Transcript Devil physics The baddest class on campus IB Physics

DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
PRE-DP PHYSICS
LSN 11-1: SIMPLE HARMONIC MOTION
LSN 11-2: ENERGY IN THE SIMPLE
HARMONIC OSCILLATOR
LSN 11-3: PERIOD AND THE SINUSOIDAL
NATURE OF SHM
Introductory Video:
Simple Harmonic Motion
Objectives
 Know the requirements for simple harmonic
motion (SHM).
 Know the terms equilibrium position,
displacement, amplitude, period, and
frequency. Be able to determine the values
for these terms from a graph.
 Calculate elastic potential energy from
displacement and spring constant.
 Calculate kinetic energy and velocity of an
oscillating object using conservation of
mechanical energy.
Objectives
 Understand the relationship between the
unit circle and SHM and how the two of
them relate to the sinusoidal nature of
SHM.
 Know the meaning of angular velocity (ω)
and how to compute it.
 Use angular velocity and amplitude to
compute position, velocity, and
acceleration.
Oscillation vs. Simple
Harmonic Motion
 An oscillation is any motion in which the
displacement of a particle from a fixed
point keeps changing direction and there
is a periodicity in the motion i.e. the
motion repeats in some way.
 In simple harmonic motion, the
displacement from an equilibrium
position and the force/acceleration are
proportional and opposite to each other.
Simple Harmonic Motion:
Spring
Definitions
 Understand the terms displacement,
amplitude and period
 displacement (x) – distance from the
equilibrium or zero point
 amplitude (A) – maximum displacement
from the equilibrium or zero point
 period (T) – time it takes to complete one
oscillation and return to starting point
Definitions
Definitions
 Understand the terms period and frequency
 frequency (f) – How many oscillations are
completed in one second, equal to the inverse of
the period
 period (T) – Time for one complete oscillation
1
T
f
1
f 
T
Simple Harmonic Motion
 In simple harmonic motion, the
displacement from an equilibrium
position and the force/acceleration are
proportional and opposite to each other.
Simple Harmonic Motion:
Spring
 The spring possesses an intrinsic restoring
force that attempts to bring the object back
to equilibrium:
F   kx
 This is Hooke’s Law
 k is the spring constant (kg/s2)
 The negative sign is because the force acts in
the direction opposite to the displacement -restoring force
Simple Harmonic Motion:
Spring
 Meanwhile, the inertia of the mass
executes a force opposing the spring,
F=ma:
 spring executing force on mass
F   kx
 mass executing force on spring
F  ma
Simple Harmonic Motion:
Spring
 Elastic Potential Energy:
PE  1 2 kx
2
 Kinetic Energy:
KE  1 2 mv
2
Simple Harmonic Motion:
Spring
 Conservation of Energy:
1 2 kx  1 2 mv  1 2 kx2  1 2 mv2
2
1
2
1
2
1 2 1
1 2
2
kx  mv  kA
2
2
2
2
Simple Harmonic Motion
 Understand that in simple harmonic motion
there is continuous transformation of energy
from kinetic energy into elastic potential
energy and vice versa
Simple Harmonic Motion:
Spring
ETotal  PE  KE  0  0
ETotal  1 2 kx2  0
ETotal  1 2 kx2 1 2 mv2
ETotal  0 1 2 mv2
ETotal  1 2 kx2  0
Simple Harmonic Motion:
Spring
no displ, no energy, no accl
max displ, max PE,
max accl, zero KE
half max displ, half max PE,
half max accl, half max KE
max displ, max PE,
max accl, zero KE
zero displ, zero PE,
zero accl, max KE
Simple Harmonic Motion:
Spring
 These forces remain in balance
throughout the motion:
ma  kx
 The relationship between acceleration
and displacement is thus,
k
a x
m
Simple Harmonic Motion:
Spring
k
a x
m
 Satisfies the requirement for SHM that
displacement from an equilibrium
position and the force/acceleration are
proportional and opposite to each other
Relating SHM to Motion
Around A Circle
Velocity
d
v
t
C  2r
2r
v0 
T
2A
v0 
 2Af
T
Period
2A
v0 
T
2A
T 
v0
1 2 kA  1 2 m v0
2
A

v0
m
k
2
Period
2A
T 
v0
A

v0
T  2
m
k
m
k
Frequency
T  2
1
f 
T
1
f 
2
m
k
k
m
Radians
 One radian is defined as
the angle subtended by
an arc whose length is
equal to the radius
l

r
lr
 1
Radians
Circum ference  2r
l

r
l  2r
Circum ference  2 rad 
Angular Velocity
2r
v0 
T

360  2
2

 2f
T
Position
x  A cos
x  A cost
x  A cos2ft
2t
x  A cos
T
Velocity
v  v0 sin 
v  v0 sin t
v  v0 sin 2ft
2t
v  v0 sin
T
Acceleration
k
a x
m
k
a0   A
m
a   a0 cos2ft
2t
a   a0 cos
T
Relating SHM to Motion
Around A Circle
 These equations yield the following graphs
Relating SHM to Motion
Around A Circle
 These equations yield the following graphs
Relating SHM to Motion
Around A Circle
 These equations yield the following graphs
Relating SHM to Motion
Around A Circle
 These equations yield the following graphs
Relating SHM to Motion
Around A Circle
 These equations yield the following graphs
Relating cos to sin
x  A cos2ft
2t
x  A cos
T
x  A sin 2ft
2t
x  A sin
T
Definitions
 Understand the terms displacement,
amplitude and period
 displacement (x) – distance from the
equilibrium or zero point
 amplitude (A) – maximum displacement
from the equilibrium or zero point
 period (T) – time it takes to complete one
oscillation and return to starting point
Definitions
Objectives
 Know the requirements for simple harmonic
motion (SHM).
 Know the terms equilibrium position,
displacement, amplitude, period, and
frequency. Be able to determine the values
for these terms from a graph.
 Calculate elastic potential energy from
displacement and spring constant.
 Calculate kinetic energy and velocity of an
oscillating object using conservation of
mechanical energy.
Objectives
 Understand the relationship between the
unit circle and SHM and how the two of
them relate to the sinusoidal nature of
SHM.
 Know the meaning of angular velocity (ω)
and how to compute it.
 Use the relationship between the unit
circle and SHM to compute position,
velocity, and acceleration.
QUESTIONS?
Homework
#1 - 12