Study Guide for Test 4
Gravity on the large scale
You should know the gravitational force law and energy formula,
|ī
Fg|=Gm1m2
r2,U
g=āGm1m2
r,G=6.67 Ć10ā11 N-m2/kg2,
and be able to use these formulas in constrained motion problems and in energy conserva-
tion problems. You should understand the concept of escape speed.
Fluid statics
You should know how density is deļ¬ned, how to convert units of density, and the approx-
imate values of the density of air and water.
You should understand the deļ¬nition of pressure (P=F/A) and why it depends on depth
when gravity is present. Please memorize the approximate value of atmospheric pressure
at sea level, 105N/m2or 1 bar. You should be able to compute the pressure as a function
of depth in a ļ¬uid of uniform density:
P(h)=P0+Ļgh.
You should understand the concept of buoyant force and Archimedesā principle.
Oscillations
You should understand how Newtonās second law for a mass on a spring predicts oscillatory
motion:
d2x
dt2=āks
mxāx(t)=Acos Ļt, with Ļ=īks
m.
You should know how the frequency (f=Ļ/2Ļ) and period (T=1/f) related to the
angular frequancy (Ļ). You should be able to interpret similar behavior in other oscillating
systems such as a simple pendulum in the small-amplitude limit.
Waves
You should understand the following terms as applied to waves: transverse; longitudinal;
amplitude; frequency; angular frequency; period; wavelength; angular wave number; speed;
superposition; interference.
Given a mathematical formula for a pulse or periodic wave traveling in one dimension (as
on a string), you should be able to determine any of the relevant quantities (amplitude,
frequency, etc.) in the preceding list. Given a suļ¬cent number of these quantities, you
should be able to write down a mathematical formula describing the pulse or wave.
You should know the formulas for the speed of a transverse wave on a taut string, or a
sound wave, in terms of the elastic and inertial properties of the medium:
vstring =ītension
mass/length;vsound =ībulk modulus
density .
