Kinetic Energy
Chapter 6:
Work and Energy
Energy associated with the motion of an
object
1
KE = mv 2
2
Scalar quantity with the same units as work
Work is related to kinetic energy
Work-Kinetic Energy Theorem
Work and Kinetic Energy
When work is done
Chapter 16: Waves and Sound
A wave is a disturbance that propagates from
one place to another.
Notice that the wave can move a great
distance even though the medium moves
very little.
For example:
water waves
sound waves
waves on a string
EM waves (no
Sound
Sound is a longitudinal pressure wave.
The speed of sound in air is 343 m/s at standard
temperature and pressure. It increases with
increasing temperature.
The speed of sound in solids is greater than in gasses.
It is greater for stiffer material
Superposition and Interference
of Waves
If two or more waves are moving through a medium,
the resultant wave is found by adding together
the displacements of the individual waves, point
by point.
As a result of superposition, waves can interfere.
Interfer
Chapter 18
Electric Charges, Forces, and Fields
Energy in our World
Nuclear Fusion in sun E=mc2
Fundamental Forces in Physics
Gravity (gravitons)
Electromagnetism (photons)
Weak Interaction (W and Z bosons)
Strong Interaction (gluons)
All of physics is b
Spherical Charge Distributions
In general a spherical charge distribution
behaves as if all of its charge were at the
center of the sphere. Use the distance to the
center of the sphere to calculate the
electrostatic force.
q2
q1q2
q1
F =k
r
2
r
Newton: Ac
Electric Potential and
Electric Potential Energy
Symbol for electric potential is V
We will first define Electric Potential Energy
Symbol is U
Scalar quantity
(a magnitude, positive or negative, not a direction)
Unit is Joule (J)
Chapter 19
Electrostati
Conductors
Chapter 20
Electrostatic Potential Energy
Electrostatic Potential
Recall that the boundary condition for just outside a
conductor is that the electric field is perpendicular to the
surface, and inside the electric field is zero.
If a charge mov
Electric field points from higher electric
potential to lower electric potential.
A positive charge accelerates from a
region of higher electric potential energy
(or higher potential) toward a region of
lower electric potential energy (or lower
potentia
Charges in Motion = Current
Electric Current
and
Direct Current Circuits
Chapter 20
Current
In an amount of time t, an amount of charge Q,
flows through the area A, under the influence of
the electric field E. The current, I, produced by
this flow of cha
Direct Current (DC) Circuits
Electric Current
and
Direct Current Circuits
Chapter 20
A circuit is a loop comprised of elements such as batteries, wires,
resistors, and capacitors through which current flows.
Current can only flow around a loop if the loop
Archimedes Principle
Because the pressure in a fluid is greater below the
object than above, there is an upward buoyant force Fb
on any object in a fluid.
Archimedes Principle:
The upward buoyant force on an object is
equal to the weight of the displaced
Chapter 11: Fluids
Density
A fluid is a gas or a liquid.
A gas expands to fill any container
A liquid (at fixed pressure and temperature),
has a fixed volume, but deforms to the
shape of its container.
The density of a substance of uniform
composition is
Chapter 10: Oscillatory Motion
Simple Pendulum
A simple pendulum also exhibits periodic
motion
The motion occurs in the vertical plane and is
driven by gravitational force
The motion is very close to that of the SHM
oscillator
If the angle is <10o
Th
Potential Energy
Chapter 6:
Work and Energy
Potential energy is associated with the
position of the object within some system
Potential energy is a property of the system, not
the object
A system is a collection of objects interacting
via forces or proce
Escape Speed
from Earth
Gravity and BH
Escape Speed
Ei = E f
Initially, the object has
kinetic (velocity v) and
Ki + U i = K f + U f
potential energy. In order
to escape, the object must
1 mv 2 G mM = 0 + 0
have just enough energy to 2
R
reach infinity wi
Chapter 7
Linear Momentum and Collisions
Linear momentum is defined as:
p = mv
Momentum is given by mass times velocity.
Momentum is a vector.
The units of momentum are (no special unit):
[p] = kgm/s
Since p is a vector, we can also consider the
component
Chapter 7
Linear Momentum and Collisions
Linear momentum is defined as:
p = mv
Momentum is given by mass times velocity.
Momentum is a vector.
The units of momentum are (no special unit):
[p] = kgm/s
Recall that
F = ma and
F=
mv p
=
t
t
a=
v
t
Another way
Chapter 7
Linear Momentum and Collisions
Collisions
In general, a collision is an interaction in which
two objects strike one another
the net external impulse is zero or negligibly
small (momentum is conserved)
Examples: car crash; billiard balls
Collis
Chapter 7
Linear Momentum and Collisions
Glancing Collisions
For a general collision of two objects in threedimensional space, the conservation of momentum
principle implies that the total momentum of the
system in each direction is conserved
m1v1ix + m2
Angular Position,
For circular motion, the distance (arc length) s,
the radius r, and the angle are related by:
Chapters 08,09
=
s
r
> 0 for counterclockwise
rotation from reference line
Rotational Motion
Note that is
measured in radians:
RAD =
DEG
18
Zero Torque and Static Equilibrium
Consider the wheel shown below. Two forces of equal
magnitude are acting on the wheel. Will the wheel
remain at rest? NO it will rotate!
Chapters 08,09
Rotational Motion
The net force is zero, so there will be no linear
Rolling Motion
Chapters 08,09
Rotational Motion
If an object rolls without slipping, the
instantaneous point of contact with the surface, P,
remains stationary w.r.t. the surface due to the
static friction between the object and the surface
The center o
Chapter 10: Oscillatory Motion
Oscillatory: To move back and forth
between two points
Special kind of oscillatory motion: simple
harmonic motion SHM
Any object displaced slightly from stable
equilibrium will undergo SHM when released
Such a system is
Magnetism
Chapter 21
Magnetism
Known since antiquity
Pieces of Magnetite, also called lodestone
(Fe3O4) known by Greeks to exert both forces
of attraction and repulsion on each other
Chinese invented compass for navigation
The earth exerts a force on
Magnetism
Chapter 21
Magnetic Fields
Long Straight Wire
A current-carrying wire produces a
magnetic field
The compass needle deflects in directions
tangent to the circle
The compass needle points in the direction of
the magnetic field produced by the
University of Winnipeg:
Introduction to Physics
Work and Energy
In this chapter we introduce the concepts of work, energy and power. We define
kinetic energy, gravitational potential energy, and the potential energy stored in a
compressed or stretched spr
Solution:
Figure 4.5: Problem 4.5
We apply the 2nd law separately to each box.
For the 10 kg box:
y direction:
N2 - m2g
N2
=
=
m2g,
x direction:
T - fk 2 = m2a
= m2 a
T-
N2
= m2a.
T-
(13)
m2 g
For the 7 kg box:
y direction:
N1 = m1gcos
,
x direction:
m1gs
= m(g + a).
(10)
Fs
This gives:
a)
Fs = 50(9.8 + 0.5) = 515 N
b)
Fs = 50(9.8 + 0) = 490 N
c)
Fs = 50(9.8 - 1.0) = 440 N
A wooden plank is raised at one end to an angle of 30 o . A 2.0 kg box is placed on the
incline 1.0 m from the lower end and given a sl
80 m. Find a) the frictional force acting on the puck and b) the coefficient of kinetic
friction between the puck and the surface.
Solution:
Figure 4.2: Problem 4.2
a)
First we find the acceleration of the puck from the kinematic equations of
motion. We h