12PHB Flashcards
Base SI units
Kg (Kilograms), m (Meters), s (Seconds), A (Amps), K (Kelvin), mol (Moles)
tera ( T )
1x10^12
giga ( G )
1x10^9
mega ( M )
1x10^6
kilo ( K )
1x10^3
deci ( d )
1x10^-1
centi ( c )
1x10^-2
milli ( m )
1x10^-3
micro ( µ )
1x10^-6
nano ( n )
1x10^-9
pico ( p )
1x10^-12
How to reduce random error
Repeat measurements several times and calculate an average from them
Random error
Unpredictable fluctuations in an instrument’s reading as a result of uncontrollable factors, such as environmental conditions
Systematic errors
Arise from the use of faulty instruments or from flaws in the experimental method
To reduce systematic errors
Instruments should be recalibrated, or different instruments should be used.
Zero errors
This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero
To account for zero errors
Take the difference of the offset for each value
Precision
When there is very little spread about the mean value
Accuracy
If the values are close to the true value
Reliability
A measure of the ability of an experimental procedure to produce the expected results when using the same method and experiment
Validity
A measure of the sustainability of an experimental procedure to measure what it is intended to measure
Multiplication and Devision Uncertainty adding
The errors need to be converted to a percentage error then added together and converted back to an uncertainty
Power, uncertainty adding
Multiply the percentage uncertainty by the power then convert back to an uncertainty
Scalar Quantity
a quantity which only has magnitude (size)
Vector Quantity
a quantity which has both magnitude and direction
Vectors (5)
Displacement, Velocity, Acceleration, Force, Momentum
Newtons 1st Law
A body will remain at rest or move with constant velocity unless acted on by a resultant force
Newtons 2nd Law
The resultant force on an object is directly proportional to its acceleration (F=ma)
Newtons 3rd Law
If an object exerts a force on another object, then that object will exert a force on the initial object which is equal in magnitude but opposite in direction
Contact forces
Friction, Fluid resistance or viscous drag, Tension, Normal (reaction) force
NonContact forces
Gravitational attraction, Electrostatic Forces, Magnetic Forces
Newtons 2nd Law in terms of momentum
The resultant force of an object is equal to the rate of change of momentum (p=mv)
What are the effects of air resistance
Time of flight decreases, Horizontal velocity decreases, Horizontal acceleration decreases, Range decreases, Shape of trajectory is no longer a parabola
Equation for static force
f <= μN
f = Friction force
N = Reaction/Normal Force
μ = Coefficient of static force
Equation for Dynamic Friction
f = μN
f = Friction force
N = Reaction/Normal Force
μ = Coefficient of dynamic friction
Hooke’s Law
The restoring force acting to return a spring to its length is proportional to the extension of the spring.
Hooke’s Law Equation
Fh=-kx
F = Elastic Restoring Force
k = Spring Constant
x = Displacement of spring
Elastic potential energy equation
E = 1/2 kx^2
E = Elastic potential energy
k = Spring constant
x = Displacement of spring
Viscous Drag force equation (Stoke’s law)
Fd = 6πηrv
Fd = Viscous drag force
η = fluid viscosity
r = radius of sphere
v = velocity of sphere
Contact force
A force which acts between objects that are physically touching
Non-Contact force
A force which acts at a distance, without any physical contact between bodies, due to the action of a field
Buoyancy Equation
Fb = ρVg
Fb = buoyancy force
ρ = density of fluid
V = Volume of fluid displaced
g = Acceleration of free fall
Elastic restoring force
- The force that returns a spring to its natural length
- The direction of the force is always toward the natural length.
- The elastic restoring force follows Hooke’s Law.
Viscous Drag force
Depends on the viscosity of a fluid. A lower viscosity means it is easier for a fluid to flow
Buoyancy Force
- The force experienced by a body when it is partly or fully immersed in a fluid
- The buoyancy force is exerted on a body due to the displacement of the fluid it is immersed in.
Archimedes’ principle
The upward buoyancy force on an object completely or partially submerged in a fluid, is equal to the weight of fluid displaced by the object
The fraction of an object’s volume that is below the water
(density of object)/(density of fluid)
Equation Weight of sphere in fluid
W = Fd + Fb
W = Weight of the sphere
Fd = Drag force
Fb = Buoyancy force
Weight of sphere equations
Ws = ρVg or Ws = 4/3 π r^3 ρg
V = Volume of sphere
ρ = density of sphere
r = radius of sphere
g = acceleration of free fall
Terminal velocity is (In terms of proportion):
- Directly proportional to the square of the radius of the sphere
Impulse Equation
J = FΔt
Define Change in Momentum
An object experiences a force for a given amount of time that results in its mass undergoing a change in velocity
Impulse and Change in Momentum
Impulse and Change in Momentum are equal (FΔt = mΔv)
Decreasing Impact
Minimise a force, by increasing the time of contact, ∆t.
Effect of Seatbelt when stopping a car
Car travelling comes to a sudden stop, (momentum → zero). If not wearing a seatbelt, the force that decelerates the object will likely be the force from the seat or dashboard in front. ↓time = ↑force.
Period (T)
The time taken for the object to complete one revolution
Frequency (f)
the number of complete revolutions in one second
Equation for Frequency
f = 1/T
Instantaneous speed for a circle
v = s/t = 2πr/T
Equation for circumference of a circle
C = 2πr
Centripetal acceleration equation
a = (v^2)/r
Define Centripetal Acceleration
A change in speed or in direction, always towards the centre of the circle
What affects the size of the centripetal acceleration
- speed (↑v = ↑a)
- radius (↑r = ↓a)
Velocity of an object moving in a circle
The direction of the velocity is constantly changing, this means velocity is constantly changing.
Equation for centripetal acceleration using period
a = (4(π^2)r)/T^2
Define Centripetal Force
Any force (resultant force) that keeps a body moving in a circle, always towards the centre. A force is required for an object to accelerate.
Equation for centripetal force
F = (mv^2)/r = mrω^2
Define Angular Displacement
The change in angle, in radians, of a body as it rotates around a circle
Equation for Angular displacement
θ = S/r
Define Angular Velocity
The change in angular displacement with respect to time.
Equation for Linear speed related to Angular velocity
v = rω
Equation for angular velocity
ω = 2πf = 2π/T
Equation for centripetal force provided by the force of friction
mv^2/r = μmg
Equation for maximum speed at which a body can move in a circle without issues
v = √μgr
This is because the force to keep the body in a circular motion could no be provided by the centripetal force, as it would be too fast
Define Banking
When a road is banked, the centripetal force doesn’t depend on the friction between the tyres and road. Instead, the centripetal force depends on the horizontal component of the normal force.
Define Non-Uniform Circular motion
This happens when there is a changing resultant force such as in a vertical circle.
Magnitude of tension as a body spins in a circle
- Maximum at the bottom (F centripetal = F tension – F weight)
- Minimum at the top (F centripetal = F tension + F weight)
Principle of Conservation of Energy
Energy cannot be created or destroyed, it can only be transferred from one form to another
Define system
An object or group of objects
Define Kinetic Energy
The energy of a moving object
Types of Kinetic Energy
Chemical, Internal (Thermal/Heat), Light
Types of Potential Energy
Gravitational, Elastic, Nuclear, Chemical
Types of Mechanical Energy
Kinetic energy, gravitational potential energy and elastic potential
Energy Dissipation
No energy transfer is 100% efficient. When energy is transformed from one form to another, some of the energy is dissipated to the surroundings. Usually regarded as wasted energy.
Equation for Loss in Kinetic Energy
Gain in Ep + Work done against Friction
Use of Sankey Diagrams
Used to represent Energy Tranfers
Define Mechanical Energy
The transfer of energy when an external force causes an object to move over a certain distance.
Equation for Kinetic energy in terms of momentum
Ek = p^2/2m
Define Gravitational Potential Energy
The energy stored in a mass due to its position in a gravitational field
Define Elastic Potential Energy
The energy stored within a material when it is stretched or compressed
Equation for Elastic Potential Energy
Eh = 1/2kx^2
Conservation of Mechanical Energy
Mechanical Energy = Ek + Ep + Eh
Spring Fully Compressed
Ep = Max
Ek = Zero
Eh = Some
Spring Normal Length
Ep = Some
Ek = Max
Eh = Some
Spring Fully Stretched
Ep = Min
Ek = Zero
Eh = Max
Define Power
The rate of work done (Energy Transfer)
Equation for power
p = ΔW/Δt = Fv
(Fv is only relevant when at constant of both terms)
Define Watt
A transfer of 1 Joule of energy in 1 second
Equation for Efficiency
η = useful work out/total work in = useful power out/total power in
Define Energy Density
The energy that an amount of fuel can provide compared to volume of fuel (Jm-3)
Equation for Energy Density
Energy Density = Energy/Volume
