3/17/2016
Waves
UH L4
(Chapter14)
Waves & Sounds
Disturbance from an
oscillating source
Energy is transferred
without transfer of mass.
Mechanical waves, such as sound, require
a medium for transmission. Sound moves
faster in solid than in liquid and a
1/5/2016
UE L2
* Conservation
of momentum
Since I = F*t = p, the condition for
conservation of momentum
(p = 0) is Fnet = 0:
* For a single object, if Fnet = 0, its
p = 0, or pf = pi
* for a two-object system, if
Fexternal, net = 0, then P = 0
or p1 + p2
3/17/2016
Wave on a rope
UH L5
Sound waves &
Doppler Effect
A 12-m rope is pulled tight with a tension
of 92 N. When one end of the rope is
given a thunk. It takes 0.45 s for the
disturbance to propagate to the other
end. What is the mass of the rope?
Spe
3/5/2016
Unit H Lesson1
(Ch13)
Periodic Motion
Simple Harmonic
Motion
Page 445 #2 A person in a rocking chair
completes 12 cycles in 21 s. What are the
period and frequency of the rocking?
T = 21 s / 12 cycles = 1.75 s / cycles
f =12 cycles / 21 s = 0.57
3/10/2016
Conservation of energy
UH L3
Conservation
of Energy in
a spring-mass system
E = kA2 = mvmax2 = kx2 + mv2
At location x where 0 < x < A,
E = kx2 + mv2
Conservation of energy U-x graph
kA2 = mvmax2 = kx2 + mv2
SHM conservation of E (page 447)
#46
3/7/2016
Solve page 446
UH L2
Period of Oscillation
- Spring-mass
- pendulum
Period of an oscillation
- a mass on a spring
T = 2
- a simple pendulum
T = 2
(Need to memorize above formula)
#14 x(t) = (5.4 cm) cos( 2t/0.73 )
#16
x(t) = Asin( 2t/T ) = (0.48
2/28/2016
UG L9
* Conservation of
Angular Momentum
* Rotational work /
power
Page 370 #69 A disk-shaped merry-go-round
of radius 2.63 m and mass 155 kg is at rest.
A 59.4-kg person running tangential to the rim
of the merry-go-round at 3.41 m/s jumps onto
2/24/2016
UG L8
Angular
Momentum
Angular Momentum
For point mass:
L=rxP
L = rmvsin = rmv
For a mass distribution:
L=I
#26 To determine the location of her center of mass, a
student lies on a lightweight plank supported by two
scales 2.50 m apart. If the l
2/23/2016
UG L7
Static
Equilibrium
Center of Mass and Balance
If an extended object is to be balanced, it must
be supported through its center of mass.
m1 > m2
m1
m2
A well-balanced meal
m3 = ?
Find m1, m2,
and m3.
net = r1 * m1g + r2 * m2g r3 * m3g = 0
2/16/2016
UG L5
Torque
F = ma
= I
A dumbbell-shaped object is composed by two
equal masses, m, connected by a rod of
negligible mass and length r. If I1 is the moment
of inertia of this object with respect to an axis
passing through the center of the ro
2/18/2016
UG L6
F = ma
= I
Static equilibrium
As shown in figure, find the acceleration a of
the block in terms of m, M, R, and g.
mg T = ma (1)
= RT = I (2)
note a =R ; divide (2) / R
T = ( MR2) a/R2 . (2)
(1) + (2) and isolate a a = mg / (m + M)
Torqu
2/10/2016
UG L4
Conservation of
Energy, again
2) Two children are riding on a merry-go-round.
Child A is at a greater distance from the axis of
rotation than child B. Which child has the larger
angular speed?
A) Child A
B) Child B
C) They have the same no
1/13/2016
UE L4
1-D inelastic
collision
Center of mass
* The center of mass of an irregular-shape
object follows a smooth trajectory like a
point mass.
Acceleration even
thought each point
on an object may move at different
acceleration, the center of m
2/4/2016
Unit G L 2
(Chapter 10)
Relating linear and
rotational quantities
Rolling motion
Angular Distance & linear distance s
s=r
#22 A CD speeds up from rest to 310 rpm in
3.3 s. Find the #revolution the CD makes.
given: 0 , , t, find , = ?
possible
2/3/2016
Unit G Lesson 1
(Chapter 10)
* Angular quantities
* Rotational
Kinematics
Angular Position 0 ,
Overview: Linear & Rotational Motion
displacement/angular ~
s
velocity/angular ~
v
acceleration/angular ~
a
force/torque
F
mass/moment of Iner
1/10/2016
UE L3
1-D inelastic
collision
2-D inelastic
collision
Completely Inelastic Collision
After collision, two objects stick
together
= their final velocities are the same
Elastic v.s. inelastic collision
Elastic collision
both the energy and the mo
1/5/2016
A review of different topics learned
Unit E Lesson1
(chapter 9)
* Linear Momentum
* Change in momentum
* Impulse
Kinematics describing motion; x, v, a, t
Newtons Law how force changes
motion; F, m, a
Work/Energy how force applied over a
distance
1/13/2016
Linear momentum of a single object
p = mv
Change in momentum
p = pf pi = mvf mvi
Total momentum of multi-objects
P = p1 + p2 +
Impulse imparts on an object
If 2-D,
Px = p1x + p2x
Impulse = change in momentum
I = p
& Py = p1y + p2y
Total kinet
11/27/2015
Unit D Lesson 1
* Work
* Work-kinetic
energy theorem
Work W = Fdcos
= F/d
= Fd/
- Is a scalar (has no direction)
- Can be +, 0, - Unit: Joule (J)
11/27/2015
Figure 7-2
Finding the work done by different forces
WN = N * d * cos(90) = 0
Wmg = m
10/5/2015
Unit A L1 (Ch2)
1-D Kinematics
distance, displacement,
average speed, average
velocity, velocity
Unit outline
distance and average speed
displacement & average velocity
position-time graph & instantaneous
velocity
average acceleration
graph
12/8/2015
Unit D Lesson 3
* Power
* Conservative force
* Potential energy
Do now: Solve page 213 #66
Hint: Consider W0 as given, you answer
will containW0 .
Given: W0 = k (0.02)2 k = 2W0 /(0.02)2
a) W = [2W0 / (0.02)2] * (0.01)2
= W0 / 4
b) W = k(0.03)2 k
12/2/2015
Solve p212
Unit D L2
* W-K theorem
* Work done
by variable forces
#26
7.2 J; 11 m/s; 18 J
#28
W = Kf Ki
W = - Fnet d Fnet = W/d
negative; 3.7 kN
Figure 7-9
Spring, spring force, and work
Hookes Law
spring force Fs = -kx
- k: (unit: N/m) spring
12/8/2015
Conservation of Mechanical energy
Unit D Lesson 4
* Potential energy
*Conservation of
mechanical
energy
Mechanical Energy
E = K + Ug + Us
* Kinetic
energy K = mv2
Gravitational potential energy
Ug = mgh
Elastic potential energy
Us = kx2
Conserva
1/23/2016
Unit B L1 (Ch4)
2-D Kinematics
Horizontal projectile
2-D 1-D
i.e. v0x = v0cos
v0y = v0sin
1-D 2-D
i.e. v = (v0x2 + v0y2)
= tan-1(v0y / v0x)
2-D motion
- 2-D motion can be represented
using two 1-D motions.
Procedure of problem solving
- 2-D two
11/18/2015
Uniform Circular Motion
Unit C L7 (Ch6)
Newtons 2nd Law
- Uniform circular
motion
speed is constant.
direction of motion continues to
change, so a 0
Acceleration associated with
direction change is called centripetal
acceleration ac
ac = v2
11/12/2015
Frictions
Unit C L5 (Ch6)
Newtons 2nd Law
- Friction
Frictions
Static friction is the friction between two
surfaces that do not move relative to
each other.
fs,max = sN is the maximum possible
static friction
The magnitude of the static fric
10/29/2015
Unit C L 1 (Ch5)
Newtons Laws
- First law
- Third law
- Free Body Diagram
Force - is capable of changing an
objects motion
- force is vector
- unit of force: N (newton)
1 N = 1 kg*m/s2
Net Force is the vector sum of all
forces act on one object
11/16/2015
Ideal Pulley
Unit C L6 (Ch6)
Newtons 2nd Law
- Pulley and multiobject system
Types of pulleys
T
massless
tension is the same anywhere in
the same rope
tension is parallel to the rope, and
pulls away from the object
2T
T
T
no friction
Solvin
11/10/2015
Unit C L4 (Ch6)
Newtons 2nd Law
in 2-Dimension
- Force not parallel to
acceleration a
Two boys are pulling a box across a
horizontal floor. If F1 = 5.00 N and F2 = 10.0
N, find the magnitude and direction of the
resultant force (net force) usin