Video: Finding the Mass of a Body Moving Vertically with Constant Acceleration with Two Vertical Forces Acting on It

The diagram shows a body of mass ๐‘š kg which moves with a constant acceleration of 0.8 m/sยฒ under the action of 3 vertical forces. Given that the weight of the body is ๐‘ค, and the forces are measured in newtons, find ๐‘š. Use ๐‘” = 9.8 m/sยฒ.

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Video Transcript

The diagram shows a body of mass ๐‘š kilograms, which moves with a constant acceleration of 0.8 meters per square second under the action of three vertical forces. Given that the weight of the body is ๐‘ค and the forces are measured in newtons, find ๐‘š. Use ๐‘” equals 9.8 meters per square second.

Weโ€™re trying to find the value of ๐‘š, but weโ€™ve got an extra unknown ๐‘ค. And weโ€™ll see how they link in a moment. To begin with, weโ€™re just going to work out the weight of the body. Weight is a force, and so weโ€™re going to use Newtonโ€™s second law of motion. Net force is equal to mass times acceleration. And so weโ€™re going to find the net force acting on this body and set that equal to mass times acceleration. And to do so, we need to find the positive direction. Letโ€™s define downwards to be positive. Then we can say in the positive direction, we have ๐‘ค. In the negative direction, we have 10 and 71. So the net force in our system is ๐‘ค minus 10 minus 71, which is ๐‘ค minus 81. Then thatโ€™s equal to mass times acceleration.

Notice that the acceleration is acting in the positive direction. So ๐‘š๐‘Ž becomes ๐‘š times 0.8. And so we can say that ๐‘ค minus 81 is 0.8๐‘š. But what is ๐‘ค and how does it link with the mass ๐‘š? Well, ๐‘ค is known as the weight of the body. And somewhat counterintuitively, that is in fact a force. In fact, as a direct result of Newtonโ€™s second law, weight is known as the mass of the object times its acceleration due to gravity. So weight is ๐‘š๐‘”.

We can therefore rewrite our equation as ๐‘š๐‘” minus 81 equals 0.8๐‘š. Remember, weโ€™re trying to find the value of ๐‘š, so we need to make ๐‘š the subject. Letโ€™s subtract 0.8๐‘š from both sides. That gives us ๐‘š๐‘” minus 81 minus 0.8๐‘š equals zero. Next, we add 81, and we then notice that on the left-hand side of our equation we can factor ๐‘š. So our equation becomes ๐‘š times ๐‘” minus 0.8 equals 81. But of course, ๐‘” is equal to 9.8. So ๐‘” minus 0.8 is 9.8 minus 0.8, and 9.8 minus 0.8 is just nine. So we get nine ๐‘š equals 81. And to solve our equation for ๐‘š, weโ€™re going to divide both sides by nine. 81 divided by nine is nine. And so the value of ๐‘š is nine. The body has a mass of nine kilograms.

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