Forces

• Newton's first law


  An object has a constant velocity unless acted on by a resultant force
• Newton's second law


  Force = mass x acceleration (F = ma)
• Newton's third law

  Every action force has an equal and opposite reaction force
• Example of Newton's third law

  • The force of the Earth's gravity on an object is equal and opposite to the force of the object's gravity on the Earth
• Motion of a body falling in a uniform gravitational field


  1. Initially, there is no air resistance and the only force acting on it is weight

  2. As it falls, it accelerates which increases its speed and hence air resistance

  3. This causes the resultant force downwards to decrease

  4. Therefore the acceleration decreases, so it is not speeding up as quickly

  5. Eventually they are equal and opposite and balance so there is no resultant force

  6. So there is no acceleration and the terminal velocity is reached
• Friction


  • A force between two surfaces which impedes motion and results in heating
  • Air resistance is a form of friction
• Finding the resultant of two or more forces acting along the same line

  1. Add them together if in the same direction

  2. Subtract if in the opposite direction
• Object moving in a circle with constant speed

  • The speed is constant, but the direction is always changing
  • This means the velocity is always changing
  • Therefore it is accelerating and there must be a force perpendicular to its velocity towards the centre of the circle
• Elastic deformation


  The object returns to its original shape when the load has been removed
• Plastic deformation


  The object does not return to its original shape when the load has been removed
• Hooke's law

  For a spring, F = kx where F is the force, k is the spring constant, and x is the extension
• Linear force-extension graph


  • Elastic deformation following Hooke's law
  • The point it stops being linear is called the limit of proportionality. From then on, it does not obey Hooke's law
  • Gradient is the spring constant, k
• Non-linear force-extension graph


  • Plastic deformation not following Hooke's law
  • After the plastic region, it will fracture
• Moment of a force

  A measure of its turning effect: moment = force x perpendicular distance
• Example of moment of a force


  • When riding a bike, pressing your foot down on the pedal causes a moment about the pivot, turning the pedal arms
• Pivot point


  The point which the object can rotate about
• Equilibrium


  When the sum of clockwise moments equals the sum of anticlockwise moments (the principle of moments) and there is no resultant force
• Principle of moments


  1. Pivot a uniform ruler at its centre

  2. Place different masses at different distances from the centre on either side until it balances

  3. Show that the clockwise and anticlockwise moments are equal
• Centre of mass

  The point at which all of a body's mass can be considered to act
• Calculating the centre of mass of a card

  1. Hang up the card and suspend a plumb line from the same place

  2. Mark the position of the thread

  3. Repeat the above steps with the card suspended from different places

  4. Where these lines intersect is the centre of mass
• If the centre of mass is below the point of suspension of an object

  It will be in stable equilibrium (e.g, a hanging plant pot)
• If the centre of mass is above the point of suspension of an object


  It will be in unstable equilibrium (e.g. a pencil placed on its sharp end)
• If the line of action of the object's weight moves outside the base


  There will be a resultant moment and it will topple
• Scalar

  Has just a magnitude
• Vector


  Has a magnitude and a direction
• Scalar examples


  • Distance
  • Speed
  • Time
• Vector examples


  • Displacement
  • Velocity
  • Acceleration
• Determining the resultant of two vectors graphically

  1. Place the vectors head to tail

  2. The line between the start and finish is the resultant