Connected Bodies - The Lift Problem | CIE A Level Maths: Mechanics Revision Notes 2020

Connected Bodies - 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

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

3-2-3-the-lift-problem-diagram-1

(↓) (M + m)g - T = (M + m)a

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

3.2.3_WE_The lift problem_1

(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.

Sketch diagrams or add to any diagrams given in a question.
If in doubt of how to start a problem, draw all diagrams and try writing an equation for each. This may help you make progress as well as picking up some marks.
Watch out for “hidden lift” problems – we’re not strictly talking elevators here! For example, a load being raised by a crane; the “lift” would be a platform (such as a pallet) and the “lift cable” would be the cable connecting the crane to the load. Another common alternative is a fast rising (or falling) fairground ride.