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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 10

Lesson 1: Introduction to work

# Introduction to work review

Review the key concepts and skills for energy and work.  Understand how work is the area under a force vs. displacement graph and how force and displacement produce work.

## Key terms

Term (symbol)Meaning
Energy (E)Measurement of the ability to do work. SI unit is joule (start text, J, end text).
Work (W)Change in energy by the transfer of energy from one system to another. Scalar quantity with units of joules (start text, J, end text).
Joules (start text, J, end text)SI unit for energy. Applying a net force of 1, start text, N, end text to an object over a displacement of 1, start text, m, end text requires 1, start text, J, end text of energy. 1, start text, J, end text, equals, 1, start text, N, end text, dot, 1, start text, m, end text, equals, 1, start text, k, g, end text, dot, start fraction, start text, m, end text, squared, divided by, start text, s, end text, squared, end fraction

## Equations

EquationSymbol breakdownMeaning in words
W, equals, F, d, cosine, thetaW is work done on an object, F is the magnitude of force on the object, d is the magnitude of the object’s displacement, and theta is the angle between the vectors of force F and displacement d.Work is the product of an object’s displacement and the component of force exerted parallel to the direction of the object’s motion.
W, equals, delta, EW is work and delta, E is the change of energy.Work is the change of energy for a system.

## How to find work from a Force vs. displacement graph

The force applied to an object can be graphed as a function of the position of the object. Work is the area under the curve of the force vs. position graph. Areas above the position axis are positive work and areas below the axis are negative work. If the force is not constant, we can divide the graph into sections with simpler shapes and add up the work in each section. To find the total work done on the object in the force vs. position graph in Figure 1 over displacement d, start subscript, 1, end subscript, plus, d, start subscript, 2, end subscript, the areas of A, start subscript, 1, end subscript and A, start subscript, 2, end subscript can be added together.
A, start subscript, 1, end subscript is a rectangle of height F, start subscript, o, end subscript and width d, start subscript, 1, end subscript. A, start subscript, 2, end subscript is a triangle of height F, start subscript, o, end subscript and base d, start subscript, 2, end subscript. The total work done on the object over d, start subscript, 1, end subscript, plus, d, start subscript, 2, end subscript is
\begin{aligned}W_{total}&= A_1+A_2\\ \\\\ &= F_od_1 + \dfrac{1}{2}F_od_2\end{aligned}
For worked examples of finding work from a force vs. displacement graph, watch our video about calculating work from force vs. displacement graphs.

## Common mistakes and misconceptions

1) People forget that forces acting perpendicular to displacement do zero work. Since cosine, 90, degrees, equals, 0, no work occurs when force F and displacement d are perpendicular even though a perpendicular force can change the object’s direction of motion. For example, if a box is pulled across the level floor, the floor does zero work on the box even though the box is moving. This is because the normal force is perpendicular to the horizontal displacement of the box.
2) People forget what the sign of work means. Positive work on a system means it receives energy from its surroundings. Negative work on a system means it gave energy to its surroundings. Negative work occurs when the force has a component in the direction opposite the displacement.