# 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 𝑚 kg which moves with a constant acceleration of 0.8 m/s² under the action of 3 vertical forces. Given that the weight of the body is 𝑤, and the forces are measured in newtons, find 𝑚. Use 𝑔 = 9.8 m/s².

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### Video Transcript

The diagram shows a body of mass 𝑚 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 𝑤 and the forces are measured in newtons, find 𝑚. Use 𝑔 equals 9.8 meters per square second.

We’re trying to find the value of 𝑚, but we’ve got an extra unknown 𝑤. And we’ll see how they link in a moment. To begin with, we’re just going to work out the weight of the body. Weight is a force, and so we’re going to use Newton’s second law of motion. Net force is equal to mass times acceleration. And so we’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. Let’s define downwards to be positive. Then we can say in the positive direction, we have 𝑤. In the negative direction, we have 10 and 71. So the net force in our system is 𝑤 minus 10 minus 71, which is 𝑤 minus 81. Then that’s equal to mass times acceleration.

Notice that the acceleration is acting in the positive direction. So 𝑚𝑎 becomes 𝑚 times 0.8. And so we can say that 𝑤 minus 81 is 0.8𝑚. But what is 𝑤 and how does it link with the mass 𝑚? Well, 𝑤 is known as the weight of the body. And somewhat counterintuitively, that is in fact a force. In fact, as a direct result of Newton’s second law, weight is known as the mass of the object times its acceleration due to gravity. So weight is 𝑚𝑔.

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