Workdone By Variable Force Formula -Definition, Introduction

Workdone by  variable force is a concept in physics that involves calculating the amount of energy transferred when an object is subjected to a force that changes in magnitude or direction as the object moves. To calculate the work done by a variable force, you typically need to use calculus, specifically integration, because the force is not constant over the entire distance the object moves.

1. Determine the expression for the force as a function of position, \(F(x)\). This could be given in the problem statement or derived from a physical model.
2. Identify the initial and final positions of the object, \(x_1\) and \(x_2\).
3. Set up the integral from \(x_1\) to \(x_2\) with \(F(x)\) as the integrand and \(dx\) as the differential displacement.
4. Evaluate the definite integral to find the work done.

Also Check - Thermodynamics formula

Also Check - Work, Energy & Power Formula

Examples Workdone By Variable Force

1. Spring Force:

2. Gravitational Force:

3. Frictional Force:

Also Check - Unit, Dimension & Vector Formula

4. Electric Force:

5. Magnetic Force:

6. Tension in a Rope:

7. Gas Expansion:

8. Variable Wind Resistance:

9. Stretching a Rubber Band:

10. Fluid Resistance: