A vector is any physical quantity that has a direction as well as a magnitude
displacement - straight line distance
velocity
force and acceleration
A scalar is any physical quantity that is not directional
Vectors and scale diagrams
OB = OA + AB to find overall displacement
sometimes need to move perpendicular lines to calculate resultant force and direction
Pythagoras and trigonometry
Use Pythagoras to calculate separate components
6.2 Balanced forces
Equilibrium of a point object
if two forces act on point object and are equal and opposite, object is in equilibrium
two forces said to be balanced
for object at rest on surface, weight = support
when three forces act on point object, to be in equilibrium, resultant components must be 0
Three forces in equilibrium test
6.3 The principle of moments
The moment of a force about any point is defined
as the force x the perpendicular distance from the
line of action of the force to the point
unit is Nm
when in equilibrium, clockwise moments = anticlockwise moments
Principle of moments
Centre of mass
The centre of mass of a body is the point through which
a single force on the body has no turning effect
irregular shapes
plumb line from three points
Calculating the weight of a uniform metre rule
6.4 More on moments
Support forces
total weight = total upwards support force
Couples
a couple is a pair of equal and opposite forces
acting on a boy, but not along the same line
moment of a couple = force x perpendicular distance between the lines of action of the forces
turns a beam
6.5 Stability
Stable and unstable equilibrium
stable - returns to equilibrium position when displaced eg coat hanger, hanging basket
unstable - small displacement results in object moving further from equilibrium position eg plank on a barrel
Tilting and toppling
Tilting
centre of mass lies inside base still
Toppling
centre of mass has passed the pivot so object topples over
Slopes
high sided object have higher centres of mass eg lorries so when on a slope,
the angle of the slope does not have to be too great for them to topple over
6.6 Equilibrium rules
Free body diagrams
show only forces acting on an object
Triangle of forces
for equilibrium of 3 forces,a triangle should be able to be formed
vector sum F1 + F2 + F3 = 0
scale diagrams
Conditions for equilibrium of a body
resultant force must be 0
principle of moments must apply
7 ~ On the
Move
7.1 Speed and velocity
Speed
displacement is distance is given direction
speed is change of distance per unit time
velocity is change of displacement per unit time
Motion at constant speed
v=s/t
moving in a circle: v =2πr/T where T is time to move round once
Motion at changing speed
average speed =s/t
v=Δs/Δt
Distance-time graphs
gradient = speed of object
take gradient of tangent at a point for object with changing speed
Displacement-time graphs
when displacement = 0,
object at initial point
7.2 Acceleration
Acceleration is the change of velocity per unit time
deceleration is negative acceleration
Uniform acceleration
a=(v-u)/t
v=u+at
Non-uniform acceleration
find gradient of tangent on velocity-time graph
7.3 Motion along a straight line at constant acceleration
v=u+at
s=(u+v)t/2
s=ut+0.5 x at^2
v^2=u^2+2as
7.4 Free Fall
objects fall at the same rate even if they have different masses - discovered by Galileo
inclined plane test show a ball gains speed as it moves down the slope
Acceleration due to gravity
on Earth, g=9.81ms^-2
7.5 Motion graphs
distance-time and displacement-time
speed-time and velocity-time
7.6 More calculations on motion along a straight line
two stage problems
7.7 Projectile Motion 1
SUVAT
if horizontal projection
involved, ignore effects of
air resistance so horizontal
component is constant
7.8 Projectile Motion 2
be able to consider effects of air resistance
8 ~ Newton's
Laws of Motion
8.1 Force and acceleration
Motion without force
ice - no friction
air track allows motion to be observed in the absence
of friction as glider on air track floats on cushion of air
provided track is level, glider moves at constant velocity
along the track because friction is absent
Newton's first law of motion
objects either stay at rest or moves with
constant velocity unless acted on by a force
Investigating force and motion
Newton's second law of motion
F=ma
Weight
W=mg
mass of an object is a measure of its inertia, which
is its resistance to change of motion
8.2 Using F=ma
Two forces in opposite directions
where F1>F2, resultant force, F1 - F2 = ma
towing a trailer
F=Ma+ma=(M+m)a
Further F-ma problems
pulley problems
Mg-mg=(M+m)a
sliding down slopes
8.3 Terminal speed
drag force depends on object shape, speed and viscosity of the fluid it is travelling through
Motion of an object falling in a fluid
speed of object released from rest in fluid increases as it falls until it
reaches terminal speed, when drag force is equal and opposite to weight
Motion of a powered vehicle
top speed depends on engine power and shape
if Fe represents the motive force (driving force) provided by engine,
resultant force = Fe-Fr where Fr is resistive force opposing motion
a=(Fe-Fr)/m
8.4 On the road
Stopping distances
thinking + braking
thinking - reaction time + speed
braking - speed
Practical: Testing friction
measure limiting friction
between underside of a
block and the surface it is
on by pulling with
increasing force until it
slides. Affect of more
mass
1st law: an object remains at rest or in uniform
motion unless acted on by a force
2nd law: rate of change of momentum of an object is proportional
to the resultant force on it or the resultant force is proportional to
the change of momentum per second
impulse=FΔt=Δ(mv)
Force-time graphs
area under graph represents change of momentum or impulse of force
9.2 Impact forces
F=Δ(mv)/t=(mv-mu)/t
Force-time graphs for impacts
variation of impact force with time on a ball can be recorded using a force
sensor connected using suitably long wires or a radio link to a computer
Rebound impacts
remember direction when calculating change in
momentum and impact force
9.3 Conservation of momentum
Newton's 3rd law of motion
when two objects interact, they exert equal and opposite forces on each other
two forces must be of the same type, and acting on different objects, for the forces to be considered a force pair
Principle of conservation of momentum
for a system of interacting objects, the total momentum remains
constant, provided no external resultant force acts on the system
Testing conservation of momentum
colliding trolleys
9.4 Elastic and inelastic collisions
elastic - no loss of kinetic energy
inelastic collision occurs where the colliding objects have less kinetic energy after the collision than before the collision
9.5 Explosions
using conservation of momentum (ma)(va)+(mb)(vb)=0
Testing a model explosion
spring released between two trolleys so trolleys push each other apart
10 ~ Work, Energy,
and Power
10.1 Work and energy
Energy rules
energy needed to make stationary objects
move, change shape or warm them up.
energy types all measured in joules (J)
energy can be transferred between objects in
difference ways, including: by radiation (e.g. light),
electrically, mechanically (e.g. by sound)
energy cannot be created or destroyed
(principle of conservation of energy)
Forces at work
Work done = force x distance moved in the direction of the force
work done measured in Nm
Force and displacement
use trigonometry
Force-distance graphs
area under line represents work done
10.2 Kinetic energy and potential energy
Kinetic energy
Ek = (mv^2)/2
Potential energy
ΔEpmgΔh
Energy changes inloving kinetic and potential energy
equate two equations
(v^2)/2=gΔh
Pendulum bob
passes through equilibrium position at max. speed
kinetic energy = loss of potential energy from max. height,
h0 is initial height above equilibrium position
(mv^2)/2=mg(h0-h)
10.3 Power
Power and energy
energy can be transferred by work done or heat
transfer (conduction, convection, radiation) as
well as electricity, sound and em radiation
power is defined as the rate of transfer of energy =ΔE/Δt=ΔW/Δt
Power measurements
electrical
engine power
when a powered object moves at constant velocity and constant
height, resistive forces are equal and opposite to motive force
motive force=energy per second wasted due to the resistive force + gain of kinetic energy per second
10.4 Energy and efficiency
Machines at work
work done, W=Fs
output power, Pout=Fv
Efficiency measures
useful energy is energy transferred for a purpose
efficiency=useful energy transferred by machine/energy supplied to machine=work done by machine/energy supplied to machine
Improving efficiency
reduce heat production
11 ~
Materials
11.1 Density
mass per unit volume
m/v (kgm^-3)
Density of alloys
ρ=(ΡaVa+ΡbVb)/V
11.2 Springs
Hooke's Law
the force needed to stretch a spring is
directly proportional to the extension of
the spring from its natural length
only true until spring is
stretched past its elastic limit
Combinations
parallel
W=Fp+Fq=kpΔL+kqΔL=kΔL
Series
ΔL=ΔLp+ΔLq=(W/kp)+(W/kq)=W/k
Energy stored in a stretched spring
Ep=(FΔL)/2=(kΔL^2)/2
11.3 Deformation of solids
Force and solid materials
elasticity of a solid material is its ability to regain its
shape after it has been deformed or distorted and
the forces that deformed it have been released.
deformation that stretches an object is
tensile, whereas deformation that
compresses an object is compressive
Tensile stress and tensile strain
tensile stress = T/A with unit
Pascal (Pa) equal to 1 Nm^-2
tensile strain = ΔL/L this is a
ratio and therefore has no unit
Young's
Modulus =
tensile stress /
tensile strain
Graph
between elastic limit and yield
point, the wire weakens temporarily
beyond elastic limit, plastic
deformation occurs
beyond Y2, a small increase in the tensile stress
causes a large increase in tensile strain as the
material of the wire undergoes plastic flow
beyond max. tensile stress, the Ultimate Tensile
Stress (UTS), the wire loses its strength, extends
and becomes narrower at its weakest point
UTS is sometimes called the breaking stress
Stress-strain curves for different materials
stiffness is the gradient of the stress-strain line
strength is its UTS
a brittle material
snaps without any
noticaable yield eg
glass
a ductile material can
be drawn into a wire -
copper is more
ductile than steel
11.4 More about stress and strain
Loading and unloading of different materials
metal wire
same curve is limit of proportionality isn't reached
parallel curve if permanent extension occurs
rubber band
loading curve is higher than unloading
curve but returns to the same position
polythene strip
low limit of proportionality so plastic deformation occurs
meaning similar loading curve to elastic band but straight line
staying at almost the same extension as when being stretched
Strain energy
elastic energy stored in a stretched wire = 0.5 x TΔL (area under line)
area between two curves for rubber band show
difference between energy stored and recovered energy
area between curves for polythene represents
work done to deform the material permanently