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 ๐ค and the forces are measured in newtons, find ๐. Use ๐ equals 9.8 meters per square
second.
Weโre trying to find the value of
๐, but weโve got an extra unknown ๐ค. And weโll see how they link in a
moment. To begin with, weโre just going to
work out the weight of the body. Weight is a force, and so weโre
going to use Newtonโs second law of motion. Net force is equal to mass times
acceleration. And so weโre 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. Letโs define downwards to be
positive. Then we can say in the positive
direction, we have ๐ค. In the negative direction, we have
10 and 71. So the net force in our system is
๐ค minus 10 minus 71, which is ๐ค minus 81. Then thatโs equal to mass times
acceleration.
Notice that the acceleration is
acting in the positive direction. So ๐๐ becomes ๐ times 0.8. And so we can say that ๐ค minus 81
is 0.8๐. But what is ๐ค and how does it link
with the mass ๐? Well, ๐ค is known as the weight of
the body. And somewhat counterintuitively,
that is in fact a force. In fact, as a direct result of
Newtonโs second law, weight is known as the mass of the object times its
acceleration due to gravity. So weight is ๐๐.
We can therefore rewrite our
equation as ๐๐ minus 81 equals 0.8๐. Remember, weโre trying to find the
value of ๐, so we need to make ๐ the subject. Letโs subtract 0.8๐ from both
sides. That gives us ๐๐ 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,
weโre 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.
