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translational motion:
distance, velocity, acceleration. time
x = x0 + v0t + (1/2)at2
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translational motion:
velocity, acceleration and distance
v2 = v02 + 2ax
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translational motion:
velocity, acceleration and time
v = v0 + at
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how does a projectile stay in motion? what keeps it in motion?
inertia
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peak height of a projectile
v0 = sin(0) - sq.rt.(2gh)
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horizontal distance traveled of a projectile
x = vt . cos(0)
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peak velocity
no velocity, but acceleration = 10
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PE and KE of projectile object at its peak
- PE is maximized
- KE is minimized
(energy must be conserved)
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projectile path is independent of....
mass
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two objects launched with the same velocity will...
hit the ground at the same moment
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what determines the time of flight?
vertical velocity
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range of projectile is maximized at what angle from the horizontal?
450
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symmetry of projectile says what? (speed wise)
upward mirrors downward -
initial speed = final speed
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air resistance is greater on (surface area, shape, and speed)
- larger surface area
- irregularly shaped
- greater speed
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does mass affect force or path of air resistance
force = no
path = yes
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how does greater mass affect air resistance
force is the same, so it decreases acceleration
(F=ma)
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centripetal force (equation)
F = m . v2/r
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inertia
tendency of an object to stay in present state of motion
(keeps projectile in motion)
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law of universal gravitation
F = G(m1m2)/r2
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friction points in what direction?
always parallel to surface
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equation for torque
t = F r sin0
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if the board has mass, what do you do with torque?
F=mg at center of board
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equation for work (not for gases)
W = Fd cos0
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what direction is friction (relative to work)?
friction does negative work!
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work done lifting an object
W = Fd = mg x h
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what is gravitational potential energy?
work done by gravity:
change PE = -W
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energy and power
energy = work + heat
so, P = (w + q)/s
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1 revolution is equal to
2 pi r
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equation for angular momentum
L = l x m x v
l = lever arm, mv = linear momentum
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elastic collision
mechanical energy is conserved
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inelastic collision
mechanical energy is lost to internal energy (heat)
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perfect inelastic collision
2 objects stick together
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reverse inelasitc collisions (object dissipates into 2 sep. objects). In what direction do they travel
opposite to each other
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ex: man standing on a board and jumps off
what do you need to consider when determining their final positions?
move in opposite directions
consider their centers of gravity
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what is impulse?
change in momentum
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Machine: inclined plane (how is work minimized?)
straight up: W = ugh
ramp: W = mg x sin x h
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What is theta equal to in the ramp
height of ramp / distance of the ramp
the greater the distance (d) the smaller the angle, the less work needed
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Machine: lever (torque)
what does F need to equal to lift mass?
F = mg in opposite direction
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How do you decrease the force required to life the object?
increasing the lever arm
(doubling lever arm, reduces force by a factor of 2)
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In a pulley, what is the tension in the rope?
constant
Tension = Force
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In a double pulley system, what is the force required to lift mass m?
F = T
T = 2mg
F = (mg)/2
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alpha decay
2 protons, 2 neutrons
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traveling of alpha particle
not far
stopped by skin, paper
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beta decay
expulsion of an e-
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positron
B+ is emitted (-1 atomic #)
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electron capture
gain e- (-1 atomic number
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frequency of a gamma particle
high frequency particle
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fussion combining 2 (?) from (?)
combining 2 nuclei
from a heavier nucleus
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fission
splitting a single nucleus into 2 lighter nuclei
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where does energy for fusion and fission come from?
mass defect
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density formula
density = m/v
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density constant for gases and liquids?
constant for liquids and solids
change for gases, because they are compressible
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What is specific gravity?
density of a substance compared to density of water
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so specific gravity of water is
1
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formula for fluid pressure
P = F/A
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Do fluids at rest have uniform density in a sealed container?
yes
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What is the pressure experience by fluids at rest with uniform density?
P = density x g x y
y = depth of fluid
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Where is pressure greatest for a fluid at rest?
greatest depth (P=pgy)
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What if you have many fluids layered in a sealed container?
P = (pgy)1 + (pgy)2 + (pgy)3...........
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What is the pressure of a fluid at rest with uniform density in an open container
add atmospheric pressure to density x g x y
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hydraulic lift (equation)
pressure is transferred completely:
F1/A1 = F2/A2
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What is the velocity of a fluid flowing (if you don't know rate or area)?
v = sq.rt (2gh)
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buoyant force
upward force acting on a submerged object
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what is buoyant force equal to? (not equation)
weight of fluid displaced by submerged object
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equation for buoyant force
FB = (density of fluid) x (volume) x (g)
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floating object -
submerged portion of object =
density of object/density of fluid
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How much of an object will float in water if its specific gravity is 0.4?
60%
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does buoyant force change with depth?
No
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What is the apparent mass on an object (when it is submerged)?
mass of the fluid displaced
thats why we weigh so little in water
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equation for fluid flow
Q = (area)(volume)
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does fluid flow faster in a wider pipe, or a more narrow pipe?
narrow
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ideal fluid flows at a constant rate
K = Pressure + (density)(g)(h) + (1.2)(p)(v2)
K is constant, specific to fluid in a flow
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surface tension and temperature
increase temperature = weaker surface tension
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formula for stress
force/area
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formula for strain
change in dimension/original dimension
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what are stress and strain
stress is done on an object
strain is how the object responds
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modulus of elasticity
stress/strain
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What is Coloumb's law? (equation) What does it mean?
describes force between two charges
F = k (q1q2) / r
k = 9 x 109
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Coloumb's law resembles what? But?
gravitational force (G)(m 1m 2)/(r 2)
- but, gravitational force is attractive
- electrical force is repulsive
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electric field - in what way are the lines drawn? What does the length of the line indicate?
(+) ----------------> (-)
length = strength
(smaller is stronger)
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What is the electric field created by charge Q?
E = k x (Q)/(r2)
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What is the force felt by charge q in the electric field E?
F = E x q
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What makes and feels the field?
Q makes the field
q feels the field
[F = k x (Qq)/(r2)
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What is the potential energy of of the charge in electric field?
Potential energy (U) = force x displacement (like ugh)
U = Eq x h
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How does potential energy change when moving perpendicular to electric field?
doesn't change
same way that moving parallel to surface of the earth doesn't change gravitational potential energy
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What is an electric dipole?
created by 2 opposite charges with equal magnitude
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(+) and (-) fall/rise to lower/higher potential?
+ charge falls to a lower potential
- charge rises to a higher potential
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high/low potential and +/- potenital
- high potential = + potential
- low potential = - potential
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How do we measure movement of a charge?
current (A)
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So, what is current? (How is it measured)
Coloumbs/second
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Current flows in what direction (relative to potential energy)
current flows from high potential to low potential
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In what direction does current flow (relative to electron flow or electron velocity)?
current moves in opposite direction of e- flow
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conducting electricity: what are good conductors and poor conductors?
- good = allow e- to flow freely [metals]
- poor = hold e- tightly in place [resistors]
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What is induction?
charging a conductor
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circuit equations: current, voltage, resistance, capacitance
V = IR
I = Q/t
C = Q/V
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what is capacitance?
ability to store charge per unit voltage [Q/V]
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voltage is the same thing as...... and it depends on
potential energy
depends on distance
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plates that are further apart will have greater/less voltage and capacitance?
greater voltage
less capacitance
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What is a capacitor?
temporarily stores energy in a circuit
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What is the separation of charges in a capacitor?
emf between the plates
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what is resistance?
resistance to flow of charge
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resistance is directly proportionate to what?
length of wire
[R = density x (length/area)]
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resistance and temperature
resistance increases with temperature
[thermal oscillations impede with flow]
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Kirchoff's Rules:
- amount of current flowing in and out
- voltage around the circuit
-battery
- amount of flow in = amount of flow out
- votalge around any path in circuit must sum = 0
- battery adds energy to circuit
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How does battery add energy to the circuit?
increases voltage from one point to another
(emf = voltage added)
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Diaelectric constant (K)
substance between plates of a capacitor
- -must be insulator to separate charge
- -resists creating EF, in order to store energy
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Resistors in series/parallel
what is constant?
series = add [current is constant]
parallel = 1/R [voltage is constant]
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what is the terminal voltage? (equation)
V = emf - IR
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AC Current - what's going on?
e- don't move in one direction,
they oscillate back and forth
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maximum current and maximum velocity in an AC Current
Vmax = sqrt.(2) x Vmax
Imax = sqrt.(2) x Imax
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What creates a magnetic field?
charging electric field
currents (moving charges) creates the magnetic field
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+ and - of electric field corresponds to what in magnetic field?
north and south
north = + and south = -
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In what direction do magnetic lines point?
north -------> south
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Doess a stronger magnetic field have closer lines, or further apart?
closer lines = stronger fied
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How does the KE of a particle moving through the magnetic field change?
no work done by the magnetic field, means no change in KE due to the magnetic field
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What is magnetic force?
F = q x V x B x sin(0)
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force is applied in what direction relative to both velocity and magnetic field
force is perpendicular to both velocity and magnetic field
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What is the work done by magnetic force?
no work:
because it's perpendicular to velocity
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What way does magnetic field act?
like centripetal force (mv2/r)
because charged particle moves in a circle
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What will move through a magnetic field with a smaller radius: a proton or an electron
electron:
because it has smaller mass [F = mv2/r]
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Right Hand Rule
thumb = direction of current
fingers = direction of magnetic field
palm = direction of force
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What results from a change in magnetic field?
an electrical field
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What happens to the mechanical energy in a magnetic field when it is changed and creates an electric field?
mechanical energy to create the field is dissipated as heat
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What is the magnetic flux?
number of magnetic fields running through the loop
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what does change in magnetic flux do?
induces an emf
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What is a magnetic field generated by?
a moving charge
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moving charge experiences what when moving through a magnetic field?
force = qvBsin0
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In what direction is this force?
perpendicular to velocity and magnetic field (B)
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At equilibrium, in an electric and magnetic field, what is the net force acting on a particle?
0
force from electric field = force from magnetic field
Eq = qvBsin(0)
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How can we find the acceleration or distance of a particle traveling through an electric or magnetic field
F = ma
set force (Eq) or (qvbsin) = mass x acceleration
distance = (1/2)at2
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