Transcript No Slide Title

2003 AP Physics Workshop, Ted Vittitoe
Problem B-1
Problem B-2
Problem B-3
Problem B-4
Problem B-5
Problem B-6
Problem B-7
2003 AP Physics Workshop, Ted Vittitoe
Problem B-1 (15 points)
A rope of negligible mass passes over a
pulley of negligible mass attached to the
ceiling, as shown. One end of the rope is
held by Student A of mass 70 kg, who is
at rest on the floor. The opposite end of
the rope is held by Student B of mass 60
kg, who is suspended at rest above the
floor.
2003 AP Physics Workshop, Ted Vittitoe
(a) On the dots below that represent the
students, draw and label free-body
diagrams showing the forces on Student A
and on Student B.
T  mBg
T
T
N
B
mBg
A
m Ag  T  N
m Ag
2003 AP Physics Workshop, Ted Vittitoe
(b) Calculate the magnitude of the force
exerted by the floor on Student A.
T
T  mBg
F  0
T  N  m Ag
N  m A g  mBg
N  m A  mB g
N  70  60 10  
N
A
m Ag
100N
2003 AP Physics Workshop, Ted Vittitoe
Student B now climbs up the rope at a
constant acceleration of 0.25 m/s2 with
respect to the floor.
(c) Calculate the tension in the rope
while Student B is accelerating.
 FB  mBa
T'm Ag  m Aa
T'  m Aa  m Ag
T'  m A a  g   600.25  10  
615N
2003 AP Physics Workshop, Ted Vittitoe
Student B now climbs up the rope at a
constant acceleration of 0.25 m/s2 with
respect to the floor.
(d) As Student B is accelerating, is
Student A pulled upward off the
floor?
No
Justify your answer.
The tension in the rope must exceed the weight (700 N)
of Student A for him/her to be pulled off the ground.
2003 AP Physics Workshop, Ted Vittitoe
Student B now climbs up the rope at a
constant acceleration of 0.25 m/s2
with respect to the floor.
(e) With what minimum acceleration
must Student B climb up the rope to
lift Student A upward off the floor?
When T = 700 N
 FB  mBa
T  m A g  m Aa
700  6010 
T  m Ag


a
60
mA
1.67 m/s 2
2003 AP Physics Workshop, Ted Vittitoe
Problem B-2 (15 points)
A circuit contains two resistors (10 W and 20 W) and
two capacitors (12 mF and 6 mF) connected to a 6 V
battery, as shown in the diagram. The circuit has been
connected for a long time.
2003 AP Physics Workshop, Ted Vittitoe
(a) Calculate the total
capacitance of the circuit.
Capacitors is series:
126 
C1C2

 4 mF
C
C1  C2 12  6
2003 AP Physics Workshop, Ted Vittitoe
(b) Calculate the current
in the 10 W resistor.
Kirchhoff’s loop rule:
VB  IR 10  IR 20  0
VB
I
R10  R 20
6


10  20
0.20 A
2003 AP Physics Workshop, Ted Vittitoe
(c) Calculate the potential
difference between points
A and B.
The voltage between points A and B is the same as
the voltage across R20.
VR 20   IR 20  0.2020   4.0 V
2003 AP Physics Workshop, Ted Vittitoe
(d) Calculate the charge
stored on one plate of the
6 mF capacitor.
Q
C
V
Q  CV  4 mF4 V  
16 mC
2003 AP Physics Workshop, Ted Vittitoe
(e) The wire is cut at point
P. Will the potential
difference between points
A and B increase,
decrease, or remain the
same.'?
____increase
____decrease

____remain
the same
Justify your answer.
In a steady state, the capacitors represent a break in the
circuit between points A and B. Cutting the wire a point P
is just another break and will have no effect on the
potential difference between points A and B
2003 AP Physics Workshop, Ted Vittitoe
Problem B-3 (15 points)
A rail gun is a device that propels a projectile using a magnetic
force. A simplified diagram of this device is shown above. The
projectile in the picture is a bar of mass M and length D, which
has a constant current I flowing through it in the +y-direction,
as shown. The space between the thin frictionless rails contains
a uniform magnetic field B, perpendicular to the plane of the
page. The magnetic field and rails extend for a distance L. The
magnetic field exerts a constant force F on the projectile, as
shown.
2003 AP Physics Workshop, Ted Vittitoe
Express all algebraic answers to the following parts in
terms of the magnitude F of the constant magnetic force,
other quantities given above (M, D, I, B, L) , and
fundamental constants.
2003 AP Physics Workshop, Ted Vittitoe
(a) Determine the position x of the projectile as a function
of time t while it is on the rail if the projectile starts from
rest at x = 0 when t = 0.
F
a
M
vo  0
at 2
x  vot 
2
2
 F t
x  0 t    
M 2
Ft 2
2M
2003 AP Physics Workshop, Ted Vittitoe
(b) Determine the speed of the projectile as it leaves the
right-hand end of the track.
Work/Energy Theorem
W  K
Mv 2
FL 
2
2FL
v
M
2003 AP Physics Workshop, Ted Vittitoe
(c) Determine the energy supplied to the projectile by
the rail gun.
W  FL
2003 AP Physics Workshop, Ted Vittitoe
(d) In what direction must the magnetic field B point in
order to create the force F ?
+Z direction
Explain your reasoning.
The magnetic force on a current-carrying conductor
F  ID  B
(Right - Hand - Rule)
2003 AP Physics Workshop, Ted Vittitoe
(e) Calculate the speed of the bar when it reaches the end of the
rail given the following values.
B=5T
L = 10 m
2FL
v
M
2IDLB
v

M
I = 200 A
M = 0.5 kg
D = 10 cm
F  IDB
2 200 0.110 5  
0.5
63 m/s
2003 AP Physics Workshop, Ted Vittitoe
Problem B-4 (15 points)
In your physics lab, you have a concave mirror with radius of
curvature r = 60 cm. You are assigned the task of finding
experimentally the location of a lit candle such that the mirror
will produce an image that is 4 times the height of the lit
candle.
You have an optical bench, which
is a long straight track as shown.
Objects in holders can be attached
at any location along the bench. In addition to the concave
mirror and the lit candle in holders, you also have the following
equipment.
convex mirror in holder
convex lens in holder
ruler
concave lens in holder
meter stick
screen in holder
2003 AP Physics Workshop, Ted Vittitoe
(a) Briefly list the steps in your procedure
that will lead you to the location of the lit
candle that produces the desired image.
Include definitions of any parameters
that you will measure.
Place the concave mirror at one end of the optical bench (x = 0).
Place the candle 60 cm from concave mirror and adjust the
position of the screen until you get a sharp image.. Move the
candle slowly toward from the mirror while adjusting the
position of the screen to keep a sharp image. Use the ruler
to measure the height of the candle flame and its image.
Continue adjusting the position of the candle until it image
is 4 times larger than the flame.
2003 AP Physics Workshop, Ted Vittitoe
(b) On the list of equipment place check
marks beside each additional piece of
equipment you will need to do this
experiment.
____convex mirror in holder
____convex lens in holder

____ruler
____concave lens in holder

____meter
stick

____screen
in holder
2003 AP Physics Workshop, Ted Vittitoe
(c) On the scale below, draw a ray diagram of your lab
setup in part (a) to show the locations of the candle,
the mirror, and the image.
0
mirror
150 cm
object
37 cm
image
2003 AP Physics Workshop, Ted Vittitoe
(d) Check the appropriate spaces below to
indicate the characteristics of your image.

____real
____upright
____
 larger than object
____virtual
 inverted
____
____smaller than object
2003 AP Physics Workshop, Ted Vittitoe
(e) You complete your assignment and turn in your results to
your teacher. She tells you that another student, using
equipment from the same list, has found a different location
for the lit candle. However, she tells both of you that the labs
were done correctly and that neither experiment need be
repeated. Explain why both experiments can be correct.
Lenses had different focal lengths
2003 AP Physics Workshop, Ted Vittitoe
Problem B-5 (10 points)
A cylinder with a movable piston
contains 0.1 mole of a monatomic
ideal gas. The gas, initially at state
a, can be taken through either of
two cycles, abca or abcda, as
shown on the PV diagram above.
The following information is
known about this system.
Qc a  685 J along the curved path
Wc a  120 J along the curved path
U a  U b  450 J
Wa b c  75 J
2003 AP Physics Workshop, Ted Vittitoe
Qc a  685 J along the curved path
Wc a  120 J along the curved path
U a  U b  450 J
Wa b c  75 J
(a) Determine the change in internal
energy, Ua - Uc, between states a and c.
U  nc v T
3 
 U  n R   T
2 
 3
U  0.1 8.315722  271 
 2
562 J
2003 AP Physics Workshop, Ted Vittitoe
Qc a  685 J along the curved path
Wc a  120 J along the curved path
U a  U b  450 J
Wa b c  75 J
pV  nRT
pV
T
nR
(b) i. Is heat added to or removed
from the gas when the gas is taken
along the path abc ?
____
 removed from the gas
____added to the gas
ii. Calculate the amount added or removed.
Qabc  Qab  Qbc
Qabc  nc v Tab  ncp Tbc
Qabc  n 3 RTab  n 5 RTbc
2
2
Qabc  nR 3 Tab  5 Tbc
2
2
2

Ta  722 K
Tb  361 K
Tc  271 K

Qabc  0.18.315  3  361  5  90    637 J
2
2003 AP Physics Workshop, Ted Vittitoe
(c) How much work is done on
the gas in the process cda?
W  pd Vda


W  6x105 Pa 2.5x10 4 m 3 
150 J
2003 AP Physics Workshop, Ted Vittitoe
(d) Is heat added to or removed
from the gas when the gas is
taken along the path cda?
____added to the gas

____removed from the gas
Explain your reasoning.
In process cd: Heat must be added to increase
the internal energy
In process da: Heat must be added to do work
and also to increasethe internal energy
2003 AP Physics Workshop, Ted Vittitoe
Problem B-6 (10 points)
A diver descends from a salvage ship to the ocean floor at a
depth of 35 m below the surface. The density of ocean water
is 1.025 × 103 kg/m.
(a) Calculate the gauge pressure on the diver on the ocean
floor.
p  gh
p  1.025 x 103 10 35 
3.52 x 105 Pa
2003 AP Physics Workshop, Ted Vittitoe
(b) Calculate the absolute pressure on the diver
on the ocean floor.
p  po  gh
p  1.013 x 105  1.025 x 103 10 35 
4.53 x 105 Pa
2003 AP Physics Workshop, Ted Vittitoe
The diver finds a rectangular aluminum plate having
dimensions 1.0 m × 2.0 m × 0.03 m. A hoisting cable is
lowered from the ship and the diver connects it to the
plate. The density of aluminum is 2.7 × 103 kg/m( Ignore
the effects of viscosity.
(c) Calculate the tension in the cable if it lifts the plate
upward at a slow, constant velocity.
w  m Al g
B   w Vw g
w   Al V g
T  wB
T   Al Vg   w Vg


T   Al   w Vg  2.7 x 103  1.025 x 103 0.06 9.8  
985 N
2003 AP Physics Workshop, Ted Vittitoe
The diver finds a rectangular aluminum plate having
dimensions 1.0 m × 2.0 m × 0.03 m. A hoisting cable is
lowered from the ship and the diver connects it to the
plate. The density of aluminum is 2.7 × 103 kg/m
(Ignore the effects of viscosity.
(d) Will the tension in the hoisting cable increase,
decrease, or remain the same if the plate accelerates
upward at 0.05 m/s2?

____increase
____decrease
____remain the same
2003 AP Physics Workshop, Ted Vittitoe
Problem B-7 (10 points)
Energy-level diagrams for atoms that comprise a helium-neon
laser are given above. As indicated on the left, the helium atom
is excited by an electrical discharge and an electron jumps from
energy level Eo to energy level E2. The helium atom (atomic
mass 4) then collides inelastically with a neon atom (atomic
mass 20), and the helium atom falls to the ground state, giving
the neon atom enough energy to raise an electron from Eo' to
E2'. The laser emits light when an electron in the neon atom
falls from energy level E2' to energy level El'.
2003 AP Physics Workshop, Ted Vittitoe
 3.298 x 1018 J
 3.306 x 1018 J
(a) Calculate the minimum speed the helium atom must have
in order to raise the neon electron from Eo' to E2'.
K  E'E
m He v 2
 E'2  E'o  E 2  Eo 
2

v
2

E'2

 E'o
 E2  Eo 


2 3.306 x 1018  3.298 x 1018
m He

4 1.66 x 10 27


v  1,550 m/s
2003 AP Physics Workshop, Ted Vittitoe
(b) Calculate the DeBroglie wavelength of the helium
atom when it has the speed determined in (a).
h
p   m He v He

6.63 x 10 34
h




27
m He v He
4 1.66 x 10
1550


6.44 x 1011 m
2003 AP Physics Workshop, Ted Vittitoe
 3.306 x 1018 J
 2.992 x 1018 J
(c) The excited neon electron then falls from E2' to El' and
emits a photon of laser light. Calculate the wavelength of
this light.
hc
E 

1.99 x 10  25
7
hc 
6
.
34
x
10
m


E 3.306 x 10 18  2.992 x 10 18
2003 AP Physics Workshop, Ted Vittitoe
(d) This laser light is now used to repair a detached retina in
a patient' s eye. The laser puts out pulses of length 20 × 10-3
s that average 0.50 W output per pulse. How many photons
does each pulse contain?
 hc 
n 
E  
P
t
t
Pt 0.500.02 6.34 x 10  7
n



2
5
hc
1.99 x 10
3.19 x 1016 photons
2003 AP Physics Workshop, Ted Vittitoe
END
2003 AP Physics Workshop, Ted Vittitoe