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DYNAMICS
Dynamics is the study of things that
move,
….. And why they move.
OVERVIEW OF DYNAMICS
Conservation
Laws
Motion
Conservation of
Momentum
Forces
Work and
Energy
Conservation
of Energy
MOTION
Describing motion
Motion can be described using
• Words
• Numbers
• Graphs
• Equations
• Vector diagrams
v f  v i  at
Equations
• V = d/t Only used for constant speed
• Use kinematic equations for constant
acceleration
• vf = vi + at
• d = vit + ½ at2
• Vf2 = vi2 + 2ad
• d = vi +vf t
2
Vectors
• Displacement, velocity and acceleration are
vectors quantities – have size and direction
• Use vector diagrams to add/subtract vector
quantities – join vectors head to tail
• Solve using scale drawing or pythagorus
and SOCATOH
A-B
A
-B
B
A+B
A
Vector components
• Vectors can be split into vertical and
horizontal components
V
V sin θ
θ
V cos θ
Relative motion
• The motion may have a different
appearance as viewed from a different
reference frame,
• Relative velocities are used to describe the
motion of an airplane in the wind or a boat
in a current.
Example
Vboat rel water
Vboat rel ground
Vwater rel
graound
Boat is traveling at 4 ms-1, river is flowing at 3 ms-1;
Calculate speed of boat relative to ground
FORCES
•
•
•
•
A force is a push or pull
A force affects the motion of an object
It is a vector quantity
Measured in Newtons
Types of Forces
Non-contact
Contact
Gravity
Friction
Electric
Support
magnetic
tension
Friction
• A friction force tries to prevent two surfaces
from moving past each other
• It depends on the roughness of the surfaces
• Moving things need a force to keep them
moving because friction slows them down
i.e. Work must be done to overcome friction
• When work is done against friction, energy
is converted to heat
More Friction
• Friction is also needed to make something
move
• E.g. if you wear smooth shoes on ice you
will slip – friction between your foot and
the ground provides the force that
accelerates you forwards
Support
• Support force stops something
falling
• It always acts perpendicular to the
surface
Tension
• When something is stretched or
compressed it produces tension
forces
Hookes Law
• The more you pull something,
the more it stretches
• Hookes Law F = -kx
Mass and Weight
• The mass of an object is fixed.
• The weight of an object is the force of gravity on
the object
• F=mxg
• Since weight is a force, its SI unit is the newton
• e.g. Sam has a mass of 60 kg; her weight is 60 N
Adding Forces
• There are usually multiple forces acting on an
object
• Use vector diagram to find the combined
effect of several forces acting on an object
Friction force
Support force
Fs
Sum of forces = 0 N Ff
Weight force
i.e. forces are balanced
so block does not
accelerate
Fg
Newton’s Laws
Newton’s First Law
• An object will remain at rest or in uniform
motion in a straight line unless acted upon
by an external force.
• It is a statement about inertia - objects will
remain in their state of motion unless a
force acts to change the motion.
Newton’s 2nd Law
A change in motion involves an acceleration
• Larger force greater acceleration
• Larger mass smaller acceleration
Newton’s 3rd Law
• Forces always come in
pairs.
• For every external force
that acts on an object there
is a force of equal
magnitude but opposite
direction which acts back
on the object.
Torque
• A force can cause an object to accelerate
• If it does not act through the centre of mass,
it can cause an object to rotate
• Torque is the turning effect of a force
• Torque = force x distance (perpendicular)
Example
Equilibrium
Momentum
• p=mxv
• Momentum is a vector quantity.
• The momentum of a system is the vector
sum of the momenta of the objects in the
system.
• In the absence of external forces,
momentum is conserved
Collisions
Collisions
• When objects collide, their individual
momentum will change
• Total momentum before the collision equals
total momentum after the collision (if
outside forces = 0)
Elastic Collisions
• Momentum and KE are conserved
• The car and truck collide, the car rebounds
at –40 ms-1 and the truck is stationary
• Is this collision elastic?
Inelastic Collisions
• Momentum is conserved, but KE is not (i.e. some
energy is converted to heat)
• After the car and truck collide, the car rebounds at
–10ms-1 and the truck continues at –30ms-1. Is this
collision elastic?
Explosions
• Occur when two objects move apart
• Forces exerted by objects are equal and
opposite, so momentum is conserved
• Both objects are initially stationary, so
initial total momentum and final total
momentum are zero
Impulse
•
•
•
•
Impulse = FΔt
But F = ma = mΔv/Δt
Thus FΔt = mΔv = change in momentum
i.e. the change in momentum equals the impulse of
the force
• Impulse is used to study the average force during
collisions - mass and change in velocity are easily
measured, but the force during the collision is not.
Minimising impact force
• If an impact stops a moving object, then the
change in momentum is fixed
• Since FΔt = mΔv, if Δt increases, F will decrease
• E.g. If you jump to the ground, you bend your
knees, extending the time of collision and
lessening the impact force.
• A boxer moves away from a punch, extending the
time of impact and lessening the force.
• Cars are made to collapse on impact, extending the
time of collision and lessening the impact force.
WORK AND ENERGY
Capacity to
do work
Energy changesWork
to another
form/object
Kinetic
Energy
Types of
energy
Conservation
of energy
Potential
e.g. gravtitational,
elastic
Work
• Work is done when a force moves an
object in the direction of the force
• W = F x d // (Unit: Joule)
• A force of 20 N pushing an object 5 m in
the direction of the force does 100 joules
of work.
Energy
• If something has energy, it can do work it can push something and make it move.
• Work done on an object equals energy
gained by the object
• e.g. If you lift a 5 kg object 2 m W = F x
d = 50 x 2 = 100 J. It gains 100 J of
gravitational potential energy
Types of Energy
Mechanical Energy
Active
Stored
Sound
Gravitational
Heat
Elastic
kinetic
Chemical
electrical
Radiant
Energy Conservation
• Energy cannot be created or destroyed
• Energy changes from one form to another
but total energy is constant
Power
• Power is the rate at which work is done
or the rate of using energy.
• P = W/t
(Units: Watt)
• If you do 100 joules of work in one
second (using 100 joules of energy),
the power is 100 watts
Projectile Motion
• A projectile is an object in free fall (i.e. the
only force acting on it is gravity)
• If we ignore air resistance, all objects fall at
the same rate of 10 ms-1
• The path followed by a projectile is its
trajectory
Trajectory
Projectile calculations
• You must separate the horizontal and
vertical motion
• No forces act on the projectile in the
horizontal direction => it travels at a
constant horizontal velocity
• Horizontal distance travelled dH = vH x t
Calcs (cont’d)
• It travels with a constant acceleration
vertically (+10 ms-2 down; -10 ms-2 up)
• If it is travelling upwards, its final vertical
velocity is 0 ms-1
• It is accelerating so we use the kinematic
equations for vertical motion
Example
•
A ball is thrown upwards with an initial
velocity of 5 ms-1 at an angle of 30˚ to the
horizontal.
a) What height does the ball reach
b) How long does it take to reach the
highest point?
c) What horizontal distance does it cover?
Circular Motion
• If a constant force acts on an object at right angles
to its direction of motion, the object will move in a
circular path e.g. swinging a mass on a string
• Because the direction is changing, the object’s
velocity is changing i.e. it is accelerating
• The acceleration is towards the centre of the circle
• The force causing the acceleration is the
centripetal force
Centripetal Acceleration
• The faster the object moves, the faster it
changes direction => greater centripetal
acceleration
• The smaller the radius, the faster it changes
direction => greater centripetal acceleration
• a = v2/r
Centripetal Force
• F = m x a => Fc = mv2/r
• Examples
As a car turns, friction acting on the wheels
of the car provides centripetal force
required for circular motion.
• As a bucket of water tied to a string is
spun in a circle, tension in the string
provides the centripetal force
• As the moon orbits the Earth, the force of
gravity acting upon the moon provides
the centripetal force required for circular
motion.