block it?

B. What does the law of conservation of mass say? What does the law of conservation of energy say? In classical physics, these are two separate laws. What becomes of them in relativity physics?

C. When an electric battery is charged, what happens to its mass?
When a hot body cools, what happens to its mass?
When a spring is compressed what happens to its mass?
Inside a completely isolated spacestation, an electric battery is used to warm the hands of an astronaut and to run a motor that winds a spring. What happens to the total energy of the spaceship? What happens to the total mass of the spaceship?

D. When an atom of Uranium-235 undergoes fission and breaks into parts, the total mass of the parts is less than the mass of the original atom. What happens to the missing mass? Why is this missing mass important in modern life?