FORM A
Final Physics 231
October 15, 2003
Name:__________________________________
Student Number:_________________________
Constants:
 g=9.81 m/s2
Useful Formulae:

F friction  N

W  F cos  x



1
2
1
2
p  mv
Impulse  p
collisions: m1v1  m2 v2 i  m1v1  m2 v2  f
elastic collisions:

  t 



W
t
PE spring  kx 2
KE  mv 2


P 
1
1
1
1
2
2
2
2
 m1v1  m2 v2    m1v1  m2 v2 
2
2
2
i  2
f
1 2
t
2
   0  t
v  r
v2
ac   r 
r
m1m2
r2
  F sin  r
PEg  G
Fg  G
2
m1m2
r
Solution for t to a quadratic equation at2+bt+c=0:
 b  b 2  4ac
t 
2a


PE grav  mgh
Pythagorian Theorem: c2=a2+b2
Trigonometry:
 Sin()=opposite/hypotenuse
 Cos()=adjacent/hypotenuse
 Tan()=opposite/adjacent
R3 
GM 2
T
4 2
General comment: I think that some of the questions are too difficult. Adding some
hints will help (problems 1,2,4), but especially 3,5 and 8 are beyond what they
typically did in LON-CAPA.
1) A grasshopper jumps 10.2 cm
high. If the angle with which the
grasshopper jumps is at 45o with
the horizontal, what is its total
initial speed. (hint: consider first
the vertical direction only).
a) 4.0 m/s
b) 2.0 m/s
c) 4.0 m/s2
d) 1.4 m/s
e) smaller than 1.0 m/s
answer b)
comments: change text (see above) and add hint.
2) Two objects are connected by a light string passing
over a light frictionless pulley. The 5.00 Kg object is
released from rest at a point 4.00 m above the
floor...(delete 2 dots) Which of the flowing
statements is true?
a) The speed of the 5Kg mass when it reaches the
floor is 4.43 m/s.
b) The speed of the 3 kg mass when it reached the
floor is 8.85 m/s.
c) The speed of the 5Kg mass when it reaches the
floor is 8.85 m/s
d) The speed of the 5Kg mass when it reaches the
floor is 19.6 m/s
e) None of the above.
Answer a)
Comments: small errors (see above)
Add hint: Use conservation of mechanical energy
3) A bullet is fired with an initial speed v into a block that is initially at rest at the
edge of a table of height 1.00 m. The bullet remains in the block, and after the
impact the block lands 2.00 m from the bottom of the table. If the mass of the
block of 50.0 g and the
1g
mass of the bullet is
1.00 g, what was the
initial speed v of the
50g
bullet?
a) 442 m/s
b)
c)
d)
e)
221 m/s
4.42 m/s
2.21 m/s
0.49 m/s
answer: b) although I find 226 m/s, I think you neglected the 1 g of the bullet???
I think problem 3 is much too difficult. In midterm I only 25% had the problem with
parabolic motion correct. This involves even more steps. Even though they saw this in
Lon-capa, I don’t think many students can do this in a reasonable amount of time.
4) A 600 Kg satellite is in circular orbit around the Earth at a height equal to the
Earths mean radius. What is the speed at which the satellite is orbiting?
(G=6.67x10-11 Nm2, ME=5.98x1024 Kg, RE=6.38x106 m)
a) 3.05 m/s
b) 7.91 x103 m/s
c) 5.59 x103 m/s
d) 5.60x10-8 m/s
e) 11.2x103 m/s
answer: c) Again, I think this is a difficult problem and probably a hint is a good idea.
Also small type
5) Aliens in planet X intend to launch a rocket. What is its escape speed from the
unknown planet X, if the mass is 7.36x1022 Kg and radius R is 9.82x106 m?
a) 1.00 x103 m/s
b) 7.07 x103 m/s
c) 2.00 x103 m/s
d) 0.32 m/s
e) It cannot be calculated because the mass of the rocket is not given.
I think this is much too difficult….They had no real practice with escape speed (in
lon-capa for example). You would have to give the exact equation for escape speed on
the equation sheet and then this problem just becomes a fill-in exercise.
6) A window has a glass surface of 1.60x103 cm2 and a thickness of 3.00 mm. The
thermal conductivity of the glass is 0.84 J/s m 0C. Determine the rate of energy
transfer by conduction through this pane in the summer, when the temperature of
the inside surface of the glass is 70 0 F and the outside temperature is 90 0 F is:
a) There is no thermal conduction through the window.
b) 8.98 x103 J/s
c) 896 J/s
d) 4.98 x103 J/s
e) 498 J/s
answer e) I would suggest converting at least the cm2 and mm into m2 and m so that
they only have to worry about the Fahrenheit (conversion must be on equation sheet)
7) Consider the following PV diagrams. Which of the following statements is
correct:
a) The work performed to take the gas from the initial to the final state is the
same in all cases.
b) The heat transferred to the gas is the same in all cases.
c) Diagram (c) can represent an isothermal process.
d) Diagram (b) consists of an isobaric process followed by an isovolumetric
process.
e) Diagram (a) consists of an isothermal process followed by an adiabatic
process.
Answer c). I would change the phrasing of answer d) or the intro for the problem, so
that it is more clear that it is important to consider the direction of time.
8) In one cycle, a heat engine absorbs 500 J from the hot reservoir and expels 300 J
to the cold reservoir. If the efficiency of this engine is 60% of the efficiency of a
Carnot engine, what is the ratio of the temperatures of the hot reservoir and the
cold reservoir of this Carnot engine?
a) 2/3
b) 1/3
c) 2/5
d) 5/2
e) 3/5
answer b) Wow, you are hurting them! This is much more difficult than anything in
LON-CAPA and involves ratios and percentages…..
9) A pendulum clock that works well on Earth is taken to a different planet.
Knowing that the clock in the unknown planet ticks at twice the speed, what is the
planet’s gravitational acceleration compared to that of earth (g)?
a) 2g
b) 4g
c) g/2
d) g
e) g/4
answer b) small change to text
10) The snapshot of two waves, A and B, is represented in the figure. Which of the
following statements is correct?
a) The amplitudes of the
waves are the same.
b) The wavelength of A is
twice the wavelength of
B
B.
c) The period of oscillation
of A is the same as that
of B.
d) The speed of wave A is
smaller than the speed of
wave B
e) None of the above.
Answer a). It might be wise to
indicate that the waves are
moving (arrow or so…)
11) A long open pipe is 1.715 m long. Pressing the mouth against the pipe and
blowing air into it, produces a sound (the speed of the sound is v=343m/s) that
consists of the superposition of the several harmonics of the pipe. What are the
frequencies of the first three harmonics?
a) 100 Hz, 200 Hz, 300 Hz.
b) 200 Hz, 400 Hz, 600 Hz.
c) 100 Hz, 300 Hz, 500 Hz.
d) 50 Hz, 100 Hz, 150 Hz.
e) 50 Hz, 150 Hz, 250 Hz.
Answer a)
12) You are patiently waiting for a train to arrive to Lansing. Suddenly the train
approaches at high constant speed, blowing the whistle, and just passes straight
through the station. What happens to the sound you hear?
a) As the train approaches the frequency of the sound increases and the intensity
decreases.
b) As the train approaches both the intensity and the frequency of the sound
decreases.
c) As the train approaches the intensity of the sound decreases whilst the
frequency remains constant.
d) As the train approaches both the intensity and the frequency remain constant.
e) As the train approaches both the intensity and the frequency increase.
Answer e) I would rephrase the question to something like: A train approaches the
station at constant velocity (does not intend to stop) while blowing its whistle. A
person standing on the platform notices that: