Theory of Machines — Law of the Machine For a lifting machine, the linear relationship between effort P and load W is called the law of the machine. Which form is correct (m is the slope constant and C is the constant representing friction)?

Introduction / Context:
Real machines require extra effort beyond the ideal proportional term due to friction and other losses. This relationship is captured by the law of the machine, which is a straight line when P is plotted against W.

Given Data / Assumptions:

• P: effort applied; W: load lifted.
• m: proportionality constant (slope); C: constant effort to overcome friction and other losses.

Concept / Approach:
Experimentally, P varies linearly with W. The y-intercept at W = 0 equals the constant C (pure friction effort), and slope m represents how much extra effort is needed per unit load.

Step-by-Step Solution:

Verification / Alternative check:
Plotting test data (P vs W) for hoists or jacks typically yields a line with intercept C > 0, confirming the “+ C” term.

Why Other Options Are Wrong:
“P = mW − C” would give negative effort at small loads; “m/W” is not linear in W; “C − mW” implies decreasing effort with increasing load, which is unphysical for lifting machines.

Common Pitfalls:
Confusing ideal mechanical advantage (no friction) with the real line including C; misreading axes (P vs W) when interpreting experimental graphs.

Final Answer:
P = mW + C.