AQA A Level Maths: Mechanics复习笔记3.2.3 Connected Bodies - The Lift Problem

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-1) may be positive or negative
  • Round final answers based on the number of significant figures used for g
    • if g = 10 m s-2, round to 1 s.f.
    • if g = 9.8 m s-2, round to 2 s.f.
  • 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 tow bars and ropes?

• 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 800g N 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.

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