Day 5.5 Momentum and Relativity
1) Momentum is easily confused with kinetic energy. Compare them by considering;
a) their defining equations
b) the equations that show how force changes them
In any interaction, energy is always conserved but kinetic energy usually is not. Kinetic energy is only
conserved in a perfectly elastic collision. Momentum may be exchanged between the objects, but the total
momentum will be conserved if there are no outside forces.
Example #1: An elastic collision
2) Two balls of a Newton’s cradle are released and hit the three stationary ones. What happens?
A) The three balls move away at 2/3 of the speed to conserve momentum.
B) The furthest ball moves at 2 times the speed to conserve momentum
C) The furthest ball moves away at 1.4 times the speed to conserve energy.
D) The furthest two balls move at the same speed to conserve energy and momentum.
Explain.
Example #2: An inelastic collision
3) A cart moving at speed v, hits and sticks to a stationary cart. They move together with a speed of
A) ½ v to conserve momentum
B) square root(½ v) to conserve momentum
C) ½ v to conserve energy
D) square root(½ v) to conserve energy.
Explain.
Example #3: An explosion
4) A gun with a mass of 1 kg is hanging from a string and fires a bullet of 10 g horizontally at 100 m/s.
What is conserved?
A) momentum, total energy
B) kinetic energy, total energy
C) kinetic energy, momentum
D) all three
Explain.
What kills - momentum or kinetic energy?
Watch the first 9½ minutes of Approaching the Speed of Light.
http://www.triumf.ca/home/multimedia/videos/speed-light
5) The video mentions a number of particles.
a) What particles can be found in the nucleus?
b) What particles are produced when the proton hits the carbon atom?
c) What particles are produced when these decay?
d) The electromagnets select particles with equal
6) You will be graphing momentum against velocity for subatomic particles. What will a graph of
momentum (vertical) against sped look like?
A) .
B)
C) p
D) p
p
p
v
v
Explain:
v
v
7) Each histogram shows the time of flight for the particles of equal momentum to travel 4.4 m. Each graph
has two and possibly three peaks. The peaks are due to the three different particles present; electrons,
muons and pions. The electrons move fastest and the pions move the slowest.
a) Which particle produces the peak that is furthest to the left?
b) Which particle is heaviest?
8) Use your histogram to get the speed as a fraction of c for each particle. Show your steps below.
a) Electron
b) Muon
c) Pion
9) Look at the class`s data. We can’t use the electrons’ velocities. Why not?
10) Graph p (units of MeV/c) vs. v (in units of c) for the muons and pions. Guess what you need to graph p
against to get a straight line and test it.
a) What must you graph on the horizontal axis instead of v to get a straight line?
b) What is the value of the slopes of your straight-line graphs?
c) What is the physical meaning of the slopes on your graph?
d) Calculate the % difference of your slopes and the accepted values; 105.7 MeV/c2, 139.6 MeV/c2
d) What do you think the major source of error was?
f) Why do the histogram peaks have a spread to them?
7) Your friend thinks that it is just a matter of time before we have rockets that can go faster than the speed
of light. How would you try to convince them that this will not happen?
8) Many popularizations of physics say that mass increases as you go faster. Most physicists say that mass
does not change with speed. What do physicists think is the correct interpretation and why?
Textbook: 11.2 (576 -578)
p. 578 #10-12, p. 579 #10-12