An object’s kinetic energy when it moves at different velocities is shown in the table. What is the object’s mass in grams?
Okay, so in this table, we can see that we’ve been given five different velocities in metres per second as well as the kinetic energy in joules of this particular object for each one of those five velocities. Based on this information, we’ve been asked to find the object’s mass in grams. So we need to recall the relationship between an object’s mass, its velocity, and its kinetic energy. So to do this, we can recall that the kinetic energy of an object is found by multiplying half by the mass of the object 𝑚 multiplied by the velocity of the object 𝑣 squared.
And in the table in this question, we’ve been given lots of different values of the velocity of the object and corresponding kinetic energy values for these velocities. So in order to find the mass of this object, we need to rearrange this equation. To do this, we can multiply both sides of the equation by two divided by 𝑣 squared. This way on the right-hand side, we’ve got half multiplied by two that cancels. And we’ve got 𝑣 squared in the numerator and 𝑣 squared in the denominator. That also cancels. And we’re just left with the mass on the right-hand side.
And then on the left-hand side, we’ve got two multiplied by the kinetic energy divided by 𝑣 squared. So at this point, we can take any value for the velocity of the object and its corresponding kinetic energy value and substitute these into our equation. So let’s start with this first one. We can say that two multiplied by the kinetic energy, which is 0.1 joules, divided by the velocity of the object squared, which is one metre per second whole squared, is equal to the mass of the object.
However, it is worth noting that because we’re working in base units, so that’s joules for kinetic energy and metres per second for velocity, our answer is going to be in its own base unit which is the kilogram. So when we value at the left-hand side, we find that the mass of the object 𝑚 is 0.2 kilograms. Now to calculate this mass, we could have picked any one of the other points as well. Try it yourself. Pick any velocity, let’s say four metres per second, and the corresponding kinetic energy, 1.6 joules. And plug it into this equation. We should get the same answer for the mass.
And so this is a good way to confirm that we’ve got the right answer because we now know that we’ve got an object whose mass is not changing. However, as we increase its velocity, its kinetic energy increasing as well. However, 0.2 kilograms is not the answer to our question because, remember, we’ve been asked to find the object’s mass in grams. And to do this, we need to recall the conversion between kilograms and grams.
Let’s recall that one kilogram is equivalent to 1000 grams. That’s what the prefix kilo means; it means 1000. And so if you want to convert 0.2 kilograms to grams, then we can say that 0.2 kilograms is equivalent to 0.2 multiplied by one kilogram which is 1000 grams. In other words, we’ve replaced these kilograms with this parenthesis, 1000 grams. And so 0.2 times 1000 grams ends up being 200 grams. And hence, we found the answer to our question which is that the mass of the object is 200 grams.