Physics Flashcards
Newton’s 1st Law (Law of inertia)
A object continues in a state of rest or motion at constant velocity, unless compelled to change that state by a net force.
Inertia: ability of an object to resist a change to its velocity
Mass: measure of object’s inertia
Force
Any influence capable of creating a mass to accelerate
A vector
Measured in Newtons (kg x m/s^2)
Center of Mass Equation
Cmass= (r1m1 + r2m2 + r3m3 + …)/mtotal
r: displacement vector between a reference point on each mass.
Step 1: choose reference point, “origin of coordinates” from which to measure each displacement vector.
Center of gravity
At the center of mass
Center of buoyancy
Center of mass of the fluid displaced by the submerged object
Newton’s 2nd Law
Fnet= ma
Constant force will not an cause an object to accelerate faster and faster, it will cause a constant (non-changing) acceleration.
Cannot accelerate a ball horizontally across a room by throwing it
Newton’s Third Law
Whenever an object exerts a force (via contact or field) on a second object, the second object always exerts an equal and opposite force on the first object.
Velocity vs speed
Velocity is a vector
Speed is a scalar
Velocity is change in displacement over change in time
Speed is change in distance over change in time
Constant velocity (or constant velocity)
Treat the same if and only if the distance traveled is on a straight line.
Constant velocity and constant speed THINK:
- no acceleration
- No note force
- all forces sum to zero
- no change in direction
- the object is in equilibrium
Acceleration
Change in velocity over change in time
Vector
If there is no net force, there can NEVER be an acceleration, however, there CAN be a force and no acceleration (forces cancel out)
Linear motion graphs:
How to interpret them
- What does the slope represent?
- Is this slope positive or negative? What does the sign of the slope tell you?
- Is the slope constant (straight line) or non constant (curved line)? What does the observation tell you?
- What value is on the y-axis?
- Is the y-value (+) or (-) (are you above or below the x-axis)? What does that tell you?
- Do you expect the value on the y-axis to be large or small at t=0?
Average velocity
v (ave)= (v1+v2)/2
Distance (or height) traveled
Distance= rate x time
Projectiles
Range: horizontal distance traveled
Range= vx x time
- Horizontal velocity NEVER changes (ignoring air resistance)
- Horizontal acceleration =0 always
- Vertical acceleration always = 10 m/s^2 downward
- Vertical behavior is exactly symmetrical (upward trip identical to downward trip)
- Time in air depends on the vertical component of the velocity only
- Range depends on both vertical and horizontal compounds
- Time is always the same for both x and y components of the motion
X= 1/2at^2
Find distance
v=(2gh)^0.5 or v=(2ax)^0.5
Use when asked for final velocity given drop height
tair= 2v/g
Used ONLY to calculate “round trip” times, or, total time in the air
Variable V must be vertical component of vi
Air resistance characteristics
Factors that affect magnitude of air resistance
- Cross Section Area: greater CSA impacting air, more air resistance
- Shape: less aerodynamic, more air resistance
- Velocity: greater velocity, more air resistance
Always assume AR is ignored! Unless specified.
At terminal velocity,
Fair= mg
Forces of gravity and air resistance are now balanced
Friction (kinetic and static)
Static: Ff= UsFn or Ff= Usmgcosx
Kinetic: Ff= UkFn or Ff= Ukmgcosx
Max static friction: friction created before an object begins to slide will always remain equal to the net applied force which the friction is opposing
Inclined planes
F=mgsinx (force down inclined plane, = to surface)
F=mgcosx (normal force on an inclined plane)
vf=(2gh)^0.5 (velocity of a particle at bottom of inclined plane)
Acceleration on projectile
Always 10 m/s^2 (downard) during entire flight. Doesn’t change at max height.
Acceleration NEVER becomes 0, even at the exact peak
VELOCITY does reach an instantaneous zero
Velocity vector is the only vector that changes direction during projectile motion
Vectors
Magnitude and direction Examples: Velocity Displacement Acceleration Force Weight Electric field Magnetic field Momentum Impulse Torque
Scalars
Magnitude only Examples: Mass Temperature Speed Work Energy Charge Time Density
Universal law of gravitation
F= Gm1m2/r^2
G= 6.67E-11 m^3/kgs^2
True everywhere
-Near earth, we assume gravity is 10 m/s^2, simplifying to F=mg
GIVES FORCE DUE TO GRAVITY
Gravity
Field that exists between any two objects switch mass
Field
Invisible influence capable of exerting a force on a mass or charge
Gravitational potential energy
PE= mgh (near earth)
PE= -Gm1m2/r (in space, near earth if not assuming g=10m/s^2)
PE per unit volume of fluid = ro(p)gh
Ro(p) = density (mass/volume)
g=Gm/r^2
- Gravity
- “Strength of gravitational field”
- Acceleration due to gravity
Hooke’s Law
Springs, resilient solids, rubber, bonds between atoms
F= k delta(x) (delta x is displacement of spring from its equilibrium point, NOT length of spring)
How to calculate spring constant of a hanging weights
For delta x, enter displacement from equilibrium point for one trial or difference in 2 trials. For F, use force applied in one trial or difference in force between 2 trials.
- Convert mass to force (F=mg)
Elastic potential energy
PE stored in a compressed spring
PE = 1/2 k (deltax)^2
This formula more likely to be used in connection with CONSERVATION OF ENERGY
Simple Harmonic Motion (SHM)
Anything that oscillates back and forth that can be represented by a sine wave.
Examples: pendulum and a mass on a spring
Essentially any mount that oscillates about an equilibrium position and shows the characteristics of sinusoidal pattern
Mass on a Spring
T= 2pi(m/k)^.5 (T=period)
Pendulum
T=2pi(L/g)^.5
T=1/f
Period is the inverse of frequency
Equilibrium
Terminal velocity Constant velocity Objects at rest Balanced fulcrums or boards hanging from strings Objects floating in a liquid
How to solve equilibrium problems?
Set forces or torques EQUAL to each other
Fleft=Fright, Fup=Fdown, etc
Draw Free body diagram
Torque
T=Fl or T=mgl or T=Frsinx l= lever arm r= distance between the force and the point of rotation rsinx(theta)= l (always) r=l only when x(theta)= 90 deg
When do I use T = Frsinx?
Use when FORCE applied is not perpendicular to r
Most are at 90deg, so sin90=1, T=Fr
ZERO NET TORQUE
If an object with a point of rotation is “stationary”, or “exactly balanced” then it must be in equilibrium and there must be ZERO NET TORQUE
Systems NOT in Equilibrium
Inclined Planes:
Fdown plane due to gravity= F=mgsinx
Ffriction is always parallel to the plane (opposite direction of sliding)
Two-Dimensional: up/down or left/right
Centripetal Force
Fc = mv^2 / r
Fc is ALWAYS caused by some other responsible force (friction, tension, gravitational force)
Centrifugal Force
Forms action-reaction pair with Fc Ball and string example: Fc= string is pulling on ball Centrifugal force= ball's force on string Newton's 3rd law
Centripetal Acceleration
ac= v^2/r
Direction of the vector: points radially toward center of circle
How to solve Centripetal Motion problems?
Set Fc=mv^2/r equal to the equation of whatever force is actually causing the force in the situation
Angular Motion
w=v/r or w=2pif w=angular velocity (in rad/sec) v= tangential velocity (in m/s) r= radius (in m, C=2pir) f= frequency (in Hz)
Angular Frequency
- Scalar
- Magnitude of the angular velocity vector
- In MCAT, ang. freq. and ang.velocity uses interchangeably (rad/sec)
Conversion from radians - degrees
2pi radians = 360 degrees
pi radians = 180 degrees
Rotational Equilibrium
If it’s not rotating, or rotating with a constant angular velocity (like normal equilibrium)
Momentum
p = mv
-In kg m/s
Momentum= inertia increased by velocity
Always conserved in a system
Collisions
Impulse
Change in an object’s momentum
Impulse = delta p
Impulse = m delta v
Impulse = Faverage x time (remember air bag example)
If no change in velocity, there CAN BE NO IMPULSE.
Car collisions
Collisions
Elastic: momentum and KE are both conserved
-Use conservation of Energy (ignore signs)
1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1^2 + 1/2m2v2^2 (relative speed same before and after)
Inelastic: momentum conserved, KE not conserved
-Use conservation of momentum (use SIGNS)
m1v1 + m1v2 = m1v1 + m2v2
Perfectly inelastic (Stuck together) m1v1 + m2v2 = (m1+m2)v3 where v3 is new velocity of stuck objects
Solids
Stress=Force/Area
Strain= change in dimension/ original dimension
Moduli of Elasticity
ME= stress/strain (general formula)
Young’s Modulus
Tensile or compressive stress/strain modulus (simultaneously pushing or pulling forces on both sides of an object; the two forces must be exactly aligned in both vertical or horizontal planes)
Shear Modulus
Shear stress/strain modules (simultaneously pushing or pulling forces; two forces are NOT aligned)
Bulk Modulus
Bulk stress/strain modulus (simultaneous compression from ALL sides)
Thermal Expansion
When solids are heated, they expand. When cooled, they shrink.
Delta L = alpha x L0 x Delta T
Energy
KE = (1/2)mv^2 PE(gravitational) = mgh or -Gmm/r PE (elastic) = (1/2)kx^2 PE (electrical) = Kqq/r or qEd or qV PE (capacitor) = 1/2QV or 1/2CV^2 or 1/2Q^2/C
Mechanical Energy
ME = KE + PE
In the absence of non-conservative forces such as friction, drag, air resistance, etc., mechanical energy is ALWAYS CONSERVED (total energy)
Law of conservation of energy
Energy in an ISOLATED system is always conserved
Open System
Both mass and energy can be exchanged with the surrondings
Closed System
Energy, but NOT mass, can be exchanged
Isolated system
NEITHER energy nor mass can be exchanged
Work= change in energy
1) W = Change in Energy. Think like this FIRST, if energy changed, then it’s WORK
- Change in velocity (change in KE=work, most common)
- Change in height (change in grav. PE = work)
- Change in position of masses/planets/etc. in space ( change in grav. PE)
- Change in position of charge (change in electrical PE = work)
- Compression of a spring (change in elastic PE = work)
- Friction (change in internal energy = work)
Work = Fdcos(o)
2) Think like this second. Any time force is applied across a displacement, work has been done.
UNITES = Joules
Work POSITIVE= Force and displacement in same direction
Work NEGATIVE= Force and displacement in opposite directions
1st Law of Thermodynamics
E = W + Q (W = energy transfer via a force, Q = energy transfer via energy flow from hot to cold)
Work-Energy Theorem
If a net force does work on a rigid object, the work done on that object is equal to the change in the KE of the object.
W = KEfinal - KEinitial
Machines
They reduce the amount of force necessary to perform a given amount of work. MACHINES NEVER REDUCE OF CHANGE THE AMOUNT OF WORK.
Ramps
Fmachine = mg(h/d)
- h is the height of the ramp and d is the distance along the hypotenuse. Fm is the force necessary to do the work with the machine, which will be less that doing it w/o the machine
Levers
Fm = mg(L1/L2)
L1 and L2 refer to the lever arms for the mass and the applied force, respectively.
Pulleys
Fm=mg/(# of vertical ropes directly lifting the mass)
CAUTION: not every rope that is vertically oriented should be counted and entered into the above equation. To be counted, a vertical section of rope must lift the mass DIRECTLY, either by being attached to the mass, or by lifting a pulley that is attached to the mass. To test, imagine grabbing only that rope and tugging it upward: does the mass lift??
Hydraulic Lifts
Fm=mg(h1/h2) or F= mg(A1/A2)
- h1 and h2 refer to the distance traveled by the large plunger and the small plunger respectively.
- A1 and A2 refer to the cross-sectional areas of the small plunger and large plunger, respectively.
Power
Think of POWER IN THIS ORDER 1) P = Change in Energy/time 2) P = W/t 3) P = Fdcos(o)/t 4) Pi = Fvcos(o) --- instantaneous power. Used when they ask for that POWER IN WATTS (J/s)
Intensity (Waves)
- Power per unit area. They transfer energy from one location to another within a specified time.
- THE INTENSITY OF ANY SOUND OR MECHANICAL WAVE IS DIRECTLY PROPORTIONAL TO THE AMPLITUDE SQUARED AND THE FREQUENCY SQUARED
- I is proportional to A^2f^2
- Units of W/m^2
- Area of a sphere: 4pir^2 (accounts for the denominators of the units)
Decibel System
Intensity in Decibels = 10 x log(I/I0); where I is the intensity of the sound wave in W/m^2, I0 is the threshold of human hearing (1e-12)
Types of Waves
Transverse vs Longitudinal: transverse waves displace the medium perpendicular to their direction of travel. Longitudinal waves displace the medium parallel to their direction of travel.
Transverse: electromagnetic waves, wave on string)
Longitudinal: sound waves
Electromagnetic waves
No medium required, capable of propagating in a vacuum; transfer energy and momentum.
Transverse Only
Mechanical Waves
Require a medium to propagate; transfer energy only.
Transverse: strings on a musical instrument. Cannot propagate in liquids or gases, need stiff medium.
Longitudinal: Sound waves
Wave Speed
v= lf (l is landa)
1) Wave speed is determined by the medium and sometimes (for a “dispersive medium”) wavelength and frequency.
2) Frequency NEVER changes when a wave moves from medium to medium
3) Wavelength DOES change when a wave moves from medium to medium
Wave Velocity in Mediums
v=sqrt(elastic/inertial)
On a string: v=sqrt(T/u); T:tension u:mass/length (thicker string < vel)
In a gas: v=sqrt(B/p). B: bulk modulus, p:denisty
In a solid: MUCH FASTER THAN ANY OTHER MEDIUM, since elastic moduli are much larger.
Superposition of waves
Constructive Interference: regions where the amplitudes or superimposed waves ADD to each other, increasing amplitude.
Destructive interference: regions where the amplitudes of superimposed waves subtract from each other, decreasing amplitude
Waves 360 degrees out of phase is the same as “in phase”, so there will be constr. inter. 180 deg. out of phase, waves will cancel out. 270 deg. out of phase, there will be multiple areas of const. and dest. interference, creating a new wave form.
Standing Waves
Special case of simultaneous constr. and destr. interference between two waves with identical f’s moving through the same medium in OPPOSITE DIRECTIONS. At points maximum destructive int. the waves cancel entirely (NODE) and at points of max const. interference (antinode)
Standing wave shows NO NET TRANSPORT OF ENERGY and does not PROPAGATE.
Beat Frequency
When two waves with close to the same freq. interfere
fbeat = l f1-f2 l
The Doppler Effect
Δf/fs= v/c
Δλ/λ= v/c
The Doppler shift perceived by the observer is DEPENDENT upon the relative velocity between the source and the observer. THE GREATER THE RELATIVE V THE GREATER THE SHIFT IN F OR λ
COLOR SHIFT DUE TO DOPPLER
White light can shift blue if the Doppler effect causes an INCREASE in f (decrease in λ) and red if Doppler effect causes decrease in f (increase in λ)
IMPORTANT NOTE ON THE DOPPLER EFFECT
- Add to the frequency (or SUBTRACT from the wavelength) if relative motion is TOWARD EACH OTHER.
- Subtract from f (add to wavelength) if relative motion is AWAY FROM EACH OTHER.
Sound
Sound is ALWAYS CREATED BY A VIBRATING MEDIUM. Vibrations propagate through liquids or solids, and generate pressure waves that propagate through gases such as air. SOUND CAN’T PROPAGATE IN A VACUUM.
Pitch
Higher pitch sounds have HIGHER f. Lower pitch sounds have LOWER f.
Infrasound: sound of a frequency too LOW to be perceived by ear
Ultrasound: sound of f too high to be perceived by human ear.
Harmonics
L = nλ/2 (string or pipe with matching ends- both nodes or both antinodes). λ= 2L/n
- Gives all harmonics n=1,2,3…
L = nλ/4 (one node and one antinode; pipe open at one end only) λ=4L/n
-Gives only ODD harmonics n=1,3,5..
IT IS IMPOSSIBLE TO HAVE A NODE AT THE OPEN END OF A PIPE AND IMPOSSIBLE TO HAVE AN ANTINODE AT THE CLOSED END.
Fundamental f
Frequency of the first harmonic.
Frequency of any harmonic = fundamental f x n
-Each harmonic always has ONE MORE NODE, AND ONE MORE ANTINODE, than the previous harmonic.
Overtones
The 2nd harmonic is called the 1st overtone, and so on.
FOR OSCILLATORS WITH MATCHING ENDS, THE λ OF THE 2ND HARMONIC = LENGTH OF STRING OR PIPE (λ=L)
Light
Photoelectric Effect
Observation that electrons are ejected from a material when light of sufficiently high frequency is used, but not until a threshold frequency is reached.
Energy of a Photon
E=hf, remember c=fλ, so E=h(c/λ)
Young’s Double Slit Experiment
Set up: Young shone a MONOCHROMATIC light through a screen with a SINGLE SLIT in it. The purpose of this slit was to create coherent wavefronts. Behind the 1st screen he placed a SECOND SCREEN with TWO NARROW, PARALLEL SLITS. These created the DIFFRACTION pattern Finally, behind the 2nd screen he placed a 3RD SCREEN. Light traveled through the firs two screens and formed alternating pattern of LIGHT AND DARK BANDS on the 3rd screen.
-Light traveling through each of the two slits in the middle must be COHERENT AND HAVE THE SAME f and polarization.
Young’s Experiment
x=λL/d
x- distance between fringes
λ- wavelength of light used
d- distance between the two slits
L- distance between the double slit (2nd screen) and final screen
- Strictly true only when x is much smaller than L
Diffraction
Tendency of light to spread out as it goes around a corner or through a slit. Without diffraction the characteristic interference patterns would not be formed.
Electromagnetic Spectrum
In order of decreasing f Gamma rays (e24-e20) > X rays (e20-e17) > UV (e16) > Visible (e15) > IR (e14-e12) > microwave (e10) > radio waves (e8-e6)
λ: Gamma (e-16-e-12) < X rays (e-10) < UV (e-8) < VISIBLE (390-700nm) < IR (e-6-e-4) < microwaves (e-2) < radio waves (e0-e2)
VISIBLE: ROY G VIB
Red light LOWEST ENERGY (lowest f and longest λ)
Violet light HIGHEST ENERGY (highest f and lowest λ)
Snell’s Law
Index of refraction: n=c/v (if n1, speed of light in medium is smaller than speed of light in vacuum)
Snell’s Law: n1sinθ1=n2sinθ2
Total Internal Reflection
For a light crossing a boundary from a slower to a faster medium (like from glass or water into air), if the angle of refraction would be 90 or more, the incident light does not enter the second medium at all, 100% of the light is REFLECTED off the boundary and back into the first medium.
FOR TOTAL INTERNAL REFLECTION, LIGHT MUST BE PASSING FROM A HIGHER INDEX MEDIUM TO LOWER INDEX MEDIUM (n1>n2)
CRITICAL ANGLE: angle of incidence for which the angle of refraction will be 90. sinθcritical= n2/n1, since n2sin90=n1sinθc would make sin90=1
Dispersion
Change in index of refraction based on the frequency (or wavelength) of a wave. In a material with dispersion, different f’s (or wavelengths) will be refracted to different angles, for the same incident angle. PRISM.
Lenses & Mirrors Image types
Virtual- there is NO ACTUAL LIGHT EMANATING FROM OR REACHING THE IMAGE (image formed behind a plane mirror)
Real- There is ACTUAL LIGHT AT THE IMAGE ( image formed on retina)
Lenses (single-lens systems)
Converging (aka, CONVEX, positive) = USUALLY produces PRI image.
-When object inside the focal point = NVU image
Diverging (concave)= ALWAYS produces NVU image
FOR OBJECTS FAR AWAY, ASSUME LIGHT RAYS HIT LENS PARALLEL. Considering convex lenses, the rays will be focused to the focal point at a distance f AWAY from the lens. As the object approaches the lens, however, the image will no longer be exactly at the focal point f.
Mirrors
Concave= like converging (convex) lens (PRI outside f, NVU inside)
Convex= like diverging (concave) lenses (ALWAYS NVU)
Also there are PLANE MIRRORS (the image and object will always be equal distances on either side of the mirror)
LENS/MIRROR CALCULATIONS
f=(1/2)r (for mirrors only)
1/f = 1/di + 1/do (thin lens equation, good for mirrors also)
M= -di/do = hi/ho
KEEP TRACK OF SIGNS
IF GET - # for M, the image is INVERTED
Four Rules (Lens and Mirrors)- single lens systems only!
1) Object distances (do) are ALWAYS +
2) Image distances (di) or focal point distances (f) are + IF THEY ARE ON THE SAME SIDE AS THE OBSERVER and - if on OPPOSITE SIDE.
3) The observer and object are on the same side for a MIRROR and on OPPOSITE sides for a lens (you have to be behind your glasses to see through them to view the object on the other side)
4) PRI/NVU: Positive, real, inverted and Negative, virtual, upright ALWAYS STAY TOGETHER. Positive means on the same side.
Near vs Far-Sighted
Near Sighted- ABLE TO FOCUS CLEARLY ON CLOSE OBJECTS, but not DISTANT OBJECTS. Image formed IN FRONT of retina.
Far Sighted- ABLE TO FOCUS ON FAR OBJECTS, but not CLOSE OBJECTS. Image formed BEHIND the retina.
Optical Power
P=1/f
When ciliary muscles contract, lens curvature increases, decreasing focal point, as focal point decreases, optical power INCREASES.
Two Lens System
Binoculars, telescopes, etc. THE IMAGE FORMED BY THE FIRST LENS BECOMES THE OBJECT FOR THE SECOND LENS.
Magnification: M= m1+m2
Power: P=p1+p2
