Final Exam Topics
Mechanics Unit I: Scientific Thinking in Experimental Settings – (1 problem)
1. Experimental design
Build a qualitative model
Identify and classify variables
2. Mathematical Modeling
Develop linear relationships
Relate mathematical and graphical expressions.
Mechanics Units II & III- Uniformly Accelerating Particle Model – (1 problem)
1. Concepts of acceleration, average vs instantaneous velocity
Contrast graphs of objects undergoing constant velocity and constant acceleration
Motion map now includes acceleration vectors
2. Multiple representations (graphical, algebraic, diagrammatic)
Introduce stack of kinematic curves
position vs. time (slope of tangent = instantaneous velocity)
velocity vs. time (slope = acceleration, area under curve = change in position)
acceleration vs. time (area under curve = change in velocity)
Mechanics Unit IV: Free Particle Model - Inertia and Interactions – (1 problem)
1. Newton's 1st law
Develop notion that a force is required to change velocity, not to produce motion
Constant velocity does not require an explanation.
2. Force concept
View force as one interaction between two objects
Express Newton's 3rd law in terms of paired forces
3. Force diagrams
Correctly represent forces as vectors originating on object
4. Statics
∑F = 0 produces same effect as no force acting on object
Mechanics Unit V: Constant Force Particle Model – (1 problem)
Newton's 2nd law
Develop mathematical models from graphs of acceleration vs force and acceleration vs mass
Create force equations from a force diagram (∑F = ma)
Mechanics Unit VI: 2-D Particle Models – (1 problem)
1. Projectile Motion (application of two particle models)
extend 1-D math models of accelerated motion to 2-D projectile motion
decompose projectile motion vectors into x and y components
describe projectile motion as the simultaneous occurrence of two 1-D motions
(horizontal and vertical)
Mechanics Unit VII – Energy – (1-2 problems)
1. View energy interactions in terms of transfer and storage
Develop concept of relationship among kinetic, potential & internal energy as modes of energy storage
emphasis on various tools (especially pie charts) to represent energy storage
apply conservation of energy to mechanical systems
2. Variable force of spring model
Interpret graphical models
area under curve on F vs x graph is defined as elastic energy stored in spring
3. Develop concept of working as energy transfer mechanism
Introduce conservation of energy
focus on W  E in this unit
Working is the transfer of energy into or out of a system by means of an external force. The energy
transferred, W is computed by W  F|| x
the area under an F-x graph, where F is the force transferring energy.
Energy bar graphs and system schema represent the relationship between energy transfer and storage
4. Power
W
Define power- rate at which energy is transferred:
P
SI unit: watt
t
Mechanics Unit VIII: Central Force Particle Model – (1 problem)
1. Uniform Circular Motion
Define the relationships between velocity and force
Define the relationships between velocity and radius
Define the relationships between velocity and mass
F
mv 2
r
2. Force Diagrams
Construct force diagrams which display the force acting on an object undergoing uniform circular
motion
Mechanics Unit IX: Impulse-Momentum Model – (1 problem)
1. Momentum
Define momentum and distinguish between momentum and velocity.
momentum = (mass)(velocity)
2. Impulse
Define impulse; distinguish between impulse and force.
I  Ft
Determine the impulse acting on an object
via a F vs t graph
given the change in momentum.
Determine the force acting on an object, given its change in momentum.
F
mv
t
3. Conservation of Momentum
Show that the system momentum before a collision is equal to the system momentum after the
collision.
system momentum = constant
Show that the total system momentum after an explosion remains zero.
Distinguish between elastic and inelastic collisions (∆Ek1 ≠ ∆Ek2)
Use conservation principles to solve momentum problems involving elastic and inelastic collisions
for initial velocity, final velocity or mass, given the other values.
E & M UNIT I – Electric Charge and Field – (1-2 problems)
By the time you finish this unit you should be able to:
1. Distinguish between the two kinds of particles that are responsible for electric interactions.
1. When two objects are electrically attracted to each other, this does NOT confirm that both objects
have a NET charge on them.
 When two objects repel each other, this DOES confirm that both objects have a net charge on
them, of the same type.
2. Distinguish between conductors and insulators.
3. Explain charging by conduction, induction and polarization in terms of the movement of electrons.
4. Use Coulomb’s Law to represent the relationship between electric force, charge and distance of
separation. Given information about the quantity of charge on two bodies and the separation distance,
determine the electrostatic force acting on the bodies.
5. Recognize that an electric charge produces an electric field. Represent the electric field produced by
point charges and charged plates.
6. Calculate the force exerted by a uniform electric field on a charged particle.
7. Use the superposition principle to calculate the strength of the electric field produced by charge(s) at
a given location.
E & M UNIT 2 – Electric Potential – (1-2 problems)
By the time you finish all labs, worksheets and related activities, you should be able to:
1
Draw parallels between gravitational and electrical: force, field, energy & potential.
Write formulas for each expression.
Solve for units for each quantity.
4. Use the volt as the unit of electric potential; use two different equations for potential.
3. Use relationships among potential, field, charge and energy to solve for missing quantities.
Waves Unit 1 – Oscillating Particles – (1 problem)
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Determine the effect of changing the amplitude of vibration, the mass, the length of string, or spring
constant in an oscillating system on the period of vibration for that system.
Compare the graphs of position vs. time, velocity vs. time and acceleration vs. time for an oscillating
system and analyze the phase relationships among the various graphs.
Examine graphs of kinetic energy vs. time, elastic energy vs. time, and total energy vs. time for the
oscillating system. Compare energy vs. time graphs to kinematic and dynamic graphs.
Waves Unit 2 – Mechanical Waves – (1 problem)
1. Demonstrate the behavior of wave pulses
 Determine the speed of a pulse through a medium and understand the speed of pulses through a
medium is constant.
 Determine how the speed of a pulse is affected by changes in amplitude, pulse length, type of pulse,
tension, or properties of the medium.
 Show that waves transfer energy without the accompanying transfer of matter.
2. Demonstrate the behavior of transverse pulses in springs interacting with a boundary.
 Show reflection of a single pulse on a spring from a fixed end and a free end.
 Show reflection and transmission of a single pulse as it passes from one medium into another.
3. Examine the interaction of multiple pulses traveling on a spring
 Apply the principle of superposition to two pulses that meet in a medium.
4.
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Demonstrate the characteristics of periodic waves
Demonstrate and give examples of how disturbances in a medium produce periodic waves.
Introduce and develop a wave vocabulary.
Explain how the frequency of mechanical wave is determined by the source, not the medium.
Show how periodic waves in a finite medium produce standing waves
Determine the relationships among frequency, wavelength and velocity using both graphical and
mathematical representations.
Quantify the effects of the elastic and inertial properties of a medium on the speed of propagation of a
wave.
Waves Unit 3 – Sound – (1-2 problems)
1. Transverse vs. longitudinal waves
 Distinguish between transverse and longitudinal waves.
 Compare and contrast standing longitudinal and transverse waves.
 Identify source, medium, and receiver for sound.
2. Speed of sound waves
 Measure the speed of sound.
 Sound travels at different speeds in different mediums
3. Resonance and standing waves
 Describe the conditions necessary for resonance.
 Be able to use the medium boundaries to determine the type of standing wave.
 Describe standing waves on strings and solid bars, in open and closed tubes.
4. Characteristics of sound waves
 Relate frequency to pitch, amplitude to loudness, and identify pressure nodes and antinodes
5. Harmonics and beats
 Describe harmonics and how they add and coexist in musical instruments.
 Describe beats and how they arise.
 Calculate beat frequency.
6. Doppler effect
 Describe the Doppler effect and why it occurs.
 Derive the simple Doppler effect formula.