Transcript Physics 504

Physics 504
Exam Review
Exam Reminders
• Bring your writing implements, a geometry
set (at least ruler and protractor), a calculator
(with/without graphic display) & your brain.
• Exam is at 9:00am on June 13th, 2010.
• Come EARLY to return your textbook
Exam Reminders (2)
• Your exam will consist of 13 extended answer
questions.
• We learned 5 main topics this year:
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Geometric Optics (GO) [Reflection & Refraction]
Kinematics (KIN)
Dynamics (DYN)
Transformation of Energy (TOE)
GO – Shadow Formation
GO – Laws of Reflection
normal
reflected ray
incident ray
i
r
i = angle of incidence
r = angle of reflection
point of incidence
LAW I
• when light is reflected from a specular surface, the incident ray, the reflected ray and the
normal all lie in the same plane
LAW II
• the angle of reflection is equal to the angle of incidence ( i =
r)
GO – Types of Mirrors
GO – Field of Vision

hi d i

ho d o
GO – Mirror Formulae
•
where:
hi = height of image
ho = height of object
di = distance of image
do = distance of object
f = focal distance
Sign Conventions:
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Distances for objects and real images are positive
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Distances for virtual images are negative
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Upright = positive; Inverted = negative
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Real focal lengths are positive (concave mirrors)
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Virtual focal lengths are negative (convex mirrors)
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NB- Distances are measured from the vertex along the principal axis
GO – Principal Ray Diagrams
GO - Refraction
GO – Laws of Refraction
LAW I
• The ratio of the sine of the angle of
incidence to the sine of the angle of
refraction is a constant (known as the
index of refraction).
LAW II
• The incident ray and refracted ray are on
opposite sides of the normal at the point
of incidence, and all three lie in the same
plane.
LAW III
• When light passes from a medium that is
more optically dense to a medium which
is less optically dense, the light will bend
away from the normal.
• When light passes from a less optically
dense medium to a more optically dense
medium, the light will bend towards the
normal.
GO – Refraction Formulae
GO – Critical Angle
Happens for
M L
only!
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By using Snell’s Law, it is possible to calculate the angle of incidence which
would yield a refracted angle of exactly 90o.
this angle, the incident angle which would yield a refracted angle of exactly 90o,
is known as the critical angle.
The symbols used to denote the critical angle ic or c
Any angle that is in excess of the critical angle would NOT result in refraction,
but would instead result in reflection within the medium. This situation is aptly
called total internal reflection.
GO - Lenses
GO – Principal Rays *Lenses*
KIN –Resultants and Equilibriants
• a resultant vector is the ‘answer’ you obtain by
doing a vector sum (i.e. the final displacement)
• an equilibriant is a vector with the same magnitude
but exact opposite direction that if applied, would
bring the vectors into equilibrium.
• The sum of the resultant and equilibriant vectors is
always zero.
KIN – Graphing Motion
POSITION-TIME GRAPHS
• another way of examining displacement over time is
to graph the results in a position-time graph. The
slope of a position-time graph is the velocity.
VELOCITY-TIME GRAPHS
• another way of examining velocity over time is to
graph the results in a velocity-time graph. The slope
of a velocity time graph will yield the acceleration,
whereas the area under the curve of the velocitytime graph will yield the displacement.
KIN – Equations of Motion
• Uniform Motion (no
acceleration)
• Non-Uniform Motion
(uniform acceleration)
Projectile Motion
• You need to able to convert kinematics
equations to projectile motion equations
• The key is that there is no horizontal
acceleration.. so there is only the uniform
motion equation can be used here
• All of the formulas apply to the vertical
component of the motion
Projectile Motion 2
Tips for Projectile Motion:
• Write down the values that you have and try
to figure out which equation(s) you can use
• Always split into horizontal and vertical
• Time connects horizontal to vertical
• The vertical acceleration is -9.8m/s2
DYN – Newton’s
st
1
Law
Newton’s First Law: Law of Inertia
• “Every body continues in its constant state of
rest or uniform motion (velocity) in a straight
line, unless it is compelled to change that
state by forces impressed upon it.”
DYN – Newton’s 2nd Law
• “The change of motion is proportional to the motive force impressed, and
is made in the direction of the straight line in which the force is
impressed.”
• Otherwise stated, A body experiencing a force F experiences an
acceleration a related to F by F = ma, where m is the mass of the body.
• The acceleration of an object as produced by a net force is directly
proportional to the magnitude of the net force, in the same direction as the
net force, and inversely proportional to the mass of the object.
DYN – Newton’s
rd
3
Law
Newton’s Third Law: Action-Reaction
• “To every action, there is always opposed an
equal reaction; or, the mutual actions of two
bodies upon each other are always equal, and
directed to contrary parts.”
• Otherwise stated, for every action, there is an
equal or opposite reaction.
Fc 
mv 2
r
Centripetal Force
• Centripetal force is calculated based on the
following equation:
mv 2
Fc 
r
• Therefore, it is affected by turning radius, velocity,
and mass
DYN - Friction
• Frictional forces are usually forces that are acting
opposite a motion. Frictional forces are complex,
and depend on a wide variety of factors, including:
DYN – Coefficient of Friction
• The interaction between the two materials determines the
frictional force, and is calculated by using a factor known as
the coefficient of friction. This is a ratio used to calculate the
force of friction acting on a sliding object.
• The equation for the coefficient of friction is given by:
DYN – Hooke’s Law
• Hooke’s law states that the amount of deformation of an elastic object is
proportional to the forces applied to deform it. This relationship is given
by the following equation:
• Where:
• F is the force applied to the spring (elastic), given in Newtons (N)
• k is the spring constant, a property of the spring, given in N/m
Connecting KIN and DYN
• Occasionally you will come across a question
involving both kinematics and dynamics, ie. given
forces and must find a velocity
• The measurement that connects these two concepts
is acceleration
• If you are given forces, you will use F=ma once you
have the net force, and then an appropriate
kinematics equation
TOE - Work
• in physics, work has a very precise meaning that is
different from colloquial use.
• Work is said to be done on an object when a force
is applied to the object, and the object moves in
the direction of the applied force.
• Where W is the work done, is the force applied and
is the displacement.
TOE - Power
• power is defined as the rate at which work is done.
where P is the power required or used, W is the work
done, and is the time elapsed in seconds.
• Power is measured in Watts (W) where one Watt is
one Joule per second (J/s).
TOE – Mechanical Energy
• Energy: is defined as the ability to do work.
• Work, as previously defined, is the result of applying a force
to an object and moving the object in the direction of the
applied force. As such, work is the transfer of energy.
W = E. When work is done on an object, energy is
transferred to the object.
• Before delving into the study of energy, we must define one
final quantity – negative work. Negative work is a result of
friction when energy is transferred FROM the object instead
of TO the object. In this case, the force (friction) is directly
opposite the motion.
TOE – Mechanical Energy (2)
• Mechanical energy is defined specifically as
the sum of the potential energy and kinetic
energy in a system.
Et = Ep + Ek
E pg1 E k1 E pg 2  E k 2
Conservation of Energy
• The Law of Conservation of Energy states
that energy cannot be created or destroyed,
only transferred or transformed. This leads us
to the following equation for a closed system.
• Ek1 + Epg1 = Ek2 + Epg2
Conservation of Total Energy
• For most problems, we ignore resistive forces
(friction, air resistance)
• However, if the problem requires you to find
the energy lost (usually as thermal energy),
we can use the following equation:
• Ek1 + Epg1 = Ek2 + Epg2 + ΔETh