CIE 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^-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 R N 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