P6 forces in equilibrium

• scalars and vectors are physical quantities
• scalars only have magnitude

  vectors have magnitude and direction
• examples of scalars: distance, speed, mass, temperature
• examples of vectors: displacement, velocity, force, acceleration
• there are two different methods of adding vectors:

  • calculation = for when the vectors are perpendicular, use pythagoras to find the resultant vector or use trigonometry to find the direction
  • scale drawing = for when the vectors are not perpendicular, use a ruler and protractor to draw the vectors, add in the missing line and measure the length or the angle
• the opposite of adding vectors is resolving vectors
• to resolve vectors, use trigonometry to find the two perpendicular components which would make the resultant vector when added together
• the formulae for resolving a vector V into horizontal x and vertical y components are:

  x = V cos theta

  y = V sin theta
• for an object to be in equilibrium, the sum of all the forces acting on it must be zero
• an object in equilibrium must be at rest or moving at constant speed as there is no resultant force
• to show that an object is in equilibrium, you can do one of two things:

  • add the horizontal and vertical components of each vector, if this makes zero it is in equilibrium
  • if there are three forces, draw them tip-to-tail, if this makes a closed triangle it is in equilibrium
• the moment of a force about a point is the force multiplied by the perpendicular distance from the line of action of the force to the pivot
• the equation for a moment is: m = Fd

  m = moment in Nm

  F = force in N

  d = distance in m
• the principle of moments states that for any point, the sum of the anticlockwise moments is equal to the sum of the clockwise moments
• the centre of mass of an object is the point through which its mass acts, where a single force will have no turning effect
• a uniform object has its centre of mass directly at its centre
• to solve problems which involve a single support, use the fact that the support force must be equal to the total downward force acting on the object
• to solve problems which involve multiple supports, use the fact that the weight must be shared between the supports according to how far the centre of mass is from each support
• when choosing where to put a pivot, choose somewhere that eliminates as many unknown forces as possible, as any forces acting on the pivot will not cause a moment as the distance is zero, so force multipled by distance is zero
• a couple is a pair of forces in the same plane, which have equal magnitudes but act in opposite directions to each other
• a couple will turn, or try to turn, the object that it acts on
• to find the moment of a couple, multiply one of the forces by the perpendicular distance between the lines of action of the forces
• stable equilibrium means that if the object is displaced, it returns to its equilibrium position
• for a stable equilibrium, the object’s centre of mass should be directly below the point of support, when the object is at rest
• unstable equilibrium means that if the object is displaced, it does not return to its equilibrium position
• for an unstable equilibrium, the object’s centre of mass should be directly above the point of support, when the object is at rest
• tilting is when an object at rest is acted on by a force which raises it up on one side
• a tilted object will topple over if it is tilted too far, too far is when the line of action of the weight passes beyond the pivot
• the position where the line of action of the weight passes through the pivot is the furthest an object can be tilted without toppling
• the lower the centre of mass of an object, the more stable it is
• the higher the centre of mass of an object is, the less stable it is