Machines - Simple Machines

A machine is a device that helps us do work by changing the magnitude, direction, or point of application of a force.

Work Done ($W$): In physics, work is done when a force $F$ causes a displacement $s$ in the direction of the force. It is given by $W = F \times s$. The SI unit is the Joule ($J$).

Mechanical Advantage ($MA$): It is the ratio of the load $L$ to the effort $E$. If $MA > 1$, the machine acts as a force multiplier. It is expressed as $MA = \frac{L}{E}$.

Velocity Ratio ($VR$): It is the ratio of the distance moved by the effort $d_E$ to the distance moved by the load $d_L$. It is given by $VR = \frac{d_E}{d_L}$.

Efficiency ($\eta$): The ratio of useful work output to the total work input. For an ideal machine, $\eta = 100\%$, but in reality, $\eta < 100\%$ due to friction and the weight of moving parts.

Relationship: The three variables are linked by the formula $MA = VR \times \eta$.

Levers: Classified into three types based on the position of the Fulcrum ($F$), Load ($L$), and Effort ($E$). In Class I, the fulcrum is in the middle; in Class II, the load is in the middle; in Class III, the effort is in the middle.

Pulleys: A single fixed pulley has a $VR = 1$ and only changes the direction of force. A single movable pulley has a $VR = 2$. For a block and tackle system with $n$ pulleys, $VR = n$.