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Vavg = (V1 + V2) / 2
Determining height reached
Time to reach peak * average velocity
Determining horizontal distance
Total time in air * X component of Vinitial
Net force = 0 means...
No acceleration. Can however have velocity but a = 0
If volume changes, is work being done?
Has both magnitude and direction.
Has only magnitude
Newton's first law
The velocity of a body remains constant unless the body is acted upon by an external force.
Newton's third law
For every action there is an equal and opposite reaction.
The ability of an object to resist a change to its velocity.
Center of Mass formula
Cmass = (r1m1 + r2m2 + r3m3...)/mtotal
r - the displacement vector between a reference point and each vector.
Center of gravity
At the center of mass.
Center of buoyancy
The geometric center, irrespective of the center of mass.
"Constant Velocity" or " Constant Speed" means
- No acceleration
- No NET force
- All forces sum to zero
- No change in direction
- The object is in equilibrium
Distance or height traveled formula
Distance = rate * time
Range (horizontal distance traveled) formula
Range = Vx * time
When facing projectiles think:
- Horizontal velocity never changes (ignoring wind resistance)
- Horizontal acceleration always = 0
- Vertical acceleration always = 10 m/s2
- Vertical behavior is always symmetrical (upward = downward)
- Time in the air depends on the vertical component of velocity only.
- Range depends on both the vertical and horizontal components.
- Time is always the same for both the x and y components of the motion.
Formula for displacement in projectile motion
X = 1/2at2
Formula for final velocity when only height is given
V = √(2gh)
Formula for "round trip" or total time in air
tair = 2V/g
V must be the vertical component of initial velocity
The effect of surface area on air resistance
Greater surface area = more air resistance
The effect of shape on air resistance
Less aerodynamic = more air resistance
The effect of contour on air resistance
Rough surface = more air resistance
The effect of velocity on air resistance
Greater velocity = more air resistance
A field that exists between any two objects with mass.
An invisible influence that can exert a force on a mass or charge.
Universal Law of Gravitation (force due to gravity)
F = mg
Formula for gravity, strength of gravitational field, acceleration due to gravity
Gravitational Potential Energy
PE = mgh
- Friction opposes sliding not motion.
- If there is sliding, it's kinetic friction; if there's no sliding, it's static friction.
- Static µ is always greater than kinetic µ.
- Surface area does not increase friction when the mass is the same.
Force due to friction formula
Force down an inclined plane formula
F = mgsin
Normal force on an inclined plane formula
Velocity at the base of an inclined plane
Vf = √(2gh)
F = k∆x
- x - displacement
- k - spring constant
Elastic Potential Energy formula
Simple Harmonic Motion formulas
T = 2π√(m/k)
(mass on a spring)
T = 2π√(L/g)
- T - period (time/wave)
- m - mass
- k - spring constant
- L - length of pendulum
- g - gravity
- Terminal velocity
- Constant velocity
- Objects at rest
- Balanced fulcrums or boards on strings
- Objects floating in liquid
Solving for systems in and not in equilibrium
Equilibrium - list all the forces and put them equal to one another.
Not Equilibrium - list all the forces and add "ma" to the loosing side.
Centripetal vs. Centrifugal
If a string is pulling a ball into a circular motion, the string's force on the ball is centripetal and the ball's force on the string is centrifugal.
Centrifugal does not exist.
- An object is in rotational equilibrium if:
- 1. It is NOT rotataing
- 2. It is rotating with a constant angular velocity/frequency
momentum is inertia increased by velocity and is always
conserved (remains constant) in an isolated system.
- Impulse = ∆
- Impulse = m∆v
- Impulse = Favgt
- If there is no change in velocity, there can be no impulse.
- The greater the change in velocity the greater the change in impulse.
- (KE1 + KE2)before + (KE1 + KE2)after
- In elastic collisions momentum and energy are both conserved.
m1v1 + m2v2 = m1v1 + m2v2
In inelastic collisions momentum is conserved but energy is not. For perfectly inelastic collisions the equations becomes:
m1v1 + m2v2 = (m1 + m2)v3
Modulus of elasticity (ME)
- Young's modulus - simultaneous pushing or pulling, perfectly lined up with one another.
- Shear modulus - simultaneous pushing or pulling not perfectly lined up.
- Bulk modulus - simultaneous compression from all sides.
Thermal expansion formula
- T - temperature
- L - length in inches
- - coefficient of thermal expansion
The energy of internal vibrations of molecules or atoms within a system.
Energy dissipated as heat. On the MCAT this usually means heat dissipated from a collision.
Heat energy and internal energy are almost synonymous.
The energy contained within chemical bonds, or the energy stored/released due to the separation and/or flow of electrons.
ME = KE + PE
- W = ∆Energy
- W = Fdcos
Units - Joules (
) or (
Force per unit area exerted upon a surface by the weight of the air above that surface in the atmosphere.
Force exerted by a fluid on a point equal to the density of the fluid times the depth.
The pressure difference between a system and the surrounding atmosphere.
1 atm equivalents
- 760 torr
- 760 mmHg
- 101 kPa
- 101,000 Pa
- 14.7 psi
General Pressure formula
P = F/A
Pressure = Force / Area
Fluid Pressure formula
P = gh
- (rho) = fluid density
- g = gravity
- h = height of fluid
Specific Gravity formula
SG = Dsubstance/DH2O
D = density
Volume measurements of water
1cm3 = 1mL
Mass of water
1L = 1kg
1mL = 1gram
For objects floating in fluid, the fraction submerged =
The ratio of the density of the object to the density of the liquid.
The buoyant force is exactly equal to the weight of the displaced fluid.
Fbuoyant = vg
- = fluid density
- v = volume of displaced fluid
- g = gravity
The apparent weight of a submerged object is the actual weight minus the buoyant force.
The apparent weight gives us 1) the buoyant force and 2) the weight of that volume of fluid.
Flow Rate formula
- Q = AV
- Q = flow
- A = cross-sectional area of tube (m2)
- V = velocity of the fluid (m/s)
Application (cardiac output = stroke volume x heart rate)
Velocity of H2O exiting a spigot formula
v = √(2gh)
The intensity of intermolecular forces per unit length at the surface of a liquid.
An attraction between unlike particles.
An attraction between particles of the same kind.
Charge magnitude of an electron
e- = 1.6 E-19 C
From positive (+) to negative (–)
From negative (–) to positive (+)
What is current?
The flow of eletrons from areas of higher density (where they strongly repel each other) to areas of lower density (where there is less repulsion).
Field = an invisible influence that can exert a force on a mass or charge.
Point Charge Field
Equates to "real" gravity or gravity in space.
Constant Electric Field
Equate to "assumed" gravity or gravity near earth.
Electric field equivalent to "g" gravity
E - Strength of electric field
Electric field equivalent to "G" gravity constant
K - constant
Electric field equivalent to "h" height
r - radius or distance
Electric field equivalent to "m" inertial component
q - charge
Strength of an e-field formula
E = V/d
- E - strength of an electric field
- V - voltage
- d - distance
Voltage for point charge e-field formula
V = Kq/r
- V - voltage
- K - constant
- r - radius
V = PE/q
Voltage is equal to potential energy over charge
R = pL/A
- p - resistivity
- L - length
- A - cross-sectional area
U = 1/2 CV2
U - PE
C - capacitance
V - voltage
C = Q/V
Q - charge
- Makes more charge build up on the plates
Variables that affect capacitance
- Plate area (directly related)
- Plate thickness (no effect)
- Distance between plates (inversely related)
- Strength of dielectric (directly related)
Capacitor charge vs. time graph
Conceptual ideas of a battery
- Positive terminal has highest electric potential.
- Electrons build up on negative terminal and move to positive.
Conceptual ideas of a resistor
- There is always a voltage drop across any resistor.
- Current through a resistor is inversely related to resistance. 2x resistance = 1/2 current.
- Must be simplified, eg. no more than one of each component.
- 1. Resistors in series: add directly
- 2. Resistors in parallel: add the inverses and take the inverse
- 3. Capacitors in series: add the inverses and take the inverse
- 4. Capacitors in parallel: add directly
- 5. Batteries in series: add directly
- 6. Batteries in parallel: total voltage = the highest voltage of any one of the batteries in parallel
V = IR
- V - voltage
- I - current
- R - resistance
Electric power formula
P = IV
P - power
AC vs. DC
- Alternating current is created by a generator and can be represented by a sine wave.
- Direct current is created by a battery.
Fmagnet on a charged particle formula
F = qvBsin