AP PhysicsMonday 14.04.21

Homework

Warm UpWhat is the Conservation of Energy Equation for Thermodynamics & for Fluids?

Agenda1. Warm Up2. Pass Back AP Exams3. Collect HW4. Pop Quiz Fluids & Thermodynamics5. Review Fluids & Thermodynamics Homework

Standards: Therm & Fluids

Objective: SWBAT recall the major concepts of fluids and thermodynamics.

Agenda1. Warm Up2. Stamp HW3. Review Fluids & Thermo Eqns4. Magnetic Induction Notes &

Reading5. Magnetic Induction Practice

Warm UpDraw the Magnetic Field around the current carrying wire. Include its direction in your drawing

HomeworkM#9

AP PhysicsTuesday 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

I

AP PhysicsWednesday 14.04.23

Agenda1. Warm Up2. Finish Magnetic

Induction3. Waves

HomeworkM#3

Warm Up

Standards: Traveling, Wave Propagation, Standing Waves & Superposition

Objective: SWBAT understand how mechanical waves interact.

5m

3m

1m

B= 4T

Find the Φ and the ΔΦ if the loop is moved completely inside of the uniform magnetic field.

AP PhysicsThursday 14.04.10

HomeworkW#1

Warm UpIf 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.

Agenda1. Warm Up2. Review HW3. Mechanical Waves Notes4. Mechanical Wave Practice

B

- +

Standards: Traveling, Wave Propagation, Standing Waves & Superposition

Objective: SWBAT understand how mechanical waves interact.

AP PhysicsFriday 14.04.11

HomeworkW#2

Warm UpWhat 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.

Agenda1. Warm Up2. Answers to M#10, & W#1

(Solutions to come this weekend)

3. Wave Properties4. Waves through mediums

Standards: B1 Interference & Diffraction single slit, double slit, diffraction

Objective: SWBAT will understand how light interferes to form patterns

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 shownabove.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 WavesElectromagnetic Waves

Mechanical Waves + Gamma Rays

Waves that don’t require 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.

c=fλ, speed of light c=3x108m/s

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

*Destructive Interference- The crest and trough of 2 waves combine to cancel out the wave. node

anti-node 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 wavesλn=2L/n. Using v=fλ -> fn=n(v/2L).

Diffraction & Interference of Light

dsinθ=mλ

d

Monochromatic light – light with one color or wavelength, like a laser

θm=1

m=2m=3

m=1

m=2

m=3

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.

y

L

Replacing sinθ with tanθ we get: d tanθ=mλ, but tanθ=opposite/adjacent so tanθ=y/L and d(y/L)=mλ

When light goes throu

Spherical MirrorsC=Center of CurvatureR=Radius of Curvaturef=Focal Length =R/2Spherical Mirror Equation:

do=object distance

di=image distanceMagnification Equation:

M>1 larger imageM<1 smaller image

C

C

Concave Mirror makes light converge.

R

Convex Mirror makes light diverge typically creating imaginary images.

R.

.

f

f

Optic axis

Optic axis

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 mirror3. 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.

C

F

• The image is inverted.• The image is reduced.• The image is real

Optic axis

Thin Lenses

f=Focal Length =R/2Thin Lens Equation:

do=object distance

di=image distanceMagnification Equation:

ho=object height

hi=image heightM>1 larger imageM<1 smaller image

C

Diverging Lens - makes light diverge as it travels through the lens . Made up of 2 concave lenses back to back.

Converging Lens makes light converge. Made up of double convex lenses.

R.

.

f

f

See. p.741

.f

.f

Optic axis

Optic axis

Imaginary, upright, reduced image

Real, inverted, magnified image

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?