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distance, velocity, acceleration. time
x = x0 + v0t + (1/2)at2
velocity, acceleration and distance
v2 = v02 + 2ax
velocity, acceleration and time
v = v0 + at
how does a projectile stay in motion? what keeps it in motion?
peak height of a projectile
v0 = sin(0) - sq.rt.(2gh)
horizontal distance traveled of a projectile
x = vt . cos(0)
no velocity, but acceleration = 10
PE and KE of projectile object at its peak
- PE is maximized
- KE is minimized
(energy must be conserved)
projectile path is independent of....
two objects launched with the same velocity will...
hit the ground at the same moment
what determines the time of flight?
range of projectile is maximized at what angle from the horizontal?
symmetry of projectile says what? (speed wise)
upward mirrors downward -
initial speed = final speed
air resistance is greater on (surface area, shape, and speed)
- larger surface area
- irregularly shaped
- greater speed
does mass affect force or path of air resistance
force = no
path = yes
how does greater mass affect air resistance
force is the same, so it decreases acceleration
centripetal force (equation)
F = m . v2/r
tendency of an object to stay in present state of motion
(keeps projectile in motion)
law of universal gravitation
F = G(m1m2)/r2
friction points in what direction?
always parallel to surface
equation for torque
t = F r sin0
if the board has mass, what do you do with torque?
F=mg at center of board
equation for work (not for gases)
W = Fd cos0
what direction is friction (relative to work)?
friction does negative work!
work done lifting an object
W = Fd = mg x h
what is gravitational potential energy?
work done by gravity:
change PE = -W
energy and power
energy = work + heat
so, P = (w + q)/s
1 revolution is equal to
2 pi r
equation for angular momentum
L = l x m x v
l = lever arm, mv = linear momentum
mechanical energy is conserved
mechanical energy is lost to internal energy (heat)
perfect inelastic collision
2 objects stick together
reverse inelasitc collisions (object dissipates into 2 sep. objects). In what direction do they travel
opposite to each other
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
what is impulse?
change in momentum
Machine: inclined plane (how is work minimized?)
straight up: W = ugh
ramp: W = mg x sin x h
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
Machine: lever (torque)
what does F need to equal to lift mass?
F = mg in opposite direction
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)
In a pulley, what is the tension in the rope?
Tension = Force
In a double pulley system, what is the force required to lift mass m?
F = T
T = 2mg
F = (mg)/2
2 protons, 2 neutrons
traveling of alpha particle
stopped by skin, paper
expulsion of an e-
B+ is emitted (-1 atomic #)
gain e- (-1 atomic number
frequency of a gamma particle
high frequency particle
fussion combining 2 (?) from (?)
combining 2 nuclei
from a heavier nucleus
splitting a single nucleus into 2 lighter nuclei
where does energy for fusion and fission come from?
density = m/v
density constant for gases and liquids?
constant for liquids and solids
change for gases, because they are compressible
What is specific gravity?
density of a substance compared to density of water
so specific gravity of water is
formula for fluid pressure
P = F/A
Do fluids at rest have uniform density in a sealed container?
What is the pressure experience by fluids at rest with uniform density?
P = density x g x y
y = depth of fluid
Where is pressure greatest for a fluid at rest?
greatest depth (P=pgy)
What if you have many fluids layered in a sealed container?
P = (pgy)1 + (pgy)2 + (pgy)3...........
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
hydraulic lift (equation)
pressure is transferred completely:
F1/A1 = F2/A2
What is the velocity of a fluid flowing (if you don't know rate or area)?
v = sq.rt (2gh)
upward force acting on a submerged object
what is buoyant force equal to? (not equation)
weight of fluid displaced by submerged object
equation for buoyant force
FB = (density of fluid) x (volume) x (g)
floating object -
submerged portion of object =
density of object/density of fluid
How much of an object will float in water if its specific gravity is 0.4?
does buoyant force change with depth?
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
equation for fluid flow
Q = (area)(volume)
does fluid flow faster in a wider pipe, or a more narrow pipe?
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
surface tension and temperature
increase temperature = weaker surface tension
formula for stress
formula for strain
change in dimension/original dimension
what are stress and strain
stress is done on an object
strain is how the object responds
modulus of elasticity
What is Coloumb's law? (equation) What does it mean?
describes force between two charges
F = k (q1q2) / r
k = 9 x 109
Coloumb's law resembles what? But?
gravitational force (G)(m1
- but, gravitational force is attractive
- electrical force is repulsive
electric field - in what way are the lines drawn? What does the length of the line indicate?
(+) ----------------> (-)
length = strength
(smaller is stronger)
What is the electric field created by charge Q?
E = k x (Q)/(r2)
What is the force felt by charge q in the electric field E?
F = E x q
What makes and feels the field?
Q makes the field
q feels the field
[F = k x (Qq)/(r2)
What is the potential energy of of the charge in electric field?
Potential energy (U) = force x displacement (like ugh)
U = Eq x h
How does potential energy change when moving perpendicular to electric field?
same way that moving parallel to surface of the earth doesn't change gravitational potential energy
What is an electric dipole?
created by 2 opposite charges with equal magnitude
(+) and (-) fall/rise to lower/higher potential?
+ charge falls to a lower potential
- charge rises to a higher potential
high/low potential and +/- potenital
- high potential = + potential
- low potential = - potential
How do we measure movement of a charge?
So, what is current? (How is it measured)
Current flows in what direction (relative to potential energy)
current flows from high potential to low potential
In what direction does current flow (relative to electron flow or electron velocity)?
current moves in opposite direction of e- flow
conducting electricity: what are good conductors and poor conductors?
- good = allow e- to flow freely [metals]
- poor = hold e- tightly in place [resistors]
What is induction?
charging a conductor
circuit equations: current, voltage, resistance, capacitance
V = IR
I = Q/t
C = Q/V
what is capacitance?
ability to store charge per unit voltage [Q/V]
voltage is the same thing as...... and it depends on
depends on distance
plates that are further apart will have greater/less voltage and capacitance?
What is a capacitor?
temporarily stores energy in a circuit
What is the separation of charges in a capacitor?
emf between the plates
what is resistance?
resistance to flow of charge
resistance is directly proportionate to what?
length of wire
[R = density x (length/area)]
resistance and temperature
resistance increases with temperature
[thermal oscillations impede with flow]
- amount of current flowing in and out
- voltage around the circuit
- amount of flow in = amount of flow out
- votalge around any path in circuit must sum = 0
- battery adds energy to circuit
How does battery add energy to the circuit?
increases voltage from one point to another
(emf = voltage added)
Diaelectric constant (K)
substance between plates of a capacitor
- -must be insulator to separate charge
- -resists creating EF, in order to store energy
Resistors in series/parallel
what is constant?
series = add [current is constant]
parallel = 1/R [voltage is constant]
what is the terminal voltage? (equation)
V = emf - IR
AC Current - what's going on?
e- don't move in one direction,
they oscillate back and forth
maximum current and maximum velocity in an AC Current
Vmax = sqrt.(2) x Vmax
Imax = sqrt.(2) x Imax
What creates a magnetic field?
charging electric field
currents (moving charges) creates the magnetic field
+ and - of electric field corresponds to what in magnetic field?
north and south
north = + and south = -
In what direction do magnetic lines point?
north -------> south
Doess a stronger magnetic field have closer lines, or further apart?
closer lines = stronger fied
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
What is magnetic force?
F = q x V x B x sin(0)
force is applied in what direction relative to both velocity and magnetic field
force is perpendicular to both velocity and magnetic field
What is the work done by magnetic force?
because it's perpendicular to velocity
What way does magnetic field act?
like centripetal force (mv2/r)
because charged particle moves in a circle
What will move through a magnetic field with a smaller radius: a proton or an electron
because it has smaller mass [F = mv2/r]
Right Hand Rule
thumb = direction of current
fingers = direction of magnetic field
palm = direction of force
What results from a change in magnetic field?
an electrical field
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
What is the magnetic flux?
number of magnetic fields running through the loop
what does change in magnetic flux do?
induces an emf
What is a magnetic field generated by?
a moving charge
moving charge experiences what when moving through a magnetic field?
force = qvBsin0
In what direction is this force?
perpendicular to velocity and magnetic field (B)
At equilibrium, in an electric and magnetic field, what is the net force acting on a particle?
force from electric field = force from magnetic field
Eq = qvBsin(0)
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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