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MCAT 2015 Physics Examkrackers
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Gravity
Terms in this set (103)
scalar
physical quantity that has magnitude but no direction
vector
Physical quantity with both magnitude and direction; examples include displacement, velocity, forces and acceleration
average speed
distance/time
average velocity
displacement/time
acceleration
change in velocity/time
uniformly accelerated motion
∆X = Vot + 1/2(at^2)
∆V = at
V^2 = Vo^2 + 2a(∆x)
Vavg = 1/2 (V+Vo)
projectile motion
Vox = Vcosθ
ax = 0
ay= -10 m/s^2
Voy = Vsinθ
Peak height of projectile: V = √2gh where g = +10 m/s^2
mass
the quantitative measure of an object's inertia. An object's ____ tells us how much that object will resist a change in its motion.
weight
the gravitational force that an object experiences when it is close to a much larger body, such as the Earth. ___ is measured in newtons (N), and is equal to 'mg' at the surface of the Earth.
center of mass
the single point at which all of the system's mass can be considered to be concentrated. It is the point through which a single force can be applied in any direction to cause all points in the system to accelerate equally.
Newton's first law
states that an object in a state of rest or in a state of motion will tend to remain in that state unless it is acted upon by a net force.
Newton's second law
F=ma
Newton's third law
for every action, there exists an equal and opposite reaction. When object A applies a force to object B, object A experiences a force that is equal in magnitude but opposite in direction.
Newton's law of universal gravitation
G = 6.67 X 10^-11 m^3/kg/s^2; the magnitude of the gravitational force is directly proportional to both of the masses and inversely proportional to the square of the distance between their centers of mass.
inclined plane forces
parallel to the plane: mgsinθ
perpendicular to the plane: mgcosθ
Hooke's law
torque
measure of a force's ability to cause rotational acceleration
τ=Frsinθ
lever arm (l)
defined as the perpendicular distance from the axis of rotation to the line of action of the force.
τ=Force x l
equilibrium
state in which there is no net force and no net torque. Objects in ___ may be moving, but they are not accelerating (i.e. moving and rotating at a constant velocity).
Fupward = Fdownward
Frightward = Fleftward
τclockwise = τcounterclockwise
static and dynamic equilibrium
______ are both defined by constant velocity. The only difference is that in the former, the constant velocity is 0. The latter could have any velocities that are non-zero.
Energy
1.mechanical: ____ of a macroscopic system; it is further divided into kinetic and potential
2. non-mechanical: ___ of microscopic objects
kinetic energy
energy of motion
potential energy
energy of position; include gravitational potential energy and elastic potential energy
gravitational potential energy
elastic potential energy
an object is said to have ____ when a restorative elastic force acts on it. Most objects follow the Hooke's law.
heat
energy transferred between a system and its surroundings
work
energy transferred for any reason other than a temperature difference
first law of thermodynamics
W + q = ∆K + ∆U
work-kinetic energy theorem
only true when all energy transfer results only in a change to kinetic energy
power
work done by a force per unit time; W/t
Law of conservation of mechanical energy
states that when only conservative forces are acting, the sum of mechanical energies remains constant. Mechanical energy before = mechanical energy after.
K1 + U1 = K2 + U2 OR 0=∆K + ∆U
machines
reduce the force required to do a given amount of work. This ability to reduce applied force is called mechanical advantage. ___ do NOT change work!
ramp
inclined plane that reduces the force needed to do work by increasing the distance over which the force is applied.
sin θ = h/d
F= mgsinθ
So, F = mg(h/d) and W = mgh
lever
a beam attached to a fulcrum (pivot point). A ___ reduces the force needed to do work by increasing the distance over which force is applied, based on the principle of torque.
torque CCW= torque CW
mgL1=FL2
mg(L1/L2) = F
W = mgh1
pulley
acts by same principle as ramp and lever: allows force to act over greater distance so same amount of work can be done with less force. A ____ uses rope to do this.
density
how much mass the fluid contains in a specific volume; liquids are far more compressible than solids and gases compress more easily than liquids, so the ___ of a gas is easily changed while that of liquid is not
specific gravity
the density of a substance compared to the density of water. A ___ of less than one indicates a substance lighter than water, equal to one indicates substance equally heavy as water, and greater than 1 indicates it is heavier than water.
ρ(water) = 1000 kg/m^3 = 1 g/cm^3
fluid pressure
All the forces exerted by the individual molecules in a fluid added together
P = F/A = mg/a = ρgh
Ptotal = ρ1gh1 + ρ2gh2 + ρ3gh3 + ....
In open container, P = ρgh + Patm where Patm = 101,000 Pa
Pascal's principle
pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout that fluid
F1d1=F2d2
F1/A1=F2/A2
buoyant force
results from the pressure difference between the upper and lower surfaces of a submerged object. Since pressure increases with depth, the lower surface of an object experiences greater pressure than the upper surface. A fully submerged object displaces its volume in fluid.
Fb=ρVg
Archimedes principle
Fb=ρVg= mg; upward buoyant force equal in magnitude to weight of displaced fluid
floating, submerged, and sunk objects
-FLOATING: ρobj/ρfluid = Vfluid/Vobj; mass of fluid = mass of object; experiences Fg = Fb; ρobj < ρfluid
-SUBMERGED: mass of fluid = mass of object and Vfluid=Vobj; experiences Fg=Fb; and has ρobj=ρfluid
-SUNK: Fb < Fg so mass of fluid < mass of object; Vfluid=Vobj; Fb + Fnormal = Fg = mg; ρfluid/ρobject = mass of fluid/mass of obj; ρobj > ρfluid
motion of moving fluids
1. random translational motion: contributes to fluid pressure as in a fluid at rest; and
2. uniform translational motion: shared equally by all the molecules at a given location in a fluid
ideal fluids
differ from real fluids in the following ways:
1. have no viscosity
2. are incompressible, with uniform density
3. lack turbulence; experience steady or laminar flow - meaning all fluid flowing through any fixed point has the same velocity
4. experience irrotational flow - will not rotate about its axis as it flows
continuity equation
Q is the volume flow rate, A is cross-sectional area, and velocity (v=d/t)
Bernoulli's equation
restates conservation of energy in terms of densities and pressures, the intensive properties to describe fluids. It states that sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume of a fluid remain constant throughout the fluid;
WARNING: y is distance above some arbitrary point, NOT the same as h in P=ρgh, which is distance beneath the surface!
Torricelli's law
Derived from Bernoulli's equation:
P1 + ρgh1 + (1/2)ρv1^2 = P2 + ρgh2 + (1/2)ρv2^2
ρgh1 = (1/2)ρv2^2
2gh = v2^2
EQUATION: √2gh1 = v2
venturi effect
the decrease in pressure that occurs when a fluid flows into a constricted region of a pipe is known as the ____.
non-ideal fluid
real fluid; a ____ does NOT behave in opposite manner to an ideal fluid. Narrowing a pipe increases the velocity of the ideal fluid, and it will probably increase the velocity of a ___ as well. But with a ___ you have to also consider drag, which impedes flow. If you narrow the pipe in a ____, velocity will probably increase, but not as much as it would if there were no drag.
fluid flow
∆P = QR where R is the resistance to flow; note similarity to Ohm's law for voltage in electricity
Poiseuille's law
surface tension
describes the intensity of the intermolecular forces of a fluid per unit length; is a function of intermolecular forces, so it is affected by the temperature of the fluid (higher temperature leads to weaker ____) and by properties of the fluid
capillary action
-cohesive forces: intermolecular forces responsible for surface tension; if these are stronger then adhesive, a CONVEX surface is formed as fluid is pulled downward
-adhesive forces: forces between the molecules of the tube and the fluid molecules; if these are stronger, a CONCAVE surface is formed as fluid is pulled upwards
Coulomb's law
describes the magnitude of the force of the repulsion or attraction between 2 charged objects
k = 8.99 x 10^9 Nm^2/C^2, q represents the respective charges, and r is the distance between the centers of charge
Universal law of conservation of charge
the universe has no net charge
center of charge
a point from which the charge generated by an object or system of objects can be considered to originate
field
some type of distortion or condition in space that creates a force on a charge; lines of force point from positive to negative in the direction of the ___.
electric field
the electrostatic force per unit charge; E is a vector pointing in the direction of the field and has units N/C or V/m. For a point charge, it is found by dividing coloumb's law by q.
Electric force experienced by charge from electric field
F = qE
Potential energy of charge
U=qED; it is the force multiplied by the displacement, d.
Voltage
potential for work by an electric field in moving any charge from one point to another; units: volts (V); V=Ed= U/q
Electric dipole field lines and equipotential surfaces
conductors and resistors
Good ___, such as metals, allow electrons to flow relatively freely. Good ___ on the other hand hold electrons tightly in place (e.g. diamond and glass)
current
moving charge; coulombs/second
resistance
the measure of an object of a particular shape and size to resist the flow of charge; units: ohms
Ohm's law
Analogous to flow rate of a real fluid moving through a horizontal pipe with constant diameter: ∆P = QR
capacitance
used to temporarily store energy in a circuit in form of separated charge between two plates of conductive material.
C= Q/V
Energy stored in capacitor: U = 1/2
QV = 1/2CV^2 = 1/2
Q^2/C
dielectric
refers to the substance between the plates of a capacitor, which must be an insulator. A ___ contains dipoles oriented in random directions, acting to resist the creation of an electric field, allowing capacitor to store more charge.
resistors
capacitors
magnetic field
measured in units of tesla, T. Only moving charges produce this. The lines of force in a ___ point from the north pole to the south pole of the magnet that created the field.
Lorentz force
F = qvBsinθ
Faraday's law
waves
types:
-transverse: medium is displaced perpendicularly to the direction of wave propagation
-longitudinal: medium is displaced parallel to the direction of wave propagation
sound waves
____ travel significantly faster in water. In general V(sound in solid)> V(sound in liquid) > V(sound in gas). Elasticity increases as intermolecular attraction between molecules increases and inertia increases as mass and density increase.
V = sqrt(B/ρ) where B = bulk modulus (measure of elasticity) and ρ = density (measure of inertia)
constructive interference
occurs when the sum of displacements results in a greater displacement
destructive interference
occurs when the sum of the displacements results in a smaller displacement
intensity level
a measure of loudness, describes how intense a sound seems to be; Io is the threshold intensity of human hearing (the lowest intensity audible by the typical human). ∆ I (x10) = ∆β (+10); I = 2pi^2ρf^2A^2v
resonance
the condition where the natural frequency and the driving frequency are equal. It is impacted by the fact that real waves undergo attenuation (damping): the decrease in intensity of a wave propagating through a medium
Doppler effect
change in perceived frequency that occurs when a wave source and its observer move towards or away from each other. As source or observer move toward each other, the distance decreases, so does the time interval between wave fronts (period), perceived as an increase in frequency.
REMEMBER: when moving towards each other, f' > f so fraction is bigger than one (+ in numerator & - in denominator). Conversely, when moving away from each other, f' < f so fraction is less than one (- in numerator, + in denominator)
ESTIMATE: = ∆f'/fs = v/c and ∆ λ'/λs = v/c
fo = fs +/- ∆ f and λo = λs +/- ∆ λ
photons
pulses of electromagnetic radiation that can be thought of as localized particles of energy. An emitted ___ has a frequency f that is proportional to the energy of the electron, E
polarized
when light is ____, its electric and magnetic fields are oriented in a particular, rather than a random, way. Light is commonly described as horizontally, vertically, circularly (consists of electric fields of constant magnitude that change direction in a rotary manner), or randomly ____ (the electrons emitting the light have no preferred vibrational direction).
incidence and reflection
the angle at which a wave strikes an interface is called the angle of ___ and the angle at which it reflects is called the angle of ___. These angles are equivalent when light reflects off a plane (flat) surface.
index of refraction
the ratio of the speed of light in a vacuum, c, to the speed of light in a particular medium, v, is known as the medium's _____. Know that for water, n = 1.3 and for glass, n=1.5.
Snell's law
n1 and n2 are the indices of refraction for the media on either side of the interface, θ1 is the angle of incidence and θ2 is the angle of refraction.
total internal reflection
when light is coming from a medium with higher index of refraction, the angle of incidence can be so great as to cause _____. In other words, if the angle of incidence is large enough, all photons will be reflected at the angle of reflection, and none will refract (this is the critical angle).
sin (θcritical) = n2/n1
dispersion
separation of light into different frequencies due to their different indices of refraction in a medium.
thin film interference
occurs when a thin layer of a substance is placed between 2 layers of another substance that has a different index of refraction. At each interface, light can either reflect or refract. Depending on the changes to wavelength, phase, and path length, either constructive or destructive interference can occur.
CONSTRUCTIVE: 2L = (m+1/2)(λ/n2) for m=0,1,2...
DESTRUCTIVE: 2L = (m)(λ/n2) for m = 0,1,2...
where n2=index of refraction of the thin layer, L = thickness of the thin layer, λ = wavelength in air, and m = integer
diffraction
spreading of light that occurs when a wave bends around the edges of an object or an opening. ___ is significant when the size of object or opening is small relative to the wavelength of the wave. The smaller the object or opening and the larger the wavelength, the greater the bending of the wave.
Young's double-slit experiment
light is projected onto a screen with 2 small slits. The light waves diffracting through the 2 slits interfere with one another and produce a predictable pattern of alternating light and dark bands (maxima and minima) on the detector screen.
diffraction grating
a series of many small slits that diffracts a light source into its component colors.
x-ray diffraction
x-rays that are projected at a crystal scatter and create regular interference patterns unique to the structure of the crystal.
2dsinθ = mλ, for m = 1,2,3... where d = distance between reflecting planes, θ is angle from reflective plane to the ray, m is the order number of the maximum, and λ = wavelength of x-ray
focal length
the ___ of a mirror is equal to half the radius of curvature; for a converging lens or mirror, it is positive and for diverging mirror or lens, it is negative
power of a lens
inverse of the focal length (in meters), and measured in diopters
converging mirror
diverging mirror
always forms smaller images
converging lens (convex)
diverging lens (concave)
always forms smaller images
thin lens equation
in single lens system, object distance is always positive! A positive image distance (real) means it is on the same side as the observer. A negative image distance (virtual) means it is on the opposite side from the observer.
lens aberrations
in reality, images are often blurred and exhibit departures from theoretical images called _____.
1. chromatic: light of higher frequencies focuses closer to a lens than does light of lower frequencies; does not apply to monochromatic light; can be reduced by combining a converging lens of one index with a diverging lens of another index
2. spherical: rays farther from the center of a lens focus at different points than do rays closer to the center; can be reduced by allowing light rays to pass only through the central portion of the lens
combination of lens
M = m1*m2
Peff = P1 + P2
nearsighted and farsighted
A ____ person can see NEAR objects clearly. The lens of this person causes light to focus too NEAR the front of the eye. A ___ person can see FAR objects clearly, and lens causes light to focus too FAR from the front of the eye.
specific rotation
equals observed rotation/(concentration of solution x length of tube).
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