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Forces and Moments

FORCES
  • Forces are measured in Newtons; Force = Mass × Acceleration
  • 1 Newton is the amount of force needed to give 1 kg an acceleration of 1 m/s2

Effects of Forces

  • A force may produce a change in size and shape of a body; give acceleration or deceleration or a change in direction depending on the direction of the force.
  • If there is no resultant force acting on a body, it either remains at rest or continues at constant speeds in a straight line.

Friction

  • Friction is the force between two surfaces which impedes motion and results in heating.
  • Air resistance is a form of friction.

Hooke’s Law

Stress-Strain Curve (Photo Credit: Quora.com)

  • Springs extend in proportion to load, as long as they are under their proportional limit.
  • Limit of Proportionality: is the point at which the load and extension are no longer proportional.
  • Elastic Limit: is the point at which the spring will not return to its original shape after being stretched.
  • Load (N) = Spring Constant × Extension
  • F = ke

Circular Motion

  • An object at a steady speed in a circular orbit is always accelerating as its direction changes, but it gets no closer to the center.
  • Centripetal force is the force acting towards the center of a circle. It is a force that is needed for circular motion, not caused by circular motion.
  • For example, when you swing a ball on a string in a circle, the tension of the string is the centripetal force. If the string is cut, then the ball will travel in a straight line at a tangent to the circle at the point where the string was cut.
  • Centrifugal Force is the force acting away from the center of a circle. This is what make a slingshot go outwards as you spin it.
  • The centrifugal force is the reaction to the centripetal force. It has the same magnitude but is opposite in direction to the centripetal force.
  • F = mv2/r

Newton’s Law

  • First Law of Motion: If no external force is acting on an object, the object will, if stationary, remain stationary, and if in motion, will remain in motion.
  • Second Law of Motion: F = ma
  • Third Law of Motion: If an object A exerts a force on an object B, then the object B will exert an equal but opposite force on object A.
MOMENT
  • Moment (Nm) = Force (N) × Distance from Pivot (m)
  • In equilibrium, clockwise moment = anticlockwise moment.
  • Increasing the force or distance from the pivot would increase the moment of a force.
  • Levers are force multipliers:
    • Turning a bolt is far easier with a wrench because the distance from the pivot is massively increased, and so is the turning effect.

Center of Mass

  • Center of mass is an imaginary point in a body where the total mass of the body seems to be acting.
  • How to work out the center of mass of a card:
    • Mark three points on the edge of the card
    • Make a hole using a pin on each point
    • Hang it on a cork board and make a line when it is stable
    • Do this for all three points
    • Where all three lines intersect is the center of mass.

Stability

  • An object will be in stable equilibrium when it returns to its original position after given a small displacement.
  • For an object to start rotating, it needs to have an unbalanced moment acting on it.

Scalars and Vectors

  • A scalar is a quantity that only has a magnitude (so it can only be positive); e.g. speed.
  • A vector quantity has a direction as well as a magnitude; e.g. velocity, which can be negative.

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