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Physics
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PHYS 2001
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Kenneth Nollett
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Lecture

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8/27/2013
1. Standards and Units
a. Use S. I. system
i. Second
ii. Meter
iii. Kilogram
b. Use scientific notation
i. 3e8 = speed of light
ii. 1e-10 = x-ray length
iii. E for computer, superscript for anything else
c. Can’t add/subtract different units
d. Can always multiply by one
i. Use it to cancel unitsstoichiometry
e. Look at given conversions!!!
f. Watch positive vs. negative exponents
i. Watch ALL exponents
ii. Negative exponents mean inverseput in denominator
iii. 1 m/s = 1mse-1
g. Dimensional analysis
i. Dimension means type of quantity
1. Length
2. Mass
3. Time
ii. Can be built from simpler dimensions
1. Velocity = length/time
iii. Things being added/subtracted must be in same dimension
iv. Use multiplication/division to change dimensions
v. Sig figs- preciseness of measurement determined by preciseness of
instrument
8/29/13 2. Formulas
a. a=f/m acceleration is inversely proportional to mass
b. A=pi(r^2)
c. Trig formulas
i. A^2+b^2=c^2
ii. S=o/h
iii. C=a/h
iv. T=o/a
v. S-1A = angle means the angle that gives a=sin(angle)
3. Scalars and Vectors (size = magnitude)
a. Scalars
i. Magnitude only: time, mass, $
ii. Use basic math, abs. value so no neg. values
iii. For 2 scalars to be equal, they must have equal magnitude
b. Vectors
i. Have magnitude and direction: force, displacement, velocity
ii. If it makes sense to put a direction, it’s a vector
iii. When doing math, must include directions (use trig!)
1. Vector + or - vector=vector, A+ or -B=R
2. Scalar x vector = vector
3. -1 (vector) = vector in opposite direction
4. Can add any # of vectors by placing tail-to-head
5. Easiest if parallel/antiparallel
6. Semi-easy if perpendicular
7. If not any of the above, break into x and y components
iv. 2 vectors are equal if same magnitude and direction
9/3/2013
v. Adding vectors by components
1. Break all vectors being added into components
2. Add all x components 3. Add all y components
4. Find magnitude & direction using trig
4. Kinematics
a. Mathematical description (NOT explanation) of motion
i. Dynamics (considering forces) includes description of what causes
motion
b. 3 quantities (all vectors) describe all motion: displacement, velocity, acceleration
i. Displacement: change of position
1. NOT the same as distance traveled (path doesn’t matter here0
2. Avg. speed = distance traveled/elapsed time
a. No direction scalar
ii. Velocity: how fast displacement is changing
1. Avg. velocity = displacement/elapsed time
2. Speed is absolute value (scalar) of velocity
iii. Acceleration: how fast velocity is changing
1. Acceleration goes the same direction as CHANGE in velocity
a. Can be in different direction than velocity itself
2. Always related to a force
c. 4 kinematics equations
i. V final = v initial +at
ii. X = ½(v initial +v final)(t)
iii. X = v initial (t) + ½ a(t^2)
iv. V final ^2 =v initial ^2 +2ax
5. Slope of a function on a graph
a. ALWAYS CHECK AXIS LABELS!!!
b. Slope is how fast the height changes as you move right
i. Rise/run
ii. How steep?
c. Up to rightpositive slope
d. Down to rightnegative slope e. Straight line has same slope everywhere, curved line=changing slope
i. Slope at 1 point is slope of tangent line
f. When finding slope, use longest possible part of line
g. Position vs. time graph
i. Shows displacement
ii. Slope is velocity
h. Velocity vs. time graph
i. Shows velocity
ii. Slope is acceleration
iii. Area under is displacement
6. Average vs. Instantaneous values
a. Average, interval from beginning to end “events”
i. Any given event has a time, location, velocity, and acceleration
ii. Use 0 for initial time and distance
b. Instantaneous-at a given instant
i. Smallest possible t
9/5/13
7. Constant acceleration
a. Constant net forceconstant acceleration
b. Change in x = v(change in t)
c. Change in v=a(change in t)
d. If a is constant, average acceleration equals instantaneous acceleration
e. Deceleration = a going opposite to v
8. Problem solving
a. Read the problem & figure out the story
b. Draw out a diagram
i. Lay out coordinate system
ii. Always convert units
c. What is known/unknown
i. What are you looking for d. What are the relevant equations/rules
e. Solve problem
9. Free fall
a. An object is in free fall when the only force acting on it is gravity
i. An object going upward CAN be in free fall
b. Near earth’s surface, gravity causes all objects in free fall to accelerate at 9.8
m/s^2
c. The magnitude of the gravitational acceleration (g) can be either direction
i. Decide which way (up/down) is positive/negative
d. G depends mainly on distance from center and mass of earth
i. Difference on space station (greater distance)
ii. Different on moon (different mass)
9/10/2013
10. Implied conditions
a. Max height-figure out implications for velocity
b. Use “just after” and “just before” to avoid complications
c. Up, down, east, west, etc. determine coordinates and signs
d. Look for connections between parts of a problem to help find variables
11. Kinematics in 2 directions
a. A 2-d problem can simplify into 2 1-d problems
i. Break the motion into x and y components
ii. Time will be the same for both
b. Velocity is tangent to trajectory
i. Points in direction of instantaneous motion
c. Same equations as 1-d motion, but twice
i. Once with x once with y
ii. Emphasize that the quantities are VECTORS since now in 2-d
d. Make sure to pick which way is +/-
12. Projectile motion:2-d free fall
a. In free fall, gravity is only forcey acceleration is 9.8 m/s^2 down b. If y axis is chosen as vertical (usually is), then ax=0 m/s^2 ay=9.8 m/s^2 down
c. The motion of a projectile can be broken into x and y components
i. Vertical and horizontal are separate
ii. Dif. horizontal components don’t matter for vertical motion
9/12/2013
13. Intro to forces
a. Equilibrium
i. Forces balanced a =0
ii. AKA if a= 0, the forces are balanced
b. Weight means force due to gravity Fg=mg
c. Force is a vector if forces are balanced, x and y are balanced in their own rights
14. Projectile motion is symmetric
a. Same y = same absolute vy
b. w/out air resistance, v has the same magnitude up and down
i. but with opposite sign
c. speed=magnitude of velocity
9/17/13
15. Free body diagrams
a. Used to keep track of forces acting on an object
b. Forces the object is inflicting on other objects are not included
c. Gives visual, helps keep track of directions
d. Procedure:
i. Draw the object as a dot or small square
ii. Draw and label an arrow for each force acting on the object, approx. to
scale
16. Newton’s laws
a. 1 law of motion: An object maintains constant velocity (can be zero) unless there
is a change in net force
i. Net force= sum of all forces on an object
ii. 0 net force can mean all forces cancel, rather than no force period iii. “an object in motion will stay in motion, an object an rest will stay at rest
unless acted upon by an outside force”
nd
b. 2 law of motion: When a net external force acts on an object with mass m, the
acceleration that results is directly proportional to the net force on the object and
has a magnitude inversely proportional to the mass
i. F=ma, a = Fnet/m
ii. Inertia = object’s tendency to resist change in motion
iii. Mass measures inertia, S.I. units are kg
c. 3 law of motion: Whenever one body exerts a force on a second body, the
second body exerts an equal and opposite force on the first body
i. Occur simultaneouslynot a reaction
ii. All forces come in pairs
iii. The two forces act on different objects, not the same one
d. Law of universal gravitation: every object in the universe attracts every other
object
i. Gravitational force between objects is along a straight line between them
ii. Magnitude depends on mass and proximity
iii. F=G(m1m2/r^2)
1. G is newton’s constant
2. R is the distance between the objects’ centers
iv. g at earth’s surface = 9.8Fg=mg
v. weight means force applied by gravityperson weighs less on mount
Everest that at dead sea b/c more distance between centers
17. Fundamental forces
a. Electroweak force
i. Electricity
ii. Magnetism
iii. Weak nuclear (nuclear decay)
b. Strong nuclear force-holds atomic nuclei together
c. Gravitational force
i. Projectile motion
ii. Orbits d. Ultimately, all are “action-at-a-distance” forces, no matter how small the distance,
but most can be treated as contact forces
9/19/2013
18. Forces review
a. The net force is proportional to acceleration,
i. as stated by Newton’s 2 law
b. Gravitational force AKA weight is proportional to mass
19. Forces cause by surfaces
a. Force perpendicular to surface: normal
i. The equal and opposite force of Newton’s 2 law
ii. Keeps things from passing through each other
iii. What is perceived as weight is really the normal force of the floor
1. This is what is read on a scale
iv. Fn=mg+may
b. Force parallel to surface: friction
i. Tries to stop things from slipping against each other
ii. Always acts in direction to stop/prevent motion
iii. Strength determined by normal force and acceleration
1. Depends on if surfaces are already slipping or not
a. If they are: Kinetic friction, Fkf=msFn
b. If not: Static friction, Fsf is less than/equal to msFn
c. Fs > fk
d. M’s are muse
2. Ms and mk are determined by the materials
3. Ms is only enough to balance the other forces, not overcome them
20. Tension force
a. Acts on hanging objects
b. No normal force because no surface contact
c. Tension restricts motion instead
i. T-mg=may ii. Fn>weight, acceleration is upFn-Fg=may>0
iii. Fn

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