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:• Geometric Optics (GO) [Reflection & Refraction]• Kinematics (KIN)• Dynamics (DYN)• Transformation of Energy (TOE)

GO – Shadow Formation

GO – Laws of Reflection

LAW I• when light is reflected from a specular surface, the incident ray, the reflected ray and the

normal all lie in the same planeLAW II• the angle of reflection is equal to the angle of incidence ( i = r)

i = angle of incidencer = angle of reflectioni r

incident rayreflected ray

point of incidence

normal

GO – Types of Mirrors

GO – Field of Vision

GO – Mirror Formulae

• where: hi = height of image di = distance of imageho = height of object do = distance of object

f = focal distanceSign Conventions:• Distances for objects and real images are positive• Distances for virtual images are negative• Upright = positive; Inverted = negative• Real focal lengths are positive (concave mirrors)• Virtual focal lengths are negative (convex mirrors)• NB- Distances are measured from the vertex along the principal axis

o

i

o

i

d

d

h

h

o

i

o

i

d

d

h

h

GO – Principal Ray Diagrams

GO - Refraction

GO – Laws of RefractionLAW 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

• 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.

Happens for M L only!

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 MotionPOSITION-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 velocity-time 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 1st 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 3rd 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.

Centripetal Force

• Centripetal force is calculated based on the following equation:

• Therefore, it is affected by turning radius, velocity, and mass

r

mvFc

2

r

mvFc

2

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

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

2211 kpgkpg EEEE 2211 kpgkpg EEEE 2211 kpgkpg EEEE 2211 kpgkpg EEEE

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