Problem 70 - Essential Calculus

Question

State the definition of work done by a variable force.

Step-by-Step Solution

Answer

Work done by a variable force is defined as the integral of the force with respect to displacement, calculated as the area under the force versus displacement graph.

Step 1: Define Work

In physics, work is defined as a process of energy transfer where force F is applied over a displacement. The amount of work done is usually symbolized by W.

Step 2: Define Variable Force

Force is defined as an interaction that, when unopposed, changes the motion of an object. A variable force is a force that changes in magnitude and/or direction over the displacement.

Step 3: Define Work Done by Variable Force

The work done by a variable force is calculated as the area under the force versus displacement graph. Mathematically, it is expressed as: work done, \( W = \int_{x_1}^{x_2} F(x)dx \) where \(F(x)\) represents the force and \(x\) represents the displacement, while \(x_1\) and \(x_2\) represent the initial and final displacement respectively. The integral calculates the entire area beneath the curve from initial to final displacement.