Lifting Machine

1. Fundamental Definitions

In any lifting machine, we deal with the relationship between the energy put in and the work done.

• Load (W): The resistance to be overcome or the weight to be lifted by the machine.
• Effort (P): The force applied to the machine to lift the load.
• Mechanical Advantage (MA): The ratio of the weight lifted to the effort applied. It is a pure number. $MA = \frac{\text{Load (W)}}{\text{Effort (P)}}$

Velocity Ratio (VR): The ratio of the distance moved by the effort (y) to the distance moved by the load (x).

$VR = \frac{\text{Distance moved by effort (y)}}{\text{Distance moved by load (x)}}$

Efficiency ($\eta$): The ratio of output work to input work.

$\eta = \frac{\text{Output Work}}{\text{Input Work}} = \frac{W \times x}{P \times y} = \frac{MA}{VR}$

2. Law of a Machine

The Law of a Machine is an equation that describes the relationship between the effort applied and the load lifted. For most machines, this follows a straight-line relationship:

P = mW + C

• m: The slope of the line (representing the constant of friction).
• C: The intercept on the effort axis, representing the initial friction (the effort required to move the machine at zero load).

3. Reversibility and Self-Locking

When the effort is removed from a machine, it may or may not move in the reverse direction under the weight of the load.

• Reversible Machine: A machine that can do work in the reverse direction after the effort is removed.
  • Condition: Efficiency $\eta$ > 50%.
• Self-Locking (Irreversible) Machine: A machine that does not move in the reverse direction even after the effort is removed. This is useful for safety (e.g., screw jacks).
  • Condition: Efficiency $\eta$ < 50%.

4. The Six Classical Simple Machines

Machine	Key Principle	Common Example
Lever	Rotates around a fixed point called a fulcrum.	Crowbar, Seesaw
Pulley	A grooved wheel with a rope; changes direction of force.	Flagpole, Block and Tackle
Wheel & Axle	Two circular objects of different diameters rotating together.	Screwdriver, Doorknob
Inclined Plane	A sloped surface used to lift loads with less force.	Loading ramp, Stairs
Wedge	Two inclined planes joined back-to-back.	Axe, Chisel, Knife
Screw	An inclined plane wrapped around a cylinder (helix).	Bolt, Jack screw

Classification of Levers

Levers are categorized into three classes based on the relative positions of the Fulcrum (F), Load (L), and Effort (E):

1. First Class: Fulcrum is in the middle (E-F-L). Example: Scissors.
2. Second Class: Load is in the middle (F-L-E). Example: Wheelbarrow.
3. Third Class: Effort is in the middle (F-E-L). Example: Tweezers.

5. Ideal vs. Actual Machines

• Ideal Machine: A theoretical machine with no friction ($\eta = 100\%$). In this case, $MA = VR$.
• Actual Machine: Friction is always present, so $MA$ is always less than $VR$, and $\eta$ is always less than $100\%$.