Mechanics and Materials Flashcards
1 gcm-³
1000 kgm-³
1 ml
1 cm³
cuboid volume equation
l x w x h
sphere volume equation
(4/3)πr³
cylinder volume equation
πr²h
Hooke’s Law
force needed to stretch a material is directly proportional to the extension of the material from its natural length, up to the limit of proportionality
cm³ to m³
x 10^-6
when a compressive force is applied to a spring
the spring squashes
when a tensile force is applied to a spring
the spring stretches
restoring force
a force that always acts to pull an oscillating system back toward equilibrium
Limit of proportionality
point past where Hooke’s law is obeyed
elastic limit
The point beyond which a material will not return to its original shape once the force is removed
elastic deformation
material returns to its original shape once the forces are removed
plastic deformation
material is permanently changed after the force has been removed
springs in series
1/K = 1/K1 + 1/K2
springs in parallel
K = K1 + K2
elastic strain energy
the work done by the load in stretching the material
Beyond elastic limit
the unloading line is parallel to loading line as k is constant
tensile stress
force per unit area
Tensile stress equation
σ = F/A
tensile strain
change in length divided by the original length of the material
tensile strain equation
ε = ΔL/L
yield point
point beyond which a small increase in stress causes a large increase in strain
ultimate tensile stress
The maximum stress that can be applied to an object before it breaks.
Young’s Modulus, E
A measure of the stiffness of an elastic material and defined by stress/strain.
brittle material
snaps without yield, obeys hooke’s law
ductile material
can be drawn into wire
stiffness of a material
a measure of how much it will extend for a given force
how is the strength of a material determined?
by the force required to break it
what is the stiffness of a material a measure of?
how much it will extend for a given force
Elastic strain energy equation
E = 1/2 FΔL
scalar quantity
a physical quantity with magnitude but no direction
vector quantity
a physical quantity with both magnitude and direction
displacement
Distance in a given direction
velocity
speed in a given direction
Representing Vectors
Arrow (representative length and arrow head for direction)
resultant
net effect of all like vectors on a single object
Addition of two perpendicular vectors
- pythagoras’ theorem
- scale diagram
resolve
to separate a vector into two perpendicular components
When an object is in equilibrium
- all the forces acting on the object are balanced
- the object will be at rest or moving with constant velocity
How to solve equilibrium problems with 3 forces
- draw a vector triangle
- resolve the forces into perpendicular directions
Moment
turning force
Moment equation
Force x perpendicular distance from pivot
principle of moments
the sum of all anticlockwise moments = the sum of all clockwise moments
resultant force is 0 (upwards and downwards)
centre of mass
The point which you can consider all of an object’s weight to act through.
When will an object topple over?
if the line of action of its weight falls outside its base
When will an object topple over?
if the line of action of its weight falls outside its base
couple
A pair of forces of equal size which act parallel to each other but in opposite directions
speed
change of distance per unit time
motion at a constant speed (equation)
s = ut
motion in a circle
v = 2πr / T
motion at changing speed
average speed = total distance travelled / total time taken
an object moving at constant velocity
moves at the same speed without changing direction
displacement - time graphs
Gradient = velocity
velocity of an object moving in a circular path
changes continuously as direction changes
velocity - time graphs
- gradient = acceleration
- straight line = uniform acceleration
- increasing gradient = increasing acceleration
- decreasing gradient = decreasing acceleration
Area under a speed-time graph
distance travelled
Area under velocity-time graph
displacement
acceleration - time graph
area under graph = velocity
SUVAT
S = displacement
U = initial velocity
V = final velocity
A = acceleration
T = time
suvat - v-t graph (gradient)
- gradient = acceleration
- v = u + at
freefall
when the gravitational force is the only force acting on an object
- acceleration = g = 9.81ms-²
3 key projectile principles
- The acceleration of the object is g and only affects the
vertical motion of the object - Neglecting the effect of air resistance, the horizontal
velocity of the object is constant - The motions in the horizontal and vertical directions are independent of each other
projectile path
parabolic
How would drag forces affect the work we did on projectiles?
- reaches lower vertical height
- in less time
- shorter horizontal range
Bernoulli’s Principle
as the speed of a moving fluid (liquid/gas) increases, the pressure of the fluid decreases
Magnus effect
sideways force on a spinning object caused by Newton’s 3rd Law
Motion of a powered vehicle
Motion of a powered vehicle
How to increase a vehicle’s top speed
- increase the driving force (engine size)
- reducing frictional forces (more streamlined shape)
- reduce the mass
Acceleration of a powered vehicle equation
(Fe - Fr) / m
Fe = engine forces
Fr = frictional forces
Newton’s First Law
an object will remain at rest or continue at a constant velocity unless acted upon by a resultant force
Newton’s Second Law
F = ma
the rate of change of momentum of an object is proportional to the resultant force acting on it. the change in momentum will be in the same direction as that force
Newton’s Third Law
Every action has an equal and opposite reaction
linear momentum
the product of the mass and velocity of an object
principle of linear momentum
assuming no external forces act, the sum of the total linear momentum before a collision is equal to the sum of the total linear momentum after
elastic collision
one where momentum and kinetic energy are conserved
inelastic collision
linear momentum is conserved but some of the kinetic energy is converted into other forms
the change in momentum of an object is increased by…
- increasing the size of the force applied
- increasing the time that the force is applied for
Impulse equation
Ft = ∆mv
impulse
the product of the average force and interval of time the force is exerted for which is also equal to the change in momentum of an object due to a force applied over time t.
impulse
the product of the average force and interval of time the force is exerted for which is also equal to the change in momentum of an object due to a force applied over time t.
Area under a force-time graph
impulse
Area under a force-displacement graph
work done
When is work done?
when energy is transferred from one form into another or when a force causes a movement
kinetic energy
energy of an object due to its motion
gravitational potential energy
energy of an object due to its position
