Forces and Newtons Laws

• Newton's second law of motion


  The force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced: F = ma
• Gravity


  The force between any object and the Earth. The force due to gravity acting on an object is called the weight of the object, acting vertically downwards.
• A body falling freely experiences an acceleration of g = 9.8 ms-2
• Free fall objects have equations of W = mg
• Solving for unknown forces X and Y

  1. Horizontal forces: X - 4 = 2 * 2, X = 8 N

  2. Vertical forces: Y - 2g = 2 * 0, Y = 2 * 9.8, Y = 19.6 N
• F = ma


  Can be used to solve problems involving vector forces acting on particles
• Solving for acceleration of a particle with a resultant force of (3i + 8j) N acting on a 0.5 kg particle

  a = 2(3i + 8j) ms-2
• Magnitude of acceleration R

  R = sqrt(6^2 + 16^2) = 17.1 N
• Bearing of acceleration


  90° - 69.4° = 20.6°
• If a system involves the motion of more than one particle, the particles may be considered separately. However, if all parts of the system are moving in the same straight line, then you can also treat the whole system as a single particle.
• Solving for acceleration and tension of a system with two connected particles P and Q


  1. Acceleration of the whole system: 40 - 10 - 6 = 8a, a = 3 ms-2

  2. Tension in the string: 40 - T - 10 = 5 * 3, T = 15 N
• Newton's third law states that for every action there is an equal and opposite reaction.
• A system with a smooth pulley means the tension of the string is the same on both sides of the pulley. You cannot treat a pulley system as a single particle as these particles move in opposite directions.
• Solving for the acceleration of two masses P and Q connected by a light inextensible string over a smooth fixed pulley

  1. T - 2mg = 2ma

  2. 3mg - T = 3ma

  3. mg = 5ma, a = 1/5 * 9.8 = 1.96 m/s^2 ≈ 2.0 m/s^2
• Force Diagrams


  • Diagram showing all the forces acting on an object, with each force shown as an arrow pointing in the direction in which the force acts
  • Used to model problems involving forces
• Equilibrium


  When the forces acting upon an object are balanced, the object is said to be in equilibrium
• Newton's first law of motion


  An object at rest will stay at rest and that an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object
• Resultant force


  A resultant force will cause the object to accelerate in the same direction as the resultant force
• Forces as vectors


  Forces can be written as vectors using i-j notation or as column vectors. Resultant of 2 or more forces can be given as vectors by adding the vectors. An object in equilibrium has a resultant vector force of 0i + 0j.
• Solving for the values of a and b in the vector equation (2i + 3j) + (4i - j) + (-3i + 2j) + (ai + bj) = 0

  a = -3, b = -4