Formulas
Uniform Acc.
Speed =
x= (u+v)t
x=ut + at x=vt - at 2
km/h -> m/s (Divide by 3.6) m/s -> km/h (multiply by 3.6)
Distance-Time – Gradient is Velocity; Velocity-Time Velocity-Time:: Gradient Gradient is is Acceleration, Area below graph is graph is displacement/distance Acceleration-Time:: Area below graph Acceleration-Time below graph is Velocity;
Velocity =
2
st
Newtons 1 Law (Inertia) Every object continues in its state of rest or uniform motion unless
Acceleration =
2
2
v =u + 2ax
made to change by a non-zero net force. rd
Newtons 3 Law For every action force there is an equal and opposite reaction force
nd
Newtons 2 Law 2
Sum of Forces = Mass (kg) x Acceleration (m/s )
In a Lift: Lift: Fnormal – Fgravity, if normal force = 0 then weightlessness
When a = 0, object is at rest or uniform motion
Tension Q (on trailer) : Ftension - Ffriction=
(pulley) Weight – Tension
Tension Q (on car): car) : Fdriving – Ftension – Ffriction =
Vector specifies unit, magnitude and direction
Inertia:: tendency of an object to continue doing what it is doing and Inertia
Displacement is Displacement is a measure of the change in position of an
resist change
object
Terminal Velocity: drag= Velocity: drag= weight, constant velocity but Net Force = 0
Velocity is a measure of the time rate of displacement, or
Friction:: force applied to the surface of an object when it is pushed or Friction
the time rate of change in position
pulled against the surface of an object
Acceleration is the rate of change of velocity
Reduce Friction Friction through through lubrication, reduce mass, reduce roughness,
Weight is the force applied to an object due to
and decrease surface area
gravitational attraction
Total final momentum = Total initial momentum
The normal reaction is a force that acts perpendicularly to
Collision: To reduce the net force acting on objects -> must increase
a surface as a result of an object applying a force to the
time interval over which the momentum change occurs
surface
Force-Time:: impulse is area below graph, Force-Time graph ,
Gravitational Field Strength : force of gravity on a unit of
2
1N= 1 kg m/s , 1N s = 1 kg m/s
mass, measured in N/kg
m1v1 + m2v2 = m1u1 + m2u2 (no external forces)
Instantaneous velocity: velocity : Velocity at an instant of time,
Momentum:: tendency of an object to keep moving with the same Momentum
midpoint of average velocity of time interval during
speed and direction
constant acceleration
P (kg m/s) = m x v | Changing momentum depends on mass and amount of change in velocity
If net force is ac ting on the body, perpendicular to the
Impulse = Impulse = change in momentum, momentum , measured in N s.
direction of motion then no work has been done Newton-Metres:: Area below graph is Newton-Metres graph is work Mechanical Energy: Energy : energy of a body due to its motion motion or or position
= mv –mu = m(v-u)=m v
Kinetic Energy: Energy : energy carried by a moving body, E k=
, Joules
Power is the rate at which energy is
If Kinetic Energy is lost, collisions are not elastic
transferred or transformed, (flight) power
Gravitational Potential Energy : energy stored in a body due to its position position relative relative
to another object to which it is a ttracted by gravity, measured in Joules
generated by the plane engine
2
Egp=m (kg) x g (9.8 m/s ) x h (metres)
Egp=Area under acc-dist. x mass (
Strain/Elastic Potential Energy : energy stored in a body that has been
Ramp questions (projectile questions (projectile motion)
R= Distance between ramps (m), g= 10 m/s
R
stretched/compressed, measured in Joules
W=
(Area (Area below Force-Displacement below Force-Displacement graph)
Hooke’s Law: behaviour of ideal spring, force required to compress/stretch spring is
directly proportional to the change in length of the spring 2
F
F=-k
F= Force exerted on spring (N), k=Spring constant (N/m), x=displacement of spring (m) Strain Potential Energy :
Fnetav=m aav = Ek/x
Circular Motion, where velocity is tangential to circular motion
√
- Mass doesn’t not affect
Grav. Force
Kepler’s Orbital Law
velocity -angle changes speed, larger = more speed
R= distance between centre of mass of planet to star (m)
T= Orbital Period in seconds M= Mass of star at centre (eg: sun) (kg) 3
G= Gravational Constant: 6.67 x 10
-11
2
Graphing R versus T , finding gradient will allow you to
2
N m /kg
find M (mass at centre)
R = Distance btn centres of bodies (m) M= big mass, m= small mass (kg) Vertical Circular Motion - Top and Bottom are important
Top
√ Bottom
FN
FG
FG
M= mass of larger object (kg) FN
,
Upside Down
m= mass of smaller object (kg) R= distance from centre of mass (m) g = Grav. Field Strength (N/kg)
FG
6
Radius of Earth: 6.38 x 10 m 24
Mass of Earth: 5.98 x 10 kg FN =0
Derived Formulas
Irregular Orbit, eg: Halley’s Comet (Highly Elliptical Orbit)
Why Velocity is faster when it approaches the Sun & Earth?
In all orbits the Total Energy = Gpe + KE, is a constant value. As the G pe is lower when the comet approaches the sun (due to a lower radius), the KE is greater to compensate for this change, which results in a greater velocity when the comet approaches the Sun. Area under acel.-dist. graph x mass = J (Gpe) Area under Grav. Field Strength – radius x mass= Gpe
V=IR Q (quantity of charge C ) = I (Amps ) x t (s)
V=
Cost = Energy (kWh) x Rate (c/kWh) J -> kWh = Divide (3.6 x 106 )& (vice versa) 3
6
9
-3
6
-9
= 10 Mega = 10 Giga = 10 Milli = 10 Micro = 10 Nano=10 1C = 6.242 x 10 18 e 1 e (elementary charge) = 1.602 x 10 -19 coulombs
] x V V = V E (Joules) = V x Q = V x I (A) x t (s) Vrms= Current Capacity= Current x Time; I = Vout=[
∑(emf ) =
E (energy transformed , Joules ) = Power ( watts ) x time (s ) = I2Rt =
Power (watts)= VI = I2R =
T(s)=
Terminal Voltage = ∑(emf ) – I x r ( internal resistance ) If no current, then V = ∑ ∑=IR + Ir or (V+Ir) R= (∑-V)/I 1. LDR – light affects resistance, slow, not suitable for transmitting data 2. Photodiode – really fast, Photoconductive mode – reverse bias, negative current increases with more light intake, current varies with light intensity Photovoltaic mode – forward bias, gets more voltage, used in solar panels More incident light in intensity (
in
out
R2
T
DC bias added in order to move input voltage into linear region to avoid clipping Capacitor in circuit removes DC from circuit.
cutoff (minimum V in) Linear region Saturation (maximum V out)
means greater
photocurrent 3. Photo-transistor doesn’t require as much light to amplify, built in gain, far more sensitive to low light levels, slower than photodiode (10x) 1. LED p-n combine to produce 1 photon of light 2. Laser Diode monochromatic light (one wavelength), greater intensity, narrow beam
Pulse Code Modulation 1. Sampling- takes voltage value at regular time intervals 2. Quantization- Rounds voltage to a certain precision eg:3 d.p’s
3. Encoding – translate voltage to binary Audio Signal (baseband)
number
+ Carrier Signal (higher frequency)
2 =10
n
n
= Modulated Radio Wave (Amplitude Modulation)
Forces that affect structures
(Yield point)
