Practice Test 3
Note: THIS TEST IS LONGER THAN THE ACTUAL TEST. It is a sample and does not
include questions on ever topic covered since the start of the semester.
Also be sure to review
homework assignments on WebAssign
Whiteboard problems worked out in class
Exercises, Examples, and Review Questions (at the end of each chapter) in your textbook
Some general rules:
• Read all problems carefully before attempting to solve them
• Your work must be legible, and the organization must be clear
• You must show all your work, including correct vector notation
• Correct answers without adequate explanation will be counted as wrong
• Incorrect work or explanations mixed in with correct work will be counted as wrong
o Cross out anything you don’t want us to read!
• Make explanations complete but brief. Do not write a lot of prose.
• Include diagrams!
• Show what goes into a calculation, not just the final number:
a !b
=
( )(
8 " 10 #3 5 " 10 6)= 5 " 10 4
c!d (
2 " 10 #5
)(
4 " 10 4
)
• Give standard SI units with your results
Unless specifically asked to derive a result, you may start from the formulas given on the
formula sheet, including equations corresponding to the fundamental concepts. If a
formula you need is not given, you must derive it.
If you cannot do some portion of a problem, invent a symbol for the quantity you can’t
calculate (explain that you are doing this), and use it to do the rest of the problem.
Problem 1
(a) How much kinetic energy in eV must an electron beam have to be able to excite atomic
hydrogen from its ground state to two levels above the ground state?
(b) How much kinetic energy in eV must an electron beam have to be able to excite a quantum
oscillator from its ground state to two levels above the ground state if the mass is 3 ! 10 "26 kg and
the spring stiffness is 80 N/m?
Problem 2
You have a cold gas of atoms, and you observe that if you shine light consisting of photons with
energy 6.0 eV through the gas, some free electrons are observed, implying that a photon of this
energy is able to ionize an atom in the gas. You find that with photons of less than 6.0 eV no
ionization occurs.
(a) What is the energy of the ground state? K+U =
Next you run a beam of electrons through the gas. The kinetic energy of the electrons is 10.0 eV.
Collisions of the electrons in the beam with the atoms of the gas excite the gas atoms to states above
the ground state. A photon detector that is sensitive to a wide range of photon energies detects that
photons are emitted with distinct energies: 0.6 eV, 0.8 eV, 1.4 eV, 3.4 eV, 4.2 eV, and 4.8 eV. No
other emission lines are seen in the spectrum.
(b) Using the information from the two experiments described above, draw a diagram of the energy
levels of one of the atoms in the gas. Draw the diagram approximately to scale.
Label the energy levels with their values of K+U. Draw and label transitions between levels. Do
not draw a potential energy curve, because these data are insufficient to determine its shape.
(c) Next you reduce the kinetic energy of the electrons in the electron beam. When the kinetic
energy of the electrons in the beam is 4.3 eV, what are the energies of the photons emitted by the
gas?
Problem 3
A runner whose mass is 50 kg accelerates from a stop to a speed of 10 m/s in 3 seconds. (A good
sprinter can run 100 meters in about 10 seconds, with an average speed of 10 m/s.)
(a) What is the average horizontal component of the force that the ground exerts on the runner’s
shoes?
(b) How much displacement is there of the force that acts on the sole of the runner’s shoes,
assuming there is no slipping?
(c) How much work is done on the real system (the runner) by the force you calculated in part (a)?
(d) How much work is done on the point particle system by this force?
(e) The kinetic energy of the runner increases. What kind of energy decreases and by how much?
Problem 4
Two astronauts in outer space are outside a space station, doing a routine inspection. Alice’s mass,
including her space suit, is 68 kg, while Brenda’s mass, including her space suit, is 73 kg. The two
astronauts suddenly realize that as a result of their maneuvering, they are drifting toward each other
and will collide. Just before impact, Alice’s velocity is m/s. To complicate matters, the two astronauts collide in an orientation that causes
Velcro patches on their spacesuits to stick together, and they move as one object, without rotation.
(a) What is the final (vector) velocity of the stuck-together astronauts? Start from a fundamental
principle, and show all your work.
(b) What is the change in thermal energy of the system consisting of the two astronauts?
(c) Is this an elastic or inelastic collision? Explain.
Problem 5
Two friends want to close their heavy door, but are too lazy to get up. They agree to throw an object
at the door to close it. Ernie suggests throwing a 300 g lump of sticky clay at the door, but Bert
argues that a 300 g tennis ball would work better if thrown at the same speed. Who is correct?
Explain in detail, basing your explanation on fundamental physics principles.
Problem 6
A 0.4 kg disk of radius 8 cm is pulled along a frictionless surface with a force of 10 N by a string
wrapped around the edge as shown.
24 cm 10 N
a) What are the magnitude and direction of the torque exerted
about the center of the disk at this instant?
8 cm
(b) At the instant shown, the angular velocity of the disk is 20 radians/sec. Calculate the magnitude
and direction of the angular momentum about the center of the disk.
(c) What are the magnitude and direction of the angular momentum about the center of the disk
0.3 s later?
(d) What are the magnitude and direction of the angular velocity at this later time?
m
Problem 7 v
A stationary uniform-density disk of radius 0.8 m is mounted in the vertical plane.
The axle is held up by supports that are not shown, and the disk is free to rotate R
on the nearly frictionless axle. The disk has a mass of 3.6 kg. A lump of clay C
with mass 0.3 kg falls and sticks to the outer edge of the wheel at the location
m. Just before the impact the clay has a speed of 8 m/s, and
the disk is rotating clockwise with angular speed 0.40 radians/s. M
(a) Just before the impact, what is the angular momentum of the combined system of wheel plus
clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen toward you.)
(b) Just after the impact, what is the angular momentum of the combined system of wheel plus clay
about the center C?
(c) Just after the impact, what is the angular velocity of the wheel?
(d) Qualitatively, what happens to the linear momentum of the combined system?
Fundamental Concepts
What you must memorize:
(1) The Momentum Principle and the definition of momentum
(2) The relationship among position, velocity and time
(3) The Energy Principle, and the definition of work
(4) The Angular Momentum Principle
MULTIPARTICLE SYSTEMS
2
1 ptotal
K total = K trans + K rel to CM = K trans + K rot + K vib K trans = M total vcm =
2
nonrelativistically
2 2M total
! ! L2 1
Ptotal = M total vcm nonrelativistically K rot = rot = I! 2 I = m1r!1 + m2 r! 2 + m3r! 3 + !
2 2 2
! ! 2I 2
! ! ! ! ! !
!Ltot, A = " net, ext, A !t LA = rA ! p for a point particle ! A = rA " F
! ! ! ! ! ! ! !
( )
LA = Ltrans, A + Lrot = RCM, A ! Ptotal + Lrot for a multiparticle system Lrot = I!
EVALUATING SPECIFIC PHYSICA QUANTITIES
! m1m ! mm
Fgrav on 2 by 1 = !G ! 2 2 rˆ Near Earth’s surface Fgrav ! mg U grav = !G 1! 2
r r
! 1 q1q2 1 q1q2 ! 1
Felec on 2 by 1 = !2 rˆ U elec = ! Fspring = ks s , opposite the stretch U s = ks s 2
4!" 0 r 4!" 0 r 2
ks 2" F /A
x = A cos (! t ) (solution to an idealized spring mass system) ! = ,!= = 2" f , Y = T
m T !L / L
( )
E 2 ! ( pc ) = mc 2 ; E = pc for massless photon
2 2
! ! ! ! !
!d p$ ! dp ! v
ˆ ! 2! r
# dt & p = Fparallel
ˆ p = p n = F!
ˆ v =
" % dt R T
m
Macro/micro connections: macro measurement of density = (micro quantities)
d3
k
macro measurement of Young’s modulus Y = s,i (micro quantities)
d
k
macro measurement of speed of sound v = d s,i (micro quantities)
ma
energy
!Ethermal = mC!T , where m is in grams if C is in (J/K)/gram Power = (watts = J/s)
time
! k $ 13.6 eV
EN = N # ! s & ; hydrogen atom: EN = ! ( N = 1, 2, …)
" m% N2
Sphere Cylinder or disk Thin rod about Solid cylinder about
axis shown axis shown
2 1 1 1 1
I= MR 2 I= MR 2 I= ML2 I= ML2 + MR 2
5 2 12 12 4
Physical Constants
1
G = 6.7 ! 10 "11 N # m 2 / kg 2 g = 9.8 N/kg = 9 # 10 9 N $ m 2 / C2
4!" 0
c = 3 ! 10 8 m/s h = 6.6 ! 10 "34 J # s ! = 1.05 ! 10 "34 J # s
M Earth = 6 ! 10 24 kg M Moon = 7 ! 10 22 kg M Sun = 2 ! 10 30 kg
Radius of the Earth = 6.4 ! 10 6 m Radius of the Moon = 1.75 ! 10 6 m
Distance from Earth to Moon = 4 ! 10 8 m Distance from Sun to Earth = 1.5 ! 1011 m
Avogadro’s number = 6 ! 10 23 molecules/mole Typical atomic radius r ! 10 "10 m
melectron = 9 ! 10 "31 kg mproton ! mneutron ! mhydrogen atom = 1.7 " 10 #27 kg
e = 1.6 ! 10 "19 C where e = charge on proton = -charge on electron 1 eV = 1.6 ! 10 -19 J
Heat capacity of water = 4.2 (J/K)/gram
Trigonometric properties
!
F !
Fy = F sin ! adj Fx opp Fy
cos! = = ! sin ! = = !
hyp F hyp F
!
!
Fx = F cos!