# 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 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. Use ๐ = 9.8 m/sยฒ.

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### Video Transcript

The diagram shows a body of mass ๐ 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. Use ๐ equals 9.8 meters per square second.

Weโre trying to find the value of ๐, 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๐ becomes ๐ times 0.8. And so we can say that ๐ค minus 81 is 0.8๐. But what is ๐ค and how does it link with the mass ๐? 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๐.

We can therefore rewrite our equation as ๐๐ minus 81 equals 0.8๐. Remember, weโre trying to find the value of ๐, so we need to make ๐ the subject. Letโs subtract 0.8๐ from both sides. That gives us ๐๐ minus 81 minus 0.8๐ equals zero. Next, we add 81, and we then notice that on the left-hand side of our equation we can factor ๐. So our equation becomes ๐ 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 equals 81. And to solve our equation for ๐, weโre going to divide both sides by nine. 81 divided by nine is nine. And so the value of ๐ is nine. The body has a mass of nine kilograms.