Forces + Motion

• What does the area under a velocity-time graph represent?

  Distance travelled by the object.
• Vector

  • acceleration
  • velocity
  • displacement
  • force
• Scalar

  • speed
  • time
  • mass
  • energy
  • distance
  • momentum
• Quantities

  • vectors - direction and magnitude
  • scalars - magnitude
• Velocity

  • speed in a direction
  • velocity = displacement/time
• Acceleration

  • the forces on an object are balanced when the sum of the individual forces equals zero - so there is zero acceleration (speed doesn't change)
  • if forces are unbalanced the object will accelerate
  • acceleration - speeding up, slowing down or changing direction
  • the rate of change of velocity - the amount that velocity changes per unit time

  a = Δv/t

  acceleration = change in velocity/time

  
  

  v^2 = u^2 + 2as

  final velocity^2 = initial velocity^2 x 2 (acceleration x displacement)

  
  

  F= ma

  force = mass x acceleration
• Distance

  the length of a path travelled by an object
• Speed

  distance travelled per unit time

  speed = distance/time
• Typical speeds

  walking - 1.5 m/s

  running - 3 m/s

  cycling - 6 m/s

  driving 13-30 m/s

  train - 50 m/s

  plane - 250 m/s
• Stopping distance

  • thinking distance + braking distance

  thinking distance = distance a vehicle travels in the time it takes for the driver to apply the brakes after he realises he needs to stop

  braking distance = distance a vehicle travels after the driver has applied the brakes
• Factors which affect thinking distance

  • reaction time
  • alcohol intake
  • tiredness
  • distractions
• Factors that affect braking distance

  • tire + brake condition
  • road condition
  • weather condition
• If the initial speed of a car is doubled, the thinking distance is doubled and the braking distance is quadrupled

  • initial speed is a factor in both thinking and braking distance
• work = force x distance

  • the brakes must apply a force over a certain distance
• momentum = mass x velocity

  p = mv

  the mass of a car also affects the braking distance - the momentum of the vehicle has to be reduced to zero

  (kg m/s)

  
  

  • momentum is conserved - total momentum before collision = total momentum after
  • when a force acts on an object that is moving, or able to move, there is a change in momentum

  F = mΔv/t

  
  

  force = mass x change in velocity / time

  
  

  • seatbelts, airbags, and crumple zones are designed to maximise the time of impact - to prevent injury
• Newton's Laws

  1. an object in motion will stay in motion unless acted upon by an unbalanced force
  2. the acceleration of an object depends on its mass and the force exerted on it
  3. when two objects interact, the forces they exert are equal and opposite (must both be the same type of force)
• Terminal Velocity

  • the velocity of an object when the frictional forces equal the driving force
  • forces are balanced
• Hooke's Law

  • describes the behaviour of a material when its shape is changed by a force - the extension is directly proportionate to the force applied
  • extension (e) - how much an object has stretched beyond its original length
  • directly proportional - means that if one quantity is doubled then it causes the second to double - has the symbol alpha
  • scale factor (k) - determines how much a particular spring extends - spring constant (stiffness of a spring)

  Force = constant x extension

  F = ke
• Limit of proportionality

  • when it stops being directly proportional
  • Hooke's law is only valid for extensions below the limit of proportionality (elastic limit)
• Elastic deformation

  • occurs below the limit - the spring will return to its original length when the weight is removed
• Plastic deformation

  • occurs above the limit - the spring will not return to its original length when the weight is removed
• Elastic potential energy in springs

  • The energy in springs when they are extended or compressed is called elastic potential energy or strain energy

  EPE = 1/2 ke^2

  EPE = elastic potential energy (J)

  k = constant(N/m)

  e = extension (m)
• Moments

  • moment = force x perpendicular distance from pivot

  M = Fd

  • turning force - measured in newtonmetre (Nm)

  If the object is balanced the total clockwise moment = total anticlockwise moments
• Force

  • a push or pull that acts on an object due to the interaction with another object.

  Non-contact forces:

  • electrostatic - charges cause attraction/repulsion
  • gravity - mass causes attraction
  • magnetism

  Contact forces:

  • normal contact force - objects are physically touching
  • friction - surfaces and their roughness cause friction when moved in contact
  • upthrust
  • tension
  • weight
• Gravity

  • all matter has a gravitational field and attracts all other matter
  • the larger the mass, the stronger the field, the greater the attraction
• Mass

  the amount of matter an object is made from
• Earth's gravitational field strength

  9.8