Mechanics and Materials Flashcards
Horizontal and Vertical motion of a projectile
-Horizontal and vertical motion are independent.
-Gravitational force only acts vertically, so projectiles only experience acceleration due to gravity in vertical direction (down)
In absence of resistive forces:
-Horizontal motion: no force horizontally, no acceleration so constant velocity = Vcosθ
-Vertical motion: constant force due to weight, uniform acceleration down (g) = Vsinθ
difference between a scalar and a vector
vector has magnitude and direction, scalar has only magnitude
examples of scalars
speed, mass, time, energy, power
examples of vectors
displacement, velocity, acceleration, force, weight
adding perpendicular vectors by calculation
- draw vectors as a right angled triangle and use pythagoras to find magnitude of resultant vector
- use SOHCAHTOA for the angle
adding vectors by scale drawing
- write down scale
- draw vectors to correct length and angle to each other “tip to tail”
- add the resultant vector line and measure length (convert with scale) and angle of resultant vector
conditions for equilibrium of two or three coplanar forces acting at a point
total resultant force equals zero OR if vectors representing forces are added together they will form a closed triangle
two conditions for a body to remain in equilibrium
- resultant force = 0
- resultant moment about any force is zero
- stationary or travelling at constant velocity
moment
force x perpendicular distance from the point to the line of action of the force
principle of moments
in equilibrium, the sum of the clockwise moments about a point = sum of anticlockwise moments
definition of a couple
a pair of equal and opposite coplanar forces - only rotational motion occurs
definition of the moment of a couple
one force x perpendicular distance between the lines of actions of the two forces
definition of centre of mass
point in a body through which weight appears to act - object will balance if supported at its COM
stability
if the centre of mass of an object lies outside its base it will topple over
how size affects COM
the wider the base, the lower its COM
contact force
force exerted between two objects when they are in contact with each other (reaction force)
tension/tensile force
force applied to an object that acts to stretch it
stable equilibrium
when a body is displaced then released it will return to its equilibrium position
displacement
distance in a given direction
velocity
rate of change of displacement
acceleration
rate of change of velocity
accelerates / decelerates definition
accelerates - velocity increases with time
decelerates - velocity decreases with time
displacement and velocity time graph
uniform acceleration - gradient increasing, directly proportional
non uniform acceleration - curve upwards = increasing gradient
gradient of displacement and velocity time graphs
gradient of a s-t graph = velocity
gradient of a v-t graph = acceleration
area under velocity and acceleration time graphs
area under a v-t graph = displacement
area under an a-t graph = velocity
average velocity
total displacement/ total time
instantaneous velocity at a point
rate of change of displacement at that point - gradient at a point on a s-t graph (tangent)
equation of motion
only apply where acceleration is uniform - both the magnitude and direction remain the same
free fall
situation when gravitational force is the only force acting on an object
g by free fall experiment
- measure height from ball to trapdoor
-flick switch to start timer and disconnect electromagnet releasing ball bearing
-the ball bearing falls knocking down the trapdoor and breaking the circuit stopping the timer- record the time
-repeat 3 times and average the time taken
-g=2xgradient of graph - use a small and heavy ball to ignore AR and have a computer release and time ball
-most error occurs in the measurement of h
drag
resistive forces like AR that act to oppose motion - negligible for objects moving slowly in air
terminal speed
Maximum speed of a falling object reached when the forces of weight and drag are equal
conditions for an object falling at terminal velocity
- resultant force on object is zero hence acceleration is zero
- objects travels at a constant velocity
factors affecting drag force on an object
- the shape and speed of the object
- the viscosity of the fluid
explain why an object reaches terminal velocity falling through air
- object dropped from rest so only force acting is weight so there is a resultant force on the object producing acceleration
- as velocity of object increases the drag force increases, reducing the resultant force. The object still accelerates, but at a decreasing rate
- Eventually object is falling fast enough for drag force to equal weight so no resultant force hence no acceleration → object falls at a uniform velocity (terminal speed)
newtons 1st law of motion
an object will continue at rest or uniform velocity unless acted on by a resultant force
newton’s 2nd law of motion
the acceleration of an object is proportional to resultant force acting on it
newton’s 3rd law of motion
in an object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A
energy conversions of an object falling in presence of resistive forces
loss in GPE = gain in KE + WD against resistance
principle of conservation of energy
energy is neither created or destroyed, only converted from one form to another
definition of mechanical work done
force multiplied by distance moved in the direction of the force - units J
power
rate at which energy is transferred
units of power
W or Js-1
density
mass per unit volume (scalar)
units of density
kg m-3
Hooke’s Law
extension is proportional to the tensile force applied, up to the limit of proportionality
features of graph of force against extension confirming Hooke’s law
straight line through the origin
units of spring constant
Nm-1
springs in series
-Both springs experience the same force F
-the total extension is the sum of the extension of each spring individually
identical springs in parallel
- the force applied to the spring combination is shared across each of the springs individually
- all springs have the same extension
- therefore they extend less than they would normally as their spring constants add up
limit of proportionality
the point beyond which force is no longer proportional to extension
elastic limit
the point beyond which a material will not return to its original length/size when the forces are removed
elastic behaviour
the material will return to its original length when forces are removed with no permanent extension
plastic behaviour
the material will be permenantly deformed when forces are removed
ethical transport design
methods to increase the time of the impact, reducing the force such as crumple zones, seat belts and air bags
area under a force/extension graph
- work done on a spring and hence the energy stored as it is loaded
OR
-work done by the spring, and hence the energy released as it is unloaded
area between the loading and unloading curves of an elastic band
internal energy retained
derivation of energy stored = ½ FΔL from a graph of force against extension
- ΔW=FΔs, so area beneath line from origin to ΔL represents the WD to compress/extend spring.
- work done on spring = energy stored
- area under graph = area of triangle = ½ base x height, therefore energy stored = ½ F x ΔL.
- OR ∆L proportional to F so produces a straight line with positive gradient hence area = area of a triangle = 0.5F∆L
derivation of energy stored = ½ FΔL
- energy stored in a stretched spring = work done stretching the spring
- work done = force x distance
-as string is stretched the force gets bigger - force is proportional to extension so average force = ½ F
-W = average force x displacement = ½ FΔL - this is the area under the graph of Force against Extension
tensile stress
tensile force divided by cross sectional area
units of stress
Pa or Nm-2
tensile strain
extension of material/original length
units of strain
none
breaking stress (ultimate tensile stress)
tensile stress needed to break a solid material
description of stiffness
requires a large force/stress for a small deformation/extension
description of fracture
non-brittle fracture: material necks which reduces the CSA so increases stress at that point until the wire breaks
brittle fracture: no plastic deformation, usually snaps suddenly without any noticeable yield through crack propagation
brittle material
a material that fractures without any plastic deformation
description of ductile
a material can be drawn into a wire. these are often polymers such as rubber which are used for activities such as bungee jumping which require elasticity
description of strength
material with a higher breaking stress
Young Modulus
tensile stress/tensile strain
units of Young Modulus
Pa or Nm-2
use of stress/strain curves to find Young Modulus
GRADIENT of the linear section of a graph of stress against strain
area under a graph of stress against strain
energy stored per unit volume
one simple method of measuring Young Modulus
measurements to make:
- original length of wire with a ruler
- diameter of a wire with a micro-meter
- mass attached to end of wire
- length of stretched wire with a ruler
Reducing uncertainty
- repeat length measurements
- repeat diameter measurements at different points of the wire
- check for zero error on micrometer and scales
Measurements used to determine Young Modulus
- F=weight=mg. Extension = ΔL
- Cross-sectional area of wire A = πd² / 4.
- Stress = F/A; Strain = ΔL/L
- Plot a graph of stress (y) against strain (x)
- Young Modulus = gradient of linear section of graph
energy transfers in a compressed spring that is released
elastic strain energy in a spring is converted to KE, which in turn is converted into GPE, as spring is thrown up into the air
