Mechanics Flashcards
speed
rate of change of distance with respect to time (ms^-1)
acceleration
rate of change of velocity with respect to time (ms^-2)
displacement
distance in a given direction (m)
vector quantity
velocity
rate of change of displacement with respect to time (ms^-1)
vector quantity
acceleration due to gravity
in the absence of air resistance, all objects near the earth’s surface, if released, will fall downwards with the same acceleration. This is acceleration due to gravity. g=9.8ms^-2
scalar
quantity with magnitude but no direction
vector
quantity with direction and magnitude (oh yeah!!)
force
anything that causes the velocity of an object to change i.e. speed up/slow down.
unit: Newton (N)
mass
(m) of a body is a measure of how difficult it is to accelerate that body
unit: kg
average speed
distance/time
the newton
1N is the force that gives a mass of 1kg an acceleration of 1ms^-1
weight
the weight of an object is the force of the earth’s gravity acting on it.
W=mg//F=ma
unit: Newton
momentum
ρ = mv
unit: kgms^-1 kilogram metre per second
Newton’s 1st law
law of inertia: a body will remain in a state of rest or travelling with a constant velocity unless an external unbalanced force acts on it
newton’s 2nd law
F = ma //
when an unbalanced force acts on a body the rate of change of the body’s momentum is directly proportional to the force and takes place in the direction of the force:
F ∝ mv-mu/t
newton’s 3rd law
every force has an equal and opposite force. i.e. friction opposes motion
friction
force that directly opposes motion in the opposite direction to the motion
principle of the conservation of momentum
momentum before = momentum after in a closed system (no external forces).
m1u1 + m2u2 = m1v1 + m2v2
density
mass per unit volume;
ρ = m/V
unit: kgm^-3
pressure
force per unit area
unit: pascal (Pa) or Nm^-2
pressure in solids
P = F/A
pressure in liquids
P = ρgh
archimedes’ principle
states that when an object is partially/fully immersed in a fluid it experiences an upthrust equal in size to the weight of the fluid displaced
law of flotation
states that the weight of a floating object is equal to the weight of the liquid displaced
boyle’s law
states that at a constant temperature the volume of a fixed mass of gas is inversely proportional to its pressure
P ∝ 1/V
PV = k
newton’s law of universal gravitation
any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
F ∝ m1m2/d^2 //
F = Gm1m2/d^2 //
F = GM/d^2
inverse square law
an inverse-square law is any scientific law stating that the observed “intensity” of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.
moment of a force
turning effect of a force
M = Fd
d = distance from fulcrum
laws of equilibrium for coplanar forces
if a body is in equilibrium then sum of upforces = sum of downforces and sum of CW moments = sum of AC moments
lever
a rigid body free to rotate around a fixed point called a fulcrum
couple
2 parallel forces equal in size acting in opposite directions with no common line of action e.g. handlebars
work
W = Fs
s = displacement
unit: Joule (J) or Nm
the joule
1J = the amount of work done when a force of 1N acts for a distance in the direction of the force
energy (E)
the ability to do work
unit: Joule
9 types of energy
- kinetic
- potential (gravitational/elastic)
- chemical
- sound
- electrical
- nuclear
- electromagnetic radiation (light)
- internal
- heat
kinetic energy
Ek: the energy a body has due to its motion
Ek = 1/2mv^2
potential energy (grav)
Ep: the energy a body has due to its position in a force field
Ep = mgh
renewable sources of energy
wind, solar, hydroelectric, geothermal, nuclear fusion, biomass, tidal
power
the rate at which work is done/energy is converted from one form to another
P = W/t //
P = E/t
unit: watt (W) or Js^-1
power efficiency
power output/power input *100
principle of the conservation of energy
energy can neither be created nor destroyed, it can only be converted from one form to another
Torque
T = Fd
// moment of a couple
terminal velocity
where air resistance (friction) is equal and opposite to the weight of the falling object
i.e. falling at constant velocity
work
when a force moves a body through displacement in the direction of the force
W=Fs
unit: Joule or Nm
energy
the ability to do work
hydrometer
based on law of flotation/buoyancy.
1. finding % alcohol
2. density of sulphuric acid in car battery
3. % of fat in milk
pressure in a gas
increases with depth, acts in all directions
atmospheric pressure
pressure of earth’s atmosphere acting on any object near the earth
at sea level atm. pressure = 1*10^5Pa = 1 atmosphere. decreases further from sea level you move
high pressure weather
dry, clear skies, little wind
low pressure weather
cloudy, wet, windy
angle in radians
θ = s/r
s = arc length
r = radius
constant angular velocity
rate of change of angle with respect to time
w = θ/t
unit: rad s^-1
centripetal force
the force acting towards the centre that is needed to keep an object moving in a circle
what does centripetal force depend on
-mass of object
-radius of turn
-velocity of object
centripetal force eqns
F = mv^2/r
F = mrw^2
linear tangential velocity
at any point on the circle the object has tangential speed (linear) i.e. if you let it go it will move in a straight line
v = rw
centripetal acceleration
if an object is moving in a circle it has acceleration towards the centre
a = v^2/r
a = rw^2
period (T) of an orbit
time taken for a satellite to go once around the central body
T = 2πr/v
kepler’s 3rd law
T^2 = 4π^2R^3/GM
T^2 ∝ R^3
T ∝ 1/√M
geostationary orbit
remains at rest above the same point on the equator.
-orbits in the equatorial plane
-period is 24 hours
-satellite moves in the same direction as the earth
-height above earth is approx 36,000km
Hooke’s law
when an object is bent, stretched or compressed by a displacement then the restoring force is directly proportional to the displacement provided the elastic limit is not reached
F = -ks
k = elastic constant
restoring force
force pulling object back to its original position
elastic limit
if an object exceeds its elastic limit it becomes permanently strained and will not return to its original shape
simple harmonic motion
object said to be moving with simple harmonic motion if
-its acceleration is directly proportional to its distance from a fixed point on its path
-its acceleration is always directed towards that point
a = -w^2s
w^2 = constant
period of SHM
T = 1/f
T = time for total oscillations/number of oscillations
T = 2π/w
amplitude
greatest displacement the particle has from the equilibrium position
