4: Mechanics and Materials Flashcards
What is the principle of moments?
-For rotational equilibrium the sum of the clockwise moments is equal to the sum of the anticlockwise moments about any given pivot
What is a couple?
-A pair of equal and coplanar forces that are in opposing directions
What is a moment?
-The force applied by an object multiplied by the perpendicular distance from the pivot
What is required for equilibrium?
-Vertical forces must be equal
-Horizontal forces must be equal
-Rotational forces must be equal
Describe a scalar quantiy
-Only has a magnitude
-Examples: time, distance, speed
Describe a vector quantity
-Has a magnitude and a direction associated with it
-Examples: velocity, displacement, force
What is the significance of the gradient of a force-extension graph?
-The gradient is equal to the spring stiffness
What is the significance of the area of a force-extension graph?
-The area underneath is equal to the strain energy
What is density?
-The ratio of the mass of a body to its volume
-Measured in kilograms per metre cubed (kg/m^3)
What is the elastic limit?
-The point at which an object will experience permanent deformation
-The object will no longer return to its original length
What is lift?
-An upward force acting upon an object in a fluid
-Caused by the object creating a change in direction of fluid flow
-Lift acts perpendiculars to direction of fluid flow
What is F.s.cosθ equal to?
-The work done on an object
-Typically for an object being pulled or pushed by an external force at an angle
Where:
F=force
s=displacement
θ=angle of force to horizontal
What is friction?
-A resistance to the motion of an object
-Friction always acts against the direction of movement
What is brittle behaviour?
-When a material fractures with little elastic deformation under stress
What is Hooke’s law?
-The extension is directly proportional to the force applied
-This applies up until the limit of proportionality
What is gravitational potential energy equal to?
Ep=m.g.h
Where:
Ep=gravitational potential energy
m=mass of object
g=acceleration due to gravity
h=height of object
What is kinetic energy equal to?
Ek=(1/2).m.v^2
Where
Ek=Kinetic energy
m=mass of object
v=velocity of object
How is energy related to power?
-Energy is the product of the power and the time elapsed
What is the principle of conservation of energy?
-Energy is neither created nor destroyed
What is efficiency?
-The ratio of the useful power output to the total power input
-Measured as a a percentage
What is the area under a force displacement graph?
-Equals the work done
What is power?
-The rate of doing work
-Measured in watts (W)
What is the area under a force time graph?
-The change in momentum
-This is equivalent to the impulse
What is an elastic collison?
-Where momentum and kinetic energy are conserved
When is momentum conserved?
-Linear momentum is conserved in all collisions so long as no external forces act
What is an impulse?
-The change in momentum
F.Δt=mv-mu
Where:
F=force
Δt=change in time
mv=final momentum
mu=initial momentum
What is the fracture point?
-The point on a stress-strain graph at which an object breaks
What is plastic behaviour?
-When a material experiences permanent deformation
-This is the elastic limit on a stress-strain graph
What is the breaking stress?
-The maximum force that can be applied to an object before it breaks
What is elastic potential energy?
-The energy stored in an elastic object eg. a spring
-Equal to (1/2).F.e
-Also equals (1/2).k.e^2
Where:
E=elastic potential energy
F=force
e=extension
k=spring stiffness
How does spring stiffness combine in series springs?
-1/Kt=1/k1+1/k2…
How does spring stiffness combine in parallel springs?
-Kt=k1+k2…
What is a ductile material?
-A material that can undergo a large amount of plastic deformation before fracturing
What is elastic deformation?
-When the force is removed and the object returns to its original length
How does speed affect air resistance?
-As the speed increase air resistance increases
What is terminal velocity?
-Point at which an object reaches its maximum velocity
-Air resistance is equal to acceleration at this point
What are the conditions for projectile motion?
-Must be no air resistance
-Thus no horizontal acceleration
-Vertical acceleration is solely due to gravity
What are the SUVAT equations?
v=u+a.t
s=u.t+(1/2).a.t^2
s=v.t-(1/2).a.t^2
v^2=u^2=2.a.s
s=1/2(u+v).t
Where:
s=displacement
u=initial velocity
v=final velocity
a=acceleration
t=time
What is the centre of mass?
-Point at which the weight of an object acts
Where is the centre of mass for a uniform object?
-At the centre of the object
What is Newton’s first law?
-A body will stay at constant velocity unless acted upon by an external force
What is Newton’s second law?
-The rate of change of momentum is equal to the resultant force
f=m.a
f=(mv-mu)/t=m(v-u)/t=m.a
Where:
f=force
m=mass
a=acceleration
t=time
u=initial velocity
v=final velocity
What is Newton’s third law?
-When two bodies interact they apply forces opposite in direction and equal in magnitude upon one another
-Must be opposing bodies
-Must be the same type of force
Why are loading and unloading lines on a force-extension graph parallel for a plastically deformed material?
-The spring stiffness hasn’t changed so forces between atoms are the same
Why isn’t all work done stored as elastic strain energy when a stretch is plastic?
-Work is done to move atoms apart so energy gets dissipated as heat
How is dissipation of energy in plastic deformation used to design safer vehicles?
-Crumple zones deform plastically so increase impact time which decrease the force felt as the impulse is the same
-Seat belts stretch to convert passenger’s kinetic energy into elastic strain energy
What energy changes occur when pulling a fixed string?
-Work done to pull the string is converted into elastic strain energy
-When the spring is released energy is converted from elastic potential to kinetic
-The kinetic energy is eventually converted into elastic potential
How do you calculate Young’s Modulus?
E= Tensile Stress/ Tensile Strain
Stress=Force/Area
Strain=Extension/Original Length
E=(ForceOriginal Length)/(AreaExtension)
Where E is the Young’s Modulus
Describe an experiment to calculate the Young’s modulus of a material
-Use a micrometer to measure the diameter in several places to find a mean diameter
-Calculate the cross-sectional area by π*(diameter^2)/4
-Clamp the wire down and attach weights until the wire is taut
-Measure the distance of the wire up until the marker with a ruler-this is the original length
-Increase weights in 50g intervals and measure the extension with a ruler
-Record the extension as well as the force applied
-Get a minimum of 8 results for different weights and remove weights
-Wait until wire is slack and repeat experiment twice more to calculate mean extensions
-Plot a graph of stress on y-axis against strain on x-axis
-The gradient of this graph is the Young’s Modulus
