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P HYSICS D EPARTMENT, S YRACUSE U NIVERSITY
PHY215 - Recitation 1/1
Julian Georg
January 17, 2017
1 U NIT C ONVERSITONS
Convert the following to SI units:
8 in
66 ft/s
65 mi/h
3h
2 days
1yr
14 in2
215 ft/s2
43.87 kg/ft3
180 nm
83 km2
12 mm
1
2 F ISSIONABLE
In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the
critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the
minimum amount that must be brought together to start a chain reaction. This element has a
density of 19.5 g/cm3 . What would be the radius of a sphere of this material that has a critical
mass?
3 E PSILON E RIDANI
A parsec is a unit to measure astronomical distances. 1 parsec is equal to 3.26 lightyears. A
lightyear is the distance light travels in one year. It is equal to 9.46 × 1012 km. The 11th closest
star to our solar system is Epsilon Eridani. It is 3.22 parsecs away. What is its distance from the
sun in meters and how many seconds does its light take to get to us?
2
4 A GE
How many years older will you be 1 gigasecond from now? (Assume a 365-day year.)
5 N EWTON
Let’s assume you do not remember the dimensions of the gravitational constant G. But you do
remember that the force of gravity in the Newtonian limit is given by
FG = G
m1 m2
.
r2
(5.1)
What are the dimensions of G?
3
6 QFT
In natural units (~ = c = k B = 1) the only dimension is mass. For example, energy has dimensions of mass according to Einstein’s Mass-Energy-Equivalence E = mc 2 . Length and time have
units of inverse mass.
(a) Integrals must produce numbers. Therefore, the action S is dimensionless and is given by
Z
S = d4 x L .
(6.1)
What are the dimensions of the Lagrangian density L ? d4 x is the volume element of 4dimensional space-time.
(b) Let’s say the Lagrangian density is given by
1
L = ∂µ φ∂µ φ + i ψ̄γµ ∂µ ψ + m 2 φ2 + m f ψψ̄
2
What are the dimensions of φ and ψ? γ is dimensionless and ∂µ is defined as
(6.2)
∂
∂x µ .
4