AP Physics
Monday 14.04.21
Standards: Therm & Fluids
Warm Up
What is the Conservation of Energy
Equation for Thermodynamics & for
Fluids?
Objective: SWBAT recall the
major concepts of fluids and
thermodynamics.
Agenda
1.
Warm Up
2.
Pass Back AP Exams
3.
Collect HW
4.
Pop Quiz Fluids & Thermodynamics
5.
Review Fluids & Thermodynamics Homework
Homework
AP Physics
Tuesday 14.04.22
Standards: E1a1 Calculate the
flux of a uniform magnetic field
through a loop of arbitrary
orientation.
Objective: SWBAT find the
magnitude and direction of
induced currents due to
magnetic flux
Agenda
1. Warm Up
2. Stamp HW
3. Review Fluids & Thermo Eqns
4. Magnetic Induction Notes &
Reading
5. Magnetic Induction Practice
Warm Up
Draw the Magnetic Field
around the current carrying
wire. Include its direction in
your drawing
I
Homework
M#9
AP Physics
Wednesday 14.04.23
Standards: Traveling, Wave
Propagation, Standing Waves &
Superposition
Warm Up
Find the Φ and the ΔΦ if the loop is moved
completely inside of the uniform magnetic field.
B= 4T
5m
Objective: SWBAT understand
how mechanical waves interact.
1m
Agenda
1. Warm Up
2. Finish Magnetic
Induction
3. Waves
3m
Homework
M#3
AP Physics
Thursday 14.04.10
Standards: Traveling, Wave
Propagation, Standing Waves &
Superposition
Warm Up
If a wire loop of radius 10 cm is initially
perpendicular to a Bar magnet giving of a B
field of 20 T is rotated 30 degrees in the
direction shown in 2 seconds. Find the
magnitude of the induced voltage and the
direction of the current through the loop.
B
Objective: SWBAT understand
how mechanical waves interact.
-
Agenda
1. Warm Up
2. Review HW
3. Mechanical Waves Notes
4. Mechanical Wave Practice
+
Homework
W#1
AP Physics
Friday 14.04.11
Standards: B1 Interference &
Diffraction single slit, double
slit, diffraction
Warm Up
What is the resonant frequency a
mechanical wave on a rope 10 m long
oscillating in the third harmonic if it
travels at 10 m/s? Draw it also.
Objective: SWBAT will
understand how light interferes
to form patterns
Agenda
1. Warm Up
2. Answers to M#10, & W#1
(Solutions to come this
weekend)
3. Wave Properties
4. Waves through mediums
Homework
W#2
Thermo & Fluids: Pop Quiz
1. What is Bernoulli’s equation?
2. What is the first Law of Thermodynamics?
3. What equation would you use to find the maximum
efficiency of a Carnot Engine?
4. How would you find the efficiency of a heat engine?
5. What is the density equation?
6. What does –PΔV equal?
7. What does the unit of measurement called Pascals
measure?
M#9
What is the meaning of each of the following equations?
Create or Describe 1 scenario where each equation would be
useful.
M#4 Magnetic Field Through
Wires
C1983E3.
a. Two long parallel wires that are a distance
2a apart carry equal currents I into the plane
of the page as shown
above.
i. Determine the resultant magnetic field
intensity at the point O midway between the
wires.
ii. Develop an expression for the resultant
magnetic field intensity at the point N. which is
a vertical distance y above point O. On the
diagram above indicate the direction of the
resultant magnetic field at point N.
You will need to do some vector addition of the B field in this problem
M#5 1st Law of Thermo.
• 1991B3 (modified) A heat engine consists of an oil-fired steam
turbine driving an electric power generator with a power
output of 120 megawatts. The thermal efficiency of the heat
engine is 40 percent.
• a. Determine the time rate at which heat is supplied to the
engine.
• b. If the heat of combustion of oil is 4.4 x 107 joules per
kilogram, determine the rate in kilograms per second at which
oil is burned.
• c. Determine the time rate at which heat is discarded by the
engine.
M#6 PV Diagrams and Carnot Cycle
• 1986B5 (modified) A proposed ocean power plant will utilize the temperature difference between
surface seawater and seawater at a depth of 100 meters. Assume the surface temperature is 25°
Celsius and the temperature at the 100-meter depth is 3° Celsius.
• a. What is the ideal (Carnot) efficiency of the plant?
• b. If the plant generates useful energy at the rate of 100 megawatts while operating with the
efficiency found in part (a), at what rate is heat given off to the surroundings?
• The diagram below represents the Carnot cycle for a simple reversible (Carnot) engine in which a
fixed amount of gas, originally at pressure po and volume Vo follows the path ABCDA.
• c. In the chart below, for each part of the cycle indicate with +, -, or 0 whether the heat
transferred Q and temperature change ΔT are positive, negative, or zero, respectively. (Q is
positive when heat is added to the gas, and ΔT is positive when the temperature of the gas
increases.)
M#7 Buoyant Force
• 2003B6.
• 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 x 103
kg/m3
• (a) Calculate the gauge pressure on the diver on the ocean floor.
• (b) Calculate the absolute pressure on the diver on the ocean floor.
The diver finds a rectangular aluminum plate having dimensions 1.0 m
x 2.0 m x 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 x 103
kg/m3. Ignore the effects of viscosity.
• (c) Calculate the tension in the cable if it lifts the plate upward at a
slow, constant velocity.
• (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. Explain your
reasoning.
M#8 Bernoulli’s Equation
• B2005B5.
• A large tank, 25 m in height and open at the
top, is completely filled with saltwater
(density 1025 kg/m3). A small drain plug with
a cross-sectional area of 4.0 x 10-5 m2 is
located 5.0 m from the bottom of the tank.
The plug breaks loose from the tank, and
water flows from the drain.
• (a) Calculate the force exerted by the water
on the plug before the plug breaks free.
• (b) Calculate the speed of the water as it
leaves the hole in the side of the tank.
• (c) Calculate the volume flow rate of the
water from the hole.
M#9 Magnetic Flux
1982B5. A circular loop of wire of resistance 0.2 ohm encloses an area 0.3 square meter and lies flat
on a wooden table as shown above. A magnetic field that varies with time t as shown below is
perpendicular to the table. A positive value of B represents a field directed up from the surface of the
table; a negative value represents a field directed into the tabletop.
a. Calculate the value of the magnetic flux through the loop at time t = 3 seconds.
b. Calculate the magnitude of the emf induced in the loop during the time interval t = 0 to 2 seconds.
c. On the axes below, graph the current I through the coil as a function of time t, and put appropriate
numbers on the vertical scale. Use the convention that positive values of I represent
counterclockwise current as viewed from above.
Electromagnetic Induction
• Emf (E)– Electromotive force (essentially this is a Voltage
because it can drive current.
• You can induce an Emf in a current loop by moving a magnet
towards or away from the current loop.
• Ultimately, a changing magnetic field will induce or cause or
create electric current.
• In other words, increasing or decreasing a magnetic field around
the current loop will cause electric charges to move along the
wire.
• This is called Electromagnetic Induction.
Magnetic Flux
-Whenever the Strength of a Magnetic Field Changes (eg. The
number of field lines increases or decreases) a current is created
in a loop.
-To quantify how much the magnetic field changes, we use the
concept of magnetic field lines. More field lines through a loop
will equal a larger magnetic flux and therefore a larger current.
-ϕ=BA cos θ where ϕ is the Magnetic Flux, B is the
magnetic field and θ is the angle between the loop
and the magnetic field. Units: Telsa meters
squared Tm2 or Wb (weber)
Faraday’s Law
To find the Emf that is driving the induced current, you need the
number of loops and the the change in Magnetic Flux through
those loops. E=-NΔϕ/Δt The minus sign means that the induced
emf is opposite to the change in magnetic flux. It is a reaction
against the changing magnetic field.
M#9
• 1986B4. A wire loop, 2 meters by 4 meters, of negligible resistance is in the
plane of the page with its left end in a uniform 0.5-tesla magnetic field directed
into the page, as shown above. A 5-ohm resistor is connected between points X
and Y. The field is zero outside the region enclosed by the dashed lines. The loop
is being pulled to the right with a constant velocity of 3 meters per second. Make
all determinations for the time that the left end of the loop is still in the field,
and points X and Y are not in the field.
• a. Determine the potential difference induced between points X and Y.
• b. On the figure above show the direction of the current induced in the resistor.
• c. Determine the force required to keep the loop moving at 3 meters per second.
• d. Determine the rate at which work must be done to keep the loop moving at 3
meters per second.
Two Types of Waves
Electromagnetic Waves
c=fλ, speed of
light c=3x108m/s
Mechanical Waves
Waves that don’t require
+ Gamma Rays a medium because they
the wave carries energy
through oscillating
Electric and Magnetic
Fields.
They require a medium, because they carry energy through
through vibrating or oscillating matter such as the air, dirt,
water.
v=fλ
Two types of Wave Motion
Longitudinal – waves where the
direction of propagation
(direction the energy is being
carried, or direction of velocity) is
the same as the direction of
vibration.
Transverse – waves where the direction of
propagation is perpendicular to the
direction of vibration.
W#1 Waves & Sound
1998B5. To demonstrate standing waves, one end of a string is attached to a tuning fork
with frequency 120 Hz. The other end of the string passes over a pulley and is connected
to a suspended mass M as shown in the figure above. The value of M is such that the
standing wave pattern has four "loops." The length of the string from the tuning fork to
the point where the string touches the top of the pulley is 1.20 m. The linear density of
the string is 1.0 x 10– kg/m, and remains constant throughout the experiment.
a. Determine the wavelength of the standing wave.
b. Determine the speed of transverse waves along the string.
c. The speed of waves along the string increases with increasing tension in the string.
Indicate whether the value of M should be increased or decreased in order to double the
number of loops in the standing wave pattern. Justify your answer.
d. If a point on the string at an antinode moves a total vertical distance of 4 cm during
one complete cycle, what is the amplitude of the standing wave?
Interference, Standing Waves,
Resonance
-Interference happens when two waves come into contact with each
other. p.454
*Constructive Interference- The crests and
troughs of multiple waves combine to make
much larger wave
node
anti-node
*Destructive Interference- The crest and
trough of 2 waves combine to cancel out the
wave.
Resonant frequencies – create standing wave patterns.
They’re called standing waves because they don’t look like
they move. To find the wavelength of standing waves
λn=2L/n. Using v=fλ -> fn=n(v/2L).
Diffraction & Interference of Light
When light goes throu
dsinθ=mλ
m=3
m=2
d
θ
y
m=1
L
m=1
Monochromatic
m=2
light – light with
one color or
m=3
wavelength, like
a laser
In order to find the width of the bright spots. If y is much much smaller than L,
we can use the small angle approximation. This helps because we don’t know
the hypotenuse of the triangle above, but we can measure y and L. Where y is
the distance between dark spots and L is the distance from the slit to the
screen.
Replacing sinθ with tanθ we get: d tanθ=mλ, but
tanθ=opposite/adjacent so tanθ=y/L and d(y/L)=mλ
Spherical Mirrors
C=Center of Curvature
R=Radius of Curvature
f=Focal Length =R/2
Optic axis
Concave Mirror
makes light
converge.
.
C
f
R
Spherical Mirror Equation:
do=object distance
1 1 1
+ =
do di f
di=image distance
Magnification Equation:
M =-
di hi
=
do ho
M>1 larger image
M<1 smaller image
Optic axis
.
f
C
R
Convex Mirror
makes light diverge
typically creating
imaginary images.
Ray Diagrams
To make a ray diagram you need 3 rays.
1. Parallel Ray – This ray is parallel to the axis and is reflected
through the focal point of the mirror.
2. Radial Ray – This ray passes through the center of curvature
of the spherical mirror
3. Focal ray - This ray passes through the focal point of the
mirror and is reflected parallel.
-- Where these three rays intersect is the height and location of
the image that will form on the mirror.
F
Optic axis
C
• The image is inverted.
• The image is reduced.
• The image is real
Diverging Lens - makes
light diverge as it travels
through the lens . Made
up of 2 concave lenses
back to back.
Thin Lenses
See. p.741
f=Focal Length =R/2
Thin Lens Equation:
o
o
ho=object height
hi=image height
M>1 larger image
M<1 smaller image
f
f
R
1 1 1
+ =do=object distance
do di f
di=image distance
di hi
M
=
=
Magnification
Equation:
d h
.
.
Optic axis
Imaginary, upright, reduced image
Optic axis
.
f
C
.
f
Real, inverted, magnified image
Converging Lens
makes light
converge. Made
up of double
convex lenses.
Ray Diagrams for Lenses
To make a ray diagram you need 3 rays.
1. Parallel Ray – This ray is parallel to the lenses optic axis and
after refraction it passes through one of the focal points
depending on the lens type
2. Central Ray – The lens passes unaffected through the center
of the lens.
3. Focal ray - This ray passes through the focal point of the lens
and then travels parallel through the lens.
-- Where these three rays intersect is the height and location of
the image that will form on the mirror.
F
• The image is inverted.
• The image is reduced.
• The image is real
F
W#2 Interference Patterns
• 1991B6. Light consisting of two wavelengths, λa = 4.4 x 10–7 meter and λb = 5.5 x 10–7
meter, is incident normally on a barrier with two slits separated by a distance d. The
intensity distribution is measured along a plane that is a distance L = 0.85 meter from
the slits as shown above. The movable detector contains a photoelectric cell whose
position y is measured from the central maximum. The first-order maximum for the
longer wavelength λb occurs at y = 1.2 x 10-2 meters.
• a. Determine the slit separation d.
• b. At what position, Ya, does the first-order maximum occur for the shorter
wavelength λa?