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PL-UY 3284 Philosophy of Relativity
Assignment #5-key: Mass and Energy
1.
From the point of view of an observer on the meteor, the dust particle speeds towards the meteor from the right at
100,000 mi/sec, and then bounces off it. After the collision, the dust particle is moving to the right at 100,000 mi/
sec with respect to the meteor (because of conservation of momentum - the meteor isn't affected by the collision, so
the initial momentum of the dust particle must be the same as its final momentum). If the dust particle is
traveling at 100,000 mi/sec with respect to the meteor after the collision, and the meteor is still traveling at
100,000 mi/sec with respect to the planet after the collision, how fast is the dust particle traveling with respect to
the planet after the collision?
(a) In classical physics, we simply add the velocity of the dust particle with respect to the meteor to the velocity of
the meteor with respect to the planet to get the velocity of the dust particle with respect to the planet:
100,000 mi/sec + 100,000 mi/sec = 200,000 mi/sec
(a) In special relativity, we know this can't be right, because it would violate the light postulate and the principle of
relativity (light travels at 186,000 mi/sec). In special relativity, we can't simply add velocities together. Instead,
we have to use the rule for combining velocities:
100,000 mi /sec +100,000 mi /sec
2
mi/ sec)
1− (100,000
(186,000 mi/ sec)2
2.
= 155,000 mi /sec
(a) With respect to a stationary observer, the mass of a spaceship increases to infinity as the spaceship gets closer
and closer to the speed of light.
(b) To accelerate the spaceship to the speed of light would require an infinite force, which no possible rocket motor
could provide.
(c) An observer on the spaceship will not see anything different about its mass when it is traveling at constant
speed very close to the speed of light.
(d) If the observer did see an increase in mass, this would allow her to tell that she was in a constantly moving
reference frame. But the Principle of Relativity forbids this - it says that the laws of physics are the same in
all constantly moving frames - no experiment can detect constant motion.
3.
(a) The total energy of the chamber and its contents remains the same (conservation of mass/energy).
(b) The mass of each molecule increases (its kinetic energy is increasing).
(c) The mass of the gas increases (its heat energy is increasing).
(d) The mass of the battery is decreasing (its electrical energy is decreasing).
(e) The total mass of the chamber and its contents remains the same (conservation of mass/energy).