Question Video: Finding the Work Done by a Force Mathematics

A body moves in a straight line against a resistance force of 360 N. Find the work done by this force over the displacement 𝐒, where |𝐒| = 390 m.

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Video Transcript

A body moves in a straight line against a resistance force of 360 newtons. Find the work done by this force over the displacement 𝐒, where the magnitude of vector 𝐒 is 390 meters.

We begin by recalling that the work done can be calculated by multiplying the force by the distance. When dealing with vectors, 𝑊 is equal to the dot product of 𝐅 and 𝐝. It is important to note that for both 𝐅 and 𝐝, direction matters. Therefore, the work can be positive, negative, or zero. In this question, we are told that the resistance force of 360 newtons acts against the direction of the body. We need to work out the work done by the force over a displacement of 390 meters.

We can calculate this work done by multiplying negative 360 by 390. The 360-newton resistive force is negative as it is acting against the motion. Negative 360 multiplied by 390 is negative 140,400. As the force is measured in newtons and distance in meters, then the work done is measured in newton meters. These are more commonly known as joules. The work done by the force over a displacement of 390 meters is negative 140,400 joules.

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