What is a lift problem in mechanics?

Lift problems involve objects in direct contact—typically a person or load inside a lift. Motion is vertical only. Use Newton's Second Law (F = ma) with g for gravity. The reaction force R between lift and load arises from Newton's Third Law. Treat as one system or separately; reaction forces cancel when combined.

1. What Is a Lift Problem?

A lift problem involves particles in direct contact – e.g. a person or crate in a lift (the object is often called a load).

Motion is vertical only
Use (g = 9.8\text{ m s}^{-2}) (acceleration due to gravity)
Gravity always acts downwards
Acceleration (a) may be positive or negative depending on direction and sign convention
Acceleration links (F = ma) and the suvat equations

2. Forces in a Lift

Key forces:

(T) = tension in cable (upwards on lift)
(Mg) = weight of lift
(mg) = weight of load
(R) = reaction force (lift on load, equal and opposite by N3L)

3. Solving Lift Problems

Same steps as rope problems:

Draw diagrams – lift, load, all forces, positive direction
Write equations – use (F = ma) for vertical motion
Solve – may need simultaneous equations

Key insight: Lift and load move in the same direction, so treat as one system. The reaction force (R) cancels when combined (internal force).

4. Equations for Lifts

5. Origin of the Reaction Force

6. Worked Example

7. Hidden Lift Problems

Not just elevators! Watch for:

Crane lifting a load – platform = "lift", cable = "lift cable"
Fairground ride – rising or falling cabin
Stacked crates – reaction between crates on a moving platform

Connected Bodies (Lifts)

Summary

1. What Is a Lift Problem?

A lift problem involves particles in direct contact – e.g. a person or crate in a lift (the object is often called a load).

Motion is vertical only
Use (g = 9.8\text{ m s}^{-2}) (acceleration due to gravity)
Gravity always acts downwards
Acceleration (a) may be positive or negative depending on direction and sign convention
Acceleration links (F = ma) and the suvat equations

2. Forces in a Lift

Key forces:

(T) = tension in cable (upwards on lift)
(Mg) = weight of lift
(mg) = weight of load
(R) = reaction force (lift on load, equal and opposite by N3L)

3. Solving Lift Problems

Same steps as rope problems:

Draw diagrams – lift, load, all forces, positive direction
Write equations – use (F = ma) for vertical motion
Solve – may need simultaneous equations

Key insight: Lift and load move in the same direction, so treat as one system. The reaction force (R) cancels when combined (internal force).

4. Equations for Lifts

System as one (taking downward as positive): [(M + m)g - T = (M + m)a]

Lift separately: ((Mg + R) - T = Ma)

Load separately: (mg - R = ma)

Where: (M) = lift mass, (m) = load mass, (T) = cable tension, (R) = reaction (load on lift floor).

Signs depend on your choice of positive direction.

5. Origin of the Reaction Force

The reaction force (R) arises from Newton's Third Law:

The lift floor exerts an upward force on the load
The load exerts an equal downward force on the lift floor
This keeps the load in contact with the floor while the lift moves
When the lift accelerates down, the load "weighs less" (smaller R); when accelerating up, it "weighs more" (larger R)

6. Worked Example

Lift 800 kg, moving down with (a = 0.3\text{ m s}^{-2}). Load mass (m) kg. Reaction on load = 399 N.

(b) Find m: Load: (mg - R = ma) → (m(g - a) = R) → (m(9.8 - 0.3) = 399) → (m = 42) kg

(c) Find T: System: ((800 + 42)g - T = 842 \times 0.3) → (T = 842 \times 9.8 - 842 \times 0.3 = 7991.6) N

7. Hidden Lift Problems

Not just elevators! Watch for:

Crane lifting a load – platform = "lift", cable = "lift cable"
Fairground ride – rising or falling cabin
Stacked crates – reaction between crates on a moving platform