Physics Section 3 - Mechanics and Materials

Physics Section 3 - Mechanics and Materials

1. 6 ~ Forces in Equilibrium

   • 6.1 Vectors and scalars
     • Representing a vector
       • 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

2. 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

3. 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
   • 8.5 Vehicle safety
     • Impact forces
       • measuring impact forces
         • F=ma
     • Contact time and impact time
       • impact time t=s2/(u+v)
       • acceleration a=(v-u)/t
     • features: bumpers, crumple zones, seat belts, collapsible steering wheel, airbags

4. 9 ~ Force and Momentum

   • 9.1 Momentum and impulse
     • Momentum
       • mass x velocity
       • unit is kg m/s or Ns
     • Momentum and Newton's laws of motion
       • 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

5. 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

6. 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

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