Posted: November 16th, 2015

Modern physics, special relativity

1- there is a ball at rest in your reference frame with mass M. a second ball also with rest mass M is moving with speed v. the two balls collide, stick together, and continue on. keep inmind that the combined mass after the collision will not be 2M.

a. write equation for conservation of relativistic momentum in terms of initial and final speeds (initial momentum=final momentum)

b. write equation for conservation of relativistic energy in terms of initial and final speeds

c. use (a) and (b) to findthe final speed of the two balls

d. from (c) find the approximate final speed in the limit of v<<c

e. from (c) find the approximate final speed in the limit of v~c

2- 1kg water has a heat capacity of 4180 joules per degree celcius. determine the mass increase of the water when it’s heated above freezing (0 deg.Celcius) to just below boiling (100 deg.Celcius). What’s the percentage change of mass?

3- F=dp/dt, where p is momentum (relativistic)

a. prove that if we apply constant force F to a mass M which starts at rest at t=0, we get p=tF

b. use p=tF to solve for speed of the mass with repect to time, v(t). Also, show that your answer reduces to the classical answer when v<<c

c. show that v(infinity)=c for any force except F=0

4- in the nuclear fission process, mass is converted into energy. let’s assume 1% of the mass of uranium is converted in the fission process. determine the total mass of uranium needed by a nuclear power plant for a year’s operation if the plant runs at 30% efficiency (nuclear energy to electrical conversion) and outputs 1 Giga-Watt electrical power.

5- a space ship is moving past you at speed v=0.7c. apitcher is on the space ship and throws a ball in the same direction as the ship is moving at speed u=0.7c. a flee jumps off the baseball after it was thrown at speed w=0.7c relative to the baseball in the same direction.

a. how fast is the flee moving relative to the baseball?

b. how fast is the flee moving relative to the spaceship?

c. how fast is the flee moving relative to the you?

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