Module 1: Mathematics & Mechanics Flashcards
If x = a^y , y= ?
y = log(subscript a)x
What does the area under a graph represent?
The axes multiplied together
E.g. velocity time graph
Area underneath= displacement
What does sin θ ≈ ?
θ
What does cos θ ≈ ?
1
What does tan θ ≈ ?
θ
Scalar quantities
Quantities which are described only by magnitude
Vector quantities
Quantities which are described by magnitude and direction
How to solve vector subtraction problem
Add vectors head to tail, but flip subtracted vector.
Find resultant vector using trigonometry.
SI unit for temperature
Kelvin K
How are v, d and t related?
d (or x) = vt
Acceleration due to gravity =
10 ms^-2
Unless specified otherwise
Relative velocity
How fast the distance between two objects changes
Newton’s first law
Objects continue at rest- or constant velocity- unless an external force acts upon them.
Newton’s second law
An external force gives the object an acceleration proportional to the force
F = ma
Newton’s third law
Forces come in equal and opposite pairs
Units of force
Newtons N
In Newton’s third law, when do the equal and opposite forces act?
At the same time
T (kinematics)
Period: time taken to travel around a circle
Circumference equation
2πr
Area of circle
πr^2
Centripetal force
F = mv^2/r
What conditions does the centre of mass fulfil? (3)
Mass one one side balances mass on the other
Forces equal due to symmetry
The object can balance on the point
Centre of gravity
Point through which an objects entire weight appears to act
Friction
Force between two surfaces. Acts parallel to them
Do surfaces applying friction forces to each other touch?
No- due to electrostatic forces
In which direction does friction act?
Opposite to the objects relative motion. Parallel to surface
f(subscript max) = ?
μN
Where μ = coefficient of friction
And N = normal force (e.g. mg)
Does friction depend on area?
No
Air resistance
Atmospheric friction/ drag due to pushing air away
As velocity increases, what happens to air resistance?
Increase
Equation relating CW and CCW torques
Fd = Fd
Class one lever
Load fulcrum effort
Class two lever
Effort load fulcrum
Class three lever
Load effort fulcrum
Describe kinetic energy
The measure of an objects capability to do work because of its motion
Units of energy
Joules J
Units of work
Joules J
Describe potential energy
A measure of an objects potential capability to do work because of its position
Two types of microscopic potential energy
Chemical potential energy
Nuclear potential energy
Mechanical energy
Total energy inside a system
Dissipating forces
Energy from the system which is lost to the surroundings
Is mechanical energy conserved?
No, but total energy is. (Just not of the system itself)
Units of power
Watts W
Efficiency equation
η = W out / E used
How do machines increase entropy of the universe?
Energy dissipates
Δp
Impulse/ change in momentum
Units of momentum
kg ms^-1
Force is the transfer of ___?
Momentum
Inelastic collision
Momentum is conserved, kinetic energy is not
Elastic collisions
Both momentum and kinetic energy are conserved
Four steps to solving a collision problem
Define a system of interest
Draw the system before and after
Decide which direction is positive/ break into components
Determine if collision is elastic or inelastic
Sticky inelastic collision
Objects stick together after they have collided
If kinetic energy is conserved during a collision, what can we infer about the relative speeds of the objects?
The relative speed of the objects before the collision = relative speed of the objects after
v1i - v2i = - (v1f - v2f)
Approach velocity
Velocity of one object as seen by the other before a collision
Recoil velocity
Velocity of one object as seen by the other after a collision
When spring is stretched/ compressed to the max, what’s going on energy wise?
At maximum potential energy
Kinetic energy = 0
At equilibrium position, how much potential energy does a spring have?
0
KE= TE
Transverse wave
Oscillation is perpendicular to propagation
Longitudinal waves
Oscillation is in direction of propagation
