Presentation on theme: "Warm-Up: January 26, 2015 A 24.0 kg mass is attached to the bottom of a vertical spring, causing it to stretch 15.0 cm. What is the spring constant? What."— Presentation transcript:
1 Warm-Up: January 26, 2015A 24.0 kg mass is attached to the bottom of a vertical spring, causing it to stretch 15.0 cm.What is the spring constant?What is the final potential energy stored in the spring?
2 First Semester Grading Scale 65-75: B55-65: C45-55: D0-45: F
4 Oscillatory Motion and Waves OpenStax Chapter 16
5 Hooke’s Law RevisitedWhen an elastic object is deformed, it experiences a restoring force.Elastic means that it is capable of returning to its original shape/size.Includes springs, plastic rulers, rubber bands, guitar strings, etc.The restoring force is given by Hooke’s Law
6 Force ConstantThe force constant, k, is related to the rigidity (or stiffness) of a system.Larger k greater restoring force stiffer systemMeasured in N/mThe slope of a Force vs. Displacement graph (if the graph is linear)
8 You-Try 16.1What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0 kg person gets in?
9 You-Try 16.1What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0 kg person gets in?6.53x104 N/m
10 Energy in Hooke’s Law Work must be done in any deformation. Assuming no energy is lost to heat, sound, etc., then all work is transferred to potential energy.Since the force increases linearly with displacement, we can easily calculate the potential energy.
12 You-Try 16.2How much energy is stored in the spring of a tranquilizer gun that has a force constant of 50.0 N/m and is compressed m?If you neglect friction and the mass of the spring, at what speed will a 2.00 g projectile be ejected from the gun?0.563 J23.7 m/s
13 AssignmentRead Section 16.1 of OpenStax textbook (online): pages
15 Warm-Up: January 27, 2015A force of 20.0 N is applied to the tip of a ruler, causing it to deflect 4.00 cm. What is the force constant of the ruler?
16 Today’s Lab You will be assigned to a group. Your group’s goal is to determine the relationship between the following:The mass at the end of the stringThe length of the stringThe period of an oscillation (the time it takes to complete one oscillation).The angle of oscillationMaterials allowed:String (and scissors to cut the string)MassesRulers/Metersticks/ProtractorStopwatch (cell phone)Be sure to record everything in your lab notebook!
29 Warm-Up: January 29, 2015A stroboscope is set to flash every 8.00x10-5 s. What is the frequency of the flashes?
30 Simple Harmonic Motion: A Special Periodic Motion OpenStax section 16.3AP Physics 1
31 Simple Harmonic Motion Simple harmonic motion is oscillatory motion for a system where the net force can be described by Hooke’s Law.Pendulums are sometimes considered simple harmonic motion – only for small angles.Equal/symmetric displacement on either side of the equilibrium position.The maximum displacement from equilibrium is called the amplitude.
33 Importance of SHMPeriod and frequency are independent of amplitude, so simple harmonic oscillators can be used as clocks.They are a good analogue for waves, including invisible ones (sound, electromagnetic)
34 Period and Frequency For simple harmonic oscillators: What do period and frequency not depend on?
35 You-Try 16.4If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping.Calculate the frequency and period of these oscillations for such a car if the car’s mass (including its load) is 900. kg and the force constant of the suspension system is 6.53x104 N/mf=1.36 HzT=0.738 s
39 Think-Pair-ShareSuppose you pluck a banjo string. You hear a single note that starts out loud and slowly quiets over time. Describe what happens to the period, frequency, and amplitude of the sound waves as the volume decreases.
40 You-Try #18A diver on a diving board is undergoing simple harmonic motion. Her mass is 55.0 kg and the period of her motion is s. The next diver is a male whose period of simple harmonic motion is 1.05 s. What is his mass if the mass of the board is negligible?
43 Warm-Up: January 30, 2015If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?
44 Lab Reports DueOne person from each group collect lab notebooks from all group members and turn them in.
57 Warm-Up: February 2, 2015Punxsutawney Phil, seer of seers, prognosticator of prognosticators, has an extremely accurate pendulum clock in his secret lair. The period of this clock is exactly six weeks.What is the length of this pendulum clock?Is your answer realistic? Why or why not?
58 American Mathematics Competition New date and timeWednesday, February 25Time TBD
62 Simple Harmonic Oscillators Energy is conservedMaximum speed occurs at equilibrium position.
63 Pendulums (small θ) Energy is conserved Maximum speed occurs at equilibrium position.
64 You-Try 16.6Suppose that a car is 900. kg and has a suspension system that has a force constant of kN/m. The car hits a bump and bounces with an amplitude of m. What is its maximum velocity (assuming no damping)?0.852 m/s
65 You-Try 36Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.00x105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven; the driving force is transferred to the object, which oscillates instead of the entire building.What effective force constant should the springs have to make the object oscillate with a period of s?What energy is stored in the springs for a 2.00 m displacement from equilibrium?
70 You-Try 40A ladybug sits 12.0 cm from the center of a Beatles album spinning at 33.3 rpm. What is the maximum velocity of its shadow on the wall behind the turntable, if illuminated parallel to the record by the parallel rays of the setting sun?0.419 m/s
73 Warm-Up: February 3, 2015The device pictured entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring.If the spring stretches m while supporting an 8.00 kg child, what is its spring constant?What is the time for one complete bounce?What is the child’s maximum velocity if the amplitude of her bounce is m?
76 Friction is Real! Friction is not always negligible. Damping is the slowing and stopping of oscillations, caused by a non-conservative force (such as friction).Damping is sometimes part of a design (such as a car’s shock absorbers).For small damping, the amplitude slowly decreases while period and frequency are nearly unchanged.
77 DampingNon-conservative work removes mechanical energy (usually to thermal energy).
78 Large DampingLarge damping causes the period to increase and the frequency to decrease.Very large damping prevents oscillation – the system just returns to equilibrium.Critical damping is the amount of damping that returns a system to equilibrium as quickly as possible.Overdamped systems return to equilibrium slower than critical damping.
79 Think-Pair-ShareWhich is critical damping?Which is overdamping?
80 Applications of Critical Damping Car shock absorbersBathroom scale
81 You-Try 16.7Suppose a kg object is connected to a spring as shown, but there is simple friction between the object and the surface, and the coefficient of kinetic friction is equal to The force constant of the spring is 50.0 N/m. Use g=9.80 m/s2.What is the frictional force between the surfaces?What total distance does the object travel if it is released from rest m from equilibrium?
83 Warm-Up: February 4, 2015A novelty clock has a kg mass object bouncing on a spring that has a force constant of 1.25 N/m.What is the maximum velocity of the object if the object bounces 3.00 cm above and below the equilibrium position?How many Joules of kinetic energy does the object have at its maximum velocity?
85 Forced Oscillations and Resonance OpenStax section 16.8AP Physics 1
86 Think-Pair-ShareWhat do you have to do to swing high on a swing?
87 Natural FrequencyThe natural frequency is the frequency at which it would oscillate if there were no driving and no damping force.If you drive a system at a frequency equal to its natural frequency, its amplitude will increase. This is called resonance.A system being driven at its natural frequency is said to resonate.
88 Resonance The highest amplitude oscillations occur when: The system is driven at its natural frequencyThere is minimal damping
89 Think-Pair-ShareA famous trick involves a performer singing a note toward a crystal glass until the glass shatters. Explain why the trick works in terms of resonance and natural frequency.
91 You-Try 46A suspension bridge oscillates with an effective force constant of 1.00x108 N/m.How much energy is needed to make it oscillate with an amplitude of m?If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00x104 J of energy each second, how long does it take for the bridge’s oscillations to go from m to m amplitude?
94 Warm-Up: February 5, 2015How much energy must the shock absorbers of a 1200 kg car dissipate in order to damp a bounce that initially has a velocity of m/s at the equilibrium position? Assume the car returns to its original vertical position.
99 WavesA wave is a disturbance that propagates, or moves from the place it was created.Waves carry energy, not matter.Similar to simple harmonic motion, waves have a period, frequency, and amplitude.Waves also have a wave velocity, the velocity at which the disturbance moves.Waves also have a wavelength, λ, the distance between identical parts of the wave.
104 Transverse vs. Longitudinal In transverse waves, also called shear waves, the direction of energy transfer and the direction of displacement are perpendicular.Examples: strings on musical instruments, lightIn longitudinal waves, also called compressional waves, the direction of energy transfer and the direction of displacement are parallel.Example: soundSome waves, such as ocean waves, are a combination of transverse and longitudinal.
105 You-Try 52What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at m/s?
106 Superposition and Interference OpenStax section 16.10AP Physics 1
107 Superposition Most real-world waves are combinations of simple waves. When two or more waves arrive at the same point, their disturbances are added together. This is called superposition.In constructive interference, crest meets crest, and trough meets trough, and the resultant is a wave with a larger amplitude.In destructive interference, crest meets trough, and resulting amplitude is smaller than either original amplitude.Amplitude is zero for pure destructive interference.
114 Standing WavesSometimes waves superimpose in a way that causes an apparent lack of sideways motion.These waves are called standing waves.Standing waves have points that do not move, called nodes.The points that move the most are called antinodes.
122 Energy in Waves: Intensity OpenStax section 16.11AP Physics 1
123 Wave Energy Wave energy is related to wave amplitude The intensity, I, of a wave is the power, P, carried through area A.
124 Intensity Valid for any flow of energy. Has units of W/m2. Other intensity units include decibels.90 decibel = 10-3 W/m2
125 You-Try 16.9The average intensity of sunlight on Earth’s surface is about 700. W/m2.Calculate the amount of energy that falls on a solar collector having an area of m2 in 4.00 hours.What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200. times smaller than its own?