Physics Section 3 - Mechanics and Materials

6 ~ Forces in Equilibrium
1. 6.1 Vectors and scalars
  1. Representing a vector
    1. A vector is any physical quantity that has a direction as well as a magnitude
      1. displacement - straight line distance
      2. velocity
      3. force and acceleration
    2. A scalar is any physical quantity that is not directional
  2. Vectors and scale diagrams
    1. OB = OA + AB to find overall displacement
    2. sometimes need to move perpendicular lines to calculate resultant force and direction
      1. Pythagoras and trigonometry
    3. Use Pythagoras to calculate separate components
2. 6.2 Balanced forces
  1. Equilibrium of a point object
    1. if two forces act on point object and are equal and opposite, object is in equilibrium
      1. two forces said to be balanced
    2. for object at rest on surface, weight = support
    3. when three forces act on point object, to be in equilibrium, resultant components must be 0
  2. Three forces in equilibrium test
3. 6.3 The principle of moments
  1. 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
  2. unit is Nm
  3. when in equilibrium, clockwise moments = anticlockwise moments
    1. Principle of moments
  4. Centre of mass
    1. The centre of mass of a body is the point through which a single force on the body has no turning effect
    2. irregular shapes
      1. plumb line from three points
  5. Calculating the weight of a uniform metre rule
4. 6.4 More on moments
  1. Support forces
    1. total weight = total upwards support force
  2. Couples
    1. a couple is a pair of equal and opposite forces acting on a boy, but not along the same line
    2. moment of a couple = force x perpendicular distance between the lines of action of the forces
    3. turns a beam
5. 6.5 Stability
  1. Stable and unstable equilibrium
    1. stable - returns to equilibrium position when displaced eg coat hanger, hanging basket
    2. unstable - small displacement results in object moving further from equilibrium position eg plank on a barrel
  2. Tilting and toppling
    1. Tilting
      1. centre of mass lies inside base still
    2. Toppling
      1. centre of mass has passed the pivot so object topples over
  3. Slopes
    1. 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. 6.6 Equilibrium rules
  1. Free body diagrams
    1. show only forces acting on an object
  2. Triangle of forces
    1. for equilibrium of 3 forces,a triangle should be able to be formed
      1. vector sum F1 + F2 + F3 = 0
    2. scale diagrams
  3. Conditions for equilibrium of a body
    1. resultant force must be 0
    2. principle of moments must apply
7 ~ On the Move
1. 7.1 Speed and velocity
  1. Speed
    1. displacement is distance is given direction
    2. speed is change of distance per unit time
    3. velocity is change of displacement per unit time
  2. Motion at constant speed
    1. v=s/t
    2. moving in a circle: v =2πr/T where T is time to move round once
  3. Motion at changing speed
    1. average speed =s/t
    2. v=Δs/Δt
  4. Distance-time graphs
    1. gradient = speed of object
      1. take gradient of tangent at a point for object with changing speed
  5. Displacement-time graphs
    1. when displacement = 0, object at initial point
2. 7.2 Acceleration
  1. Acceleration is the change of velocity per unit time
    1. deceleration is negative acceleration
  2. Uniform acceleration
    1. a=(v-u)/t
      1. v=u+at
  3. Non-uniform acceleration
    1. find gradient of tangent on velocity-time graph
3. 7.3 Motion along a straight line at constant acceleration
  1. v=u+at
  2. s=(u+v)t/2
  3. s=ut+0.5 x at^2
  4. v^2=u^2+2as
4. 7.4 Free Fall
  1. objects fall at the same rate even if they have different masses - discovered by Galileo
  2. inclined plane test show a ball gains speed as it moves down the slope
  3. Acceleration due to gravity
    1. on Earth, g=9.81ms^-2
5. 7.5 Motion graphs
  1. distance-time and displacement-time
  2. speed-time and velocity-time
6. 7.6 More calculations on motion along a straight line
  1. two stage problems
7. 7.7 Projectile Motion 1
  1. SUVAT
  2. if horizontal projection involved, ignore effects of air resistance so horizontal component is constant
8. 7.8 Projectile Motion 2
  1. be able to consider effects of air resistance
8 ~ Newton's Laws of Motion
1. 8.1 Force and acceleration
  1. Motion without force
    1. ice - no friction
    2. air track allows motion to be observed in the absence of friction as glider on air track floats on cushion of air
      1. provided track is level, glider moves at constant velocity along the track because friction is absent
  2. Newton's first law of motion
    1. objects either stay at rest or moves with constant velocity unless acted on by a force
  3. Investigating force and motion
    1. Newton's second law of motion
      1. F=ma
  4. Weight
    1. W=mg
    2. mass of an object is a measure of its inertia, which is its resistance to change of motion
2. 8.2 Using F=ma
  1. Two forces in opposite directions
    1. where F1>F2, resultant force, F1 - F2 = ma
    2. towing a trailer
      1. F=Ma+ma=(M+m)a
  2. Further F-ma problems
    1. pulley problems
      1. Mg-mg=(M+m)a
    2. sliding down slopes
3. 8.3 Terminal speed
  1. drag force depends on object shape, speed and viscosity of the fluid it is travelling through
  2. Motion of an object falling in a fluid
    1. 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
  3. Motion of a powered vehicle
    1. top speed depends on engine power and shape
    2. if Fe represents the motive force (driving force) provided by engine, resultant force = Fe-Fr where Fr is resistive force opposing motion
      1. a=(Fe-Fr)/m
4. 8.4 On the road
  1. Stopping distances
    1. thinking + braking
      1. thinking - reaction time + speed
      2. braking - speed
  2. Practical: Testing friction
    1. 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
5. 8.5 Vehicle safety
  1. Impact forces
    1. measuring impact forces
      1. F=ma
  2. Contact time and impact time
    1. impact time t=s2/(u+v)
    2. acceleration a=(v-u)/t
  3. features: bumpers, crumple zones, seat belts, collapsible steering wheel, airbags
9 ~ Force and Momentum
1. 9.1 Momentum and impulse
  1. Momentum
    1. mass x velocity
    2. unit is kg m/s or Ns
  2. Momentum and Newton's laws of motion
    1. 1st law: an object remains at rest or in uniform motion unless acted on by a force
    2. 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
    3. impulse=FΔt=Δ(mv)
  3. Force-time graphs
    1. area under graph represents change of momentum or impulse of force
2. 9.2 Impact forces
  1. F=Δ(mv)/t=(mv-mu)/t
  2. Force-time graphs for impacts
    1. 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
  3. Rebound impacts
    1. remember direction when calculating change in momentum and impact force
3. 9.3 Conservation of momentum
  1. Newton's 3rd law of motion
    1. when two objects interact, they exert equal and opposite forces on each other
      1. two forces must be of the same type, and acting on different objects, for the forces to be considered a force pair
  2. Principle of conservation of momentum
    1. for a system of interacting objects, the total momentum remains constant, provided no external resultant force acts on the system
  3. Testing conservation of momentum
    1. colliding trolleys
4. 9.4 Elastic and inelastic collisions
  1. elastic - no loss of kinetic energy
  2. inelastic collision occurs where the colliding objects have less kinetic energy after the collision than before the collision
5. 9.5 Explosions
  1. using conservation of momentum (ma)(va)+(mb)(vb)=0
  2. Testing a model explosion
    1. spring released between two trolleys so trolleys push each other apart
10 ~ Work, Energy, and Power
1. 10.1 Work and energy
  1. Energy rules
    1. energy needed to make stationary objects move, change shape or warm them up.
    2. energy types all measured in joules (J)
    3. energy can be transferred between objects in difference ways, including: by radiation (e.g. light), electrically, mechanically (e.g. by sound)
    4. energy cannot be created or destroyed (principle of conservation of energy)
  2. Forces at work
    1. Work done = force x distance moved in the direction of the force
      1. work done measured in Nm
  3. Force and displacement
    1. use trigonometry
  4. Force-distance graphs
    1. area under line represents work done
2. 10.2 Kinetic energy and potential energy
  1. Kinetic energy
    1. Ek = (mv^2)/2
  2. Potential energy
    1. ΔEpmgΔh
  3. Energy changes inloving kinetic and potential energy
    1. equate two equations
      1. (v^2)/2=gΔh
  4. Pendulum bob
    1. passes through equilibrium position at max. speed
    2. kinetic energy = loss of potential energy from max. height, h0 is initial height above equilibrium position
      1. (mv^2)/2=mg(h0-h)
3. 10.3 Power
  1. Power and energy
    1. energy can be transferred by work done or heat transfer (conduction, convection, radiation) as well as electricity, sound and em radiation
    2. power is defined as the rate of transfer of energy =ΔE/Δt=ΔW/Δt
  2. Power measurements
    1. electrical
    2. engine power
      1. when a powered object moves at constant velocity and constant height, resistive forces are equal and opposite to motive force
    3. motive force=energy per second wasted due to the resistive force + gain of kinetic energy per second
4. 10.4 Energy and efficiency
  1. Machines at work
    1. work done, W=Fs
    2. output power, Pout=Fv
  2. Efficiency measures
    1. useful energy is energy transferred for a purpose
    2. efficiency=useful energy transferred by machine/energy supplied to machine=work done by machine/energy supplied to machine
  3. Improving efficiency
    1. reduce heat production
11 ~ Materials
1. 11.1 Density
  1. mass per unit volume
  2. m/v (kgm^-3)
  3. Density of alloys
    1. ρ=(ΡaVa+ΡbVb)/V
2. 11.2 Springs
  1. Hooke's Law
    1. the force needed to stretch a spring is directly proportional to the extension of the spring from its natural length
      1. only true until spring is stretched past its elastic limit
  2. Combinations
    1. parallel
      1. W=Fp+Fq=kpΔL+kqΔL=kΔL
    2. Series
      1. ΔL=ΔLp+ΔLq=(W/kp)+(W/kq)=W/k
  3. Energy stored in a stretched spring
    1. Ep=(FΔL)/2=(kΔL^2)/2
3. 11.3 Deformation of solids
  1. Force and solid materials
    1. 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.
    2. deformation that stretches an object is tensile, whereas deformation that compresses an object is compressive
  2. Tensile stress and tensile strain
    1. tensile stress = T/A with unit Pascal (Pa) equal to 1 Nm^-2
    2. tensile strain = ΔL/L this is a ratio and therefore has no unit
    3. Young's Modulus = tensile stress / tensile strain
    4. Graph
      1. between elastic limit and yield point, the wire weakens temporarily
      2. beyond elastic limit, plastic deformation occurs
      3. 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
      4. beyond max. tensile stress, the Ultimate Tensile Stress (UTS), the wire loses its strength, extends and becomes narrower at its weakest point
      5. UTS is sometimes called the breaking stress
  3. Stress-strain curves for different materials
    1. stiffness is the gradient of the stress-strain line
    2. strength is its UTS
    3. a brittle material snaps without any noticaable yield eg glass
    4. a ductile material can be drawn into a wire - copper is more ductile than steel
4. 11.4 More about stress and strain
  1. Loading and unloading of different materials
    1. metal wire
      1. same curve is limit of proportionality isn't reached
      2. parallel curve if permanent extension occurs
    2. rubber band
      1. loading curve is higher than unloading curve but returns to the same position
    3. polythene strip
      1. 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
  2. Strain energy
    1. elastic energy stored in a stretched wire = 0.5 x TΔL (area under line)
    2. area between two curves for rubber band show difference between energy stored and recovered energy
    3. area between curves for polythene represents work done to deform the material permanently

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