Connected Bodies - The Lift Problem (Edexcel A Level Maths: Mechanics)

What is the lift problem?

• The lift problem involves objects (particles) that are directly in contact with each other – typically a person or crate in a lift
• If it is not a person in the lift the object is often referred to as a load
• There may be more than two objects involved – for example two crates stacked on top of each other on a lift floor
• Vertical motion is involved so use g m s^-2, the acceleration due to gravity, where appropriate
  • Gravity always acts vertically downwards
  • Depending on the positive direction chosen – and which other forces are acting vertically – acceleration (a m s^-2) may be positive or negative

• Remember that acceleration links F= ma (N2L) and the ‘suvat’ equations

How do I solve ‘lift problem’ type questions?

• Lift problems will only consider motion in the vertical direction
• As motion is involved Newton’s Laws of Motion apply so use “F = ma” (N2L)
• The steps for solving lift problems are the same as for solving rope problems
• As both the lift and load are travelling in the same direction the system can be treated as one particle (as well as separate particles)
  • There is no reaction force acting on the lift or load when treating the particle as one - mathematically they cancel each other out
  • You can think of the upward as counteracting the person’s weight and moving the load upwards; N3L applies so there must be an equal force acting in the opposite direction; - you can think of this as the force keeping the person in contact with the lift floor whilst it is moving

• For constant acceleration the ‘suvat’ equations could be involved

How do we form the equations for problems involving lifts?

• Form the equations as follows:
  • Treating the lift and person/load as one

(↓) (M + m)g - T = (M + m)a

• • Treating the lift and person/load separately

Lift: (↓) (Mg + R) - T = Ma

                  Person/load: (↓) mg - R = ma

• You do not necessarily need all equations but if in doubt attempt all and it may help you make progress

(a)  Briefly explain how the force of arises in this problem.

(b)  Find the mass of the load, m kg .

(c)  Find the tension,T N, in the cable of the lift.