Objects Suspended in Equilibrium (Edexcel International A Level Maths: Mechanics 2)

What is meant by objects suspended in equilibrium?

• An object can be suspended at a fixed point by a string such that it is allowed to hang freely and be in equilibrium (at rest)
  • e.g. A sign hung from the ceiling of a shop by single rope (string)
  • An object will either be a uniform lamina or a uniform framework
• Equilibrium means
  • there is zero resultant (net) force acting on the object
  • there is zero resultant (net) moments about the point of suspension

• Objects suspended in equilibrium have two forces acting on them
  • tension in the string (acting at the fixed point)
  • weight (acting at the position of the centre of mass)
• These forces act through a vertical line which passes through the point of suspension and the position of the centre of mass
• Problems often require the angle that is created between this vertical line and an edge of the object to be found

• A lamina could be suspended at a fixed point from a vertex (as above) or along an edge, or, suspended by a point on its surface that it would then be able to pivot (rotate) around
• A lamina suspended at a pivot will have two forces acting on its
  • reaction force (acting at the pivot)
  • weight (acting at the position of the centre of mass)
• As with the fixed-point scenario above, these forces will act through a vertical line which passes through the point of suspension and the position of the centre of mass

• The mathematics involved in finding the angle is the same for both the fixed-point and pivot scenarios but you should be aware of the different phrasing in questions

How do I solve problems involving freely suspended laminas and frameworks?

 

STEP 1     Sketch a diagram or use a given one and add to it as you make progress

STEP 2     Find the position of the centre of mass of the object

                            Ensure you know whether you are working with a

                           lamina or a framework and the differences in finding the

                           position of the centre of mass

STEP 3     On your diagram, add the position of the centre of mass

        Draw a line to represent the downward vertical

        This will be a straight line connecting the point at which the body is suspended to the point of the centre of mass

                           Identify the angle required

 STEP 4    Use trigonometry to find the required angle

       Interpret the result in the context of the problem and answer the question accordingly