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Chapter 5: Problem 70

State the definition of work done by a variable force.

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.

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