The Work Done By a Force in Moving From Point to Point

The equationWork Done = Force*Distance only applies when a constant force acts in the direction of movement. To find the work done when a constant force does not act in the direction in which a particle moves we use the dot product:

For, example when a particle moves fromtounder the action of the force

we first find the displacement vector from the start point to the end point:

The work done is then

The dot productwhere e-d is the unit vector in the direction ofreturns the component ofin the direction of() as shown below. Multiplying this by gives the work done by the force.

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