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Question Video: Finding the Work Done on a Body given Its Acceleration and Distance Covered Mathematics

A body of mass 0.9 kg moved a distance of 25 cm while accelerating at 8 cm/s². Find the work done 𝑊.

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Video Transcript

A body of mass 0.9 kilograms moved a distance of 25 centimeters while accelerating at eight centimeters per square second. Find the work done 𝑊.

What do we mean firstly by work done? Well, work is a measure of energy transfer when a force 𝐹 moves an object through a distance 𝐷. We say that work done is equal to this force multiplied by this distance. But we do need to be really careful with our units. Work done is generally calculated in joules. This is a result of using a force calculated in newtons and a distance measured in meters. Sometimes, though, we work in something called ergs. This relates to a force measured in dynes and a distance measured in centimeters.

In our question, we’ve been given a distance measured in centimeters, so we’re going to measure our work done in ergs. Before we do though, we’re going to begin by calculating the force that’s moving this body. This time we use the formula force is equal to mass times acceleration. And if we’re looking for a force measured in dynes, our mass must be measured in grams and our acceleration must be measured in centimeters per square second.

Well, our acceleration is already in this unit. Our mass, however, is given in kilograms, so we’re going to multiply by 1,000 to find the mass in grams. 0.9 times 1,000 is 900. So, the body has a mass of 900 grams. We can, therefore, say that the force acting upon the body measured in dynes is 900 times the acceleration, which is eight. That’s 7,200 or 7,200 dynes.

We said that the work done is calculated by finding the product of the force acting upon the body and the distance that it moves. So, that’s 7,200 times 25. That’s 180,000 ergs. We might choose to represent this using standard index form, in which case we see that the work done on the body is 1.8 times 10 to the fifth power ergs.

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