Final Exam, Physics 170, Fall 1995.
Please write your name at the top of the page. Show your work. There are 8 problems. Each is assigned 25 points. You have two hours to complete the exam.
1. Dimensional Analysis
A length L that appears in atomic physics is given by the formula
where 
is the mass of an electron, c is the
speed of light, and h is a constant known as Planck's constant.
What are the dimensions (or units) of Planck's constant, h ?
2. Conservation Laws: Energy, Momentum and Angular Momentum
An air puck with mass 0.4 kg and velocity
on a flat
frictionless table collides with
a second air puck of mass 0.5 kg and velocity 
.
As a result of the collision, the first puck stops
while the second puck starts moving.
(hint: remember these velocities are vectors and draw a clear diagram.)
(a) What is the kinetic energy of the system before the collision ?
(b) What is the kinetic energy of the second air puck after the collision ?
3. Static Equilibrium
You have been hired by Paradise Island Engineering. Your job
is to design a cable for the arrangement shown below.
A uniform beam of length L and mass M is pivoted at one end
about an attachment point in a wall. The other end is supported
by a horizontal cable also attached to the wall.
The beam makes an angle 
with the horizontal.
(a) Draw a diagram which shows the forces acting on the beam ?
(b) What is the tension in the cable ? (give your result
in terms of 
)
4. Gravity
The mass of the moon is 
kg and its radius
is 1740 km ( 
N-m 
/kg ).
(a) What is the period of a satellite in a circular orbit 1000 km above the surface ?
(b) What is the escape velocity for a projectile that is fired from the moon's surface ?
5. Oscillatory Motion
A sphere of mass M and radius R is attached to the ceiling (as shown) and allowed to oscillate.
(a) What is the period of small oscillations ?
(The momenta of inertia for a sphere about
an axis through its center is 
.)
(b) Suppose the initial amplitude is 
rad,
and the sphere starts at rest. What is 
,
the angular displacement as a function of time ?
(give your final result in terms of R, g, t).
6. Sound Waves
A organ pipe open at both ends is excited in its third harmonic. The length of the pipe is 0.3 m. The speed of sound in air is 340 m/s.
(a) What is the frequency of the sound produced ?
(b) What is the wavelength of the sound produced ?
(c) Suppose an observer is rapidly moving towards the end of the organ pipe. Will the frequency of the sound heard by the observer be higher or lower than the frequency in part (a) ? (give a short qualitative explanation of your answer).
(d) Suppose an observer is rapidly moving towards the end of the organ pipe. Will the wavelength of the sound found by the observer be higher or lower than the wavelength found in part (b) ? (give a brief qualitative explanation of your reasoning).
7. Kinetic Theory of Gases
The surface of the sun contains both hydrogen and helium atoms at 6000 K.
(a) What is the average kinetic energy for each type of atom ?
(b) What is the rms velocity for each type of atom ?
(c) Which type of gas is most likely to escape from the sun ? (give a brief qualitative explanation for your answer)
(Some of the following information
may be useful: 
J/K,
R=8.31 J/mol K, R=0.0082 L-atm/mol K,
atoms/mole, the
mass of a hydrogen atom is 
kg.
Also note that He has atomic mass 4.)
8. Thermodynamics
How much perspiration must evaporate from a large sweaty Hawaiian warrior
who weighs 150 kg
in order to reduce his temperature by 
C ? (find the
amount of perspiration in kg).
(Some of the following information may be useful:
the heat of vaporization for water at room temperature is
580 cal/g. 1 cal=4.184 J, 1 Btu= 252 cal.
The latent heat of fusion for water is 79.7 cal/g.
For the body, c=0.83 cal/g 
.)