for this section we start with hooke’s law. but we already learned this. (partially)
TRANSCRIPT
For this section we start with Hooke’s Law.
But we already learned this.(partially)
In another chapter we learnedThat the Potential energy for
A spring is
PE = ½ kx2
But Hooke’s Law is about the Force of a spring…
Felastic = -kx
If a mass of 0.55 kg attached toA vertical spring stretches the
Spring 2 cm from its equilibrium.What is the spring constant?
k = 270 N/m
So a stretched or compressedSpring has elastic potential energy.
A repeated motion, such as thatOf a spring, is called periodic
Motion.
At the equilibrium position, velocityReaches a maximum.
At maximum displacement, springForce and acceleration is
At its maximum.
In simple harmonic motion, The restoring force is proportional
To displacement.
Simple harmonic motion is the Vibration about equilibrium Position in which a restoring Force is proportional to the
Displacement from equilibrium.
A simple pendulum consists ofA mass called a bob, which isAttached to a fixed string.
The restoring force of a Pendulum is a component of
The bob’s weight.
So the forces acting on the bobAt any point include the force Exerted by the string (y) and
The bob’s weight resolved into Components in the y & x directions
For small angles, the pendulum’sMotion is simple harmonic.
At any displacement, a simple Pendulum has gravitational
Potential energy.
When measuring simple Harmonic motion, there are
3 major parts…
AmplitudePeriod
Frequency
Amplitude is the maximum Displacement from equilibrium.
The period is the time it takesTo execute a complete cycle.
Frequency is the number of Cycles (or vibrations)
Per unit time.
The SI unit for frequency is s-1, or hertz (Hz).
There is a formula for this…
f = 1T
T = Period
The period of a simple pendulumDepends on string length And free-fall acceleration.
T = 2π Lg
What is the height if a pendulumIf it has a period of 12s?
L = 36m
You can do the same thing For a spring…
The Period of a mass-springSystem depends on mass
And spring constant.
T = 2π mk
The body of a 1275 kg car is Supported on a frame by four springs
Each of which has a constant of2 X 104 . 2 people riding in the car
Have a combined mass of153 kg. Find the period of
Vibration of the car when it is Driven over a pothole on the road?
T = 0.84s
Transverse waveCompression
Wave
A wave is the motion of A disturbance through a medium.
A medium is the material throughWhich a disturbance travels.
A mechanical wave is a waveWhose propagation requiresThe existence of a medium.
A pulse wave is a single Non-periodic disturbance.
A periodic wave is a wave Whose source is some form
Of periodic motion.
Sine waves describe particlesVibrating with simple
Harmonic motion.
• Transverse Wave = the direction of the movement of the medium is perpendicular to the direction of the wave. Ex: Light.
• Longitudinal Wave = the direction of the movement of the medium is parallel to the direction of the wave. Ex: Sound.
There are 4 terms used to Describe waves…
CrestTrough
WavelengthSpeed
The crest is the highest pointAbove the equilibrium position.
A trough is the lowest point Below the equilibrium position.
The wavelength is the distance Between 2 adjacent similar
Points of the wave.
And speed is obviously how Fast the wave is moving.
A wave diagram
• Frequency = How often a wave occurs (f = 1/period)
• Period = time for 1 complete cycle
• Hertz (Hz) = the unit of frequency, in cycles per second.
Ex: A clock ticks at 1 Hz
(once per second).
To find the speed of a waveIs found through a new formula.
v = f λ
v = velocityf = frequency
λ = wavelength
The string of a piano vibrates With a frequency of 264 Hz. If the
Sound has a wavelength of 1.3 m, what is the speed?
v = 343 m/s
The law of superposition states That because waves are not Matter, but displacements of Matter, two waves can occupy
The same space at the same time.
Although when waves Interact with each other, they may
Be changed.
Constructive interference is Interference in which individualDisplacements on the same sideOf the equilibrium position are
Added together to form the Resultant wave.
Destructive interference is Interference in which individual
Displacements on oppositeSides of the equilibrium
Position are added together To form the resultant wave.
• Standing Wave = a wave in which parts of the wave appear stationary due to interference.
• Node = still part of standing wave• Antinode = max crest & trough of a standing
wave
Wave Properties
• Reflection = when a wave
hits and bounces back
The law of reflection states That the angle of incidence is
Equal to the angel of reflection.
Refraction is the change in Direction of waves at the
Boundary of 2 different media.
Diffraction is the spreading of Waves around the edge of a
Barrier.
Law of Reflection
Refraction
