MCAT - Physics Flashcards
1 Angström
10^-10 m
1 electron-volt (1eV)
1.6x10^-19J
The amount of energy gained by an electron accelerating through a potential difference of one volt.
Vector
Magnitude & direction
Scalar
Magnitude only
distance, speed, energy, pressure, mass
Vector Addition
Use tip-to-tail method when the arrows are proportional to the magnitude
You can also break vector into x- & y-components:
x = vcos(θ), y = vsin(θ)
v = sqrt(x^2 + y^2) (Pythagorean theorem)
θ = tan^-1(y/x)
Vector Subtraction
Add one vector to another vector in an opposite direction
V = A-B = A + (-B)
Then continue with tip-to-tail method
You can also use component method
Vector x Scalar
B = nA
Multiplying by a scalar of the opposite sign will flip the direction of the vector
Vector x Vector
Dot product (A . B): ABcos(θ) Creates a SCALAR product
Cross Product (AxB): ABsin(θ) Creates a VECTOR product, then use the right-hand rule to determine the direction of the resultant vector. **AxB does not equal BxA**
Displacement (denoted as x or d)
Change of position in space. Vector quantity
Distance (d)
Scalar, entire path travelled
Velocity (v)
Rate of change of displacement. Vector quantity
Units (m/s)
Speed (v)
Rate of the actual distance traveled over time
Scalar
Force (F)
Push or pull. Vector
Units (N) 1N = 1 (kg x m)/s^2
Gravity (g)
Attractive force felt by all forms of matter
Fg = (Gm1m2)/r^2,
where G = 6.67x10^-11 (N x m^2)/kg
Friction
Type of force that opposes the movement of objects. Opposite the direction of the motion. -Static friction: μN -Kinetic friction: μN Static friction > Kinetic friction Surface area doesn't matter
Mass (m)
Measure of a body’s inertia. Amount of matter in an object. Scalar
Weight (Fg)
Gravitational force on an object’s mass. Vector. Units (N)
Fg = mg
Acceleration (a)
Rate of change of velocity due to an applied force. Vector
a = Δv/Δt
Units (m/s^2)
Slope of the velocity vs. time graph = instantaneous acceleration
Newton’s 1st (N1)
Fnet = ma = 0
Inertia. Object will remain at rest unless acted on by a force
Newton’s 2nd (N2)
Fnet = ma. Nonzero resultant force vector will accelerate (a) a mass (m)
Newton’s 3rd (N3)
Fab = -Fba
Equal and opposite forces
Equations of linear motion (four of them)
vf = vi + at x = (vi)t + (at^2)/2 vf^2 = vi^2 + 2ax x = vt
Air resistance
Like a friction. Objects in free fall will experience a growing drag force as the magnitude of the velocity increases. Eventually, the drag force will equal in magnitude to the weight of the object, it will fall at a constant terminal velocity.
Projectile Motion
Motion along two dimensions.
Usually only vy changes due to gravity, vx is constant under negligible air resistance.
X and Y components are independent of each other
Inclined Planes
Divide force vectors into components that are parallel and perpendicular to the plane.
Gravity must be split.
Fg(parallel) = mgsinθ
Fg(perpendicular) = mgcosθ
Circular Motion
When motion is uniform, the instant. velocity vector is tangent to the circular path.
Object along a circular path has a tendency (inertia) to break out of the pathway.
Centripetal force
Points radially inward, prevents the object from breaking into linear motion. Generates a centripetal acceleration.
Fc = (mv^2)/r
Torque
Moment of force. Application of force at some distance from the fulcrum (fixed point a lever arm rests on).
Depends on the magnitude of the force and on the length of the lever arm (dist. b/n force and the fulcrum).
τ = r x F = rFsinθ
Clockwise = negative, Counterclockwise = positive
Mechanical Equilibrium conditions (Translational motion, rotational motion, and torque)
Vector sum of all forces is zero.
Translational: constant velocity, speed, and constant direction
Torque: object is either not rotating at all or at constant angular velocity
Energy (E)
Total Mechanical Energy
System’s ability to do work.
E = U - K
Kinetic Energy (KE) or (K)
Energy of motion.
KE = 1/2mv^2
Units (J = (kg.m)/s^2)
Potential Energy (PE) or (U)
Energy associated with a given object’s position in space or other intrinsic qualities of the system
Gravitational: Depends on object’s position w/respect to the ground (datum)
- U = mgh
Elastic: Springs and other elastic systems. When compressed or stretched from equil. length, it gains PE.
- U = 1/2kx^2
1st Law of Thermodynamics
Conservation of mechanical energy.
Conservative forces: path independent, energy change is equal regardless of the path taken. ΔE = ΔU - ΔK = 0
Non-conservative: Like friction, energy is lost from the system in another form, like heat.
ΔU = Q-W \+ΔU = increasing temp -ΔU = decreasing temp \+Q = heat flows into system -Q = heat flows out \+W = work done by the system (expansion) -W = work done on system (compression)
Work
Energy is transferred from one system to another.
W = F.d = Fdcosθ
Work done on or by a system can be determined by finding the area under pressure-volume graph. Pressure can be thought of as “energy density”
Pressure-Volume Relationships
- Gas expands: work was done, work is positive
- Volume stays constant, volume changes (ΔV = 0): No work is done, no area under curve. *Isochoric/Isovolumetric
- Pressure remains constant as volume changes (ΔP = 0), area under curve is a rectangle. W = PΔV Isobaric
Power
Rate at which energy is transferred from one system to another.
P = W/t = ΔE/t
Units (J/s)
Work-Energy Theorem
Wnet = ΔK = Kf - Ki
Mechanical Advantage
Any device that allows for work to be accomplished through a smaller applied force.
Mech. adv. = Fout/Fin
Fout = force exerted on object by simple machine
Fin = force actually applied on the simple machine
distance through which the smaller force must be applied INCREASES. Work DOESN’T CHANGE
Simple Machines (6 of them)
Wedge, wheel axle, lever, pulley, and screw
Pulleys (eq. of efficiency, how they work)
Apply a smaller force through a greater distance.
Efficiency: Wout/Win = ((load)(load distance))/((effort)(effort distance))
Load dist. is height you want to lift obj. It needs to be pulled a displacement twice that amount, the effort distance.
Adding six pulleys results in 1/6 the load, but you need to pull a length six time the desired displacement.
0th Law of Thermodynamics
If first and second object are in thermal equil., and the second is in thermal equil. with the third, then the first and third are in thermal equil.
If a = b & b = c, then a = c.
Temperature
Proportional to the average kinetic energy of the particles that makes up the substance. Spontaneous transfer of energy from high to low.
3rd Law of Thermodynamics
Entropy of a perfectly-organized crystal at absolute zero is zero.
Δ1K = Δ1C
F = 9/5C + 32
K = C + 273
Thermal Expansion (eq. of length and volumetric thermal expansion)
ΔT results in the change of a solid’s length.
- ΔL = αLΔT, α = coeff. of linear expansion, units (K^-1 or C^-1)
- ΔV = βvΔT (β = 3α)
Isolated Systems
Not capable of exchanging energy or matter with their surroundings. Total change in internal energy is zero. Ex. bomb calorimeter
Open Systems
Can exchange both energy and matter. Energy may transfer in the form of heat or work. Ex. boiling pot of water, humans, un-contained explosions
Closed Systems
Capable of exchanging energy, but not matter, with the surroundings. Ex. gases in vessels with movable pistons.
2nd Law of Thermodynamics
Objects in thermal contact not in thermal equil. will exchange heat energy from high to low until they both have same temp.
Units of heat: 1 Cal = 10^3 cal = 4184 J = 3.97 BTU
Conduction (heat transfer)
Direct transfer of energy from molecule to molecule through collisions. Must be in direct contact.
- Metals are best heat conductors b/c rapid energy transfer due to sea of e-
- Gases are poorest b/c collisions occur infrequently
Convection (heat transfer)
Transfer of heat by physical motion of a fluid over a material. Convection involves FLOW, so only liquids & gases can transfer heat this way. Ex. running a cold water bath to cool rxn
Radiation (heat transfer)
Transfer of heat by electromagnetic waves (EM). Can occur through a vacuum. Ex. the sun
Specific heat (c)
Amount of heat energy required to raise one gram of a substance by one degree C or K. Changes according to an object’s phase.
q = mcΔT
Units (1 cal/g.K) or (4.184 J/g.k)
Heat of Transformation
Phase changes occur at constant temp. Temp will not change until all of the substance has been converted from one phase into to the other.
q = mL, where L = latent heat
Heat of fusion and heat of vaporization
Adiabatic
Q = 0 ΔU = -W
Entropy
Measure of spontaneous dispersion of energy at a specific temp.
ΔS = Qrev/T
Work must be done to concentrate energy
Net entropy change is zero in physically reversible rxns
