### Video Transcript

A piece of iron is placed 23 centimeters away from a piece of nickel that has a mass of 46 kilograms. Given that the force of gravity between them is 2.9 times 10 to the power of negative eight newtons, determine the mass of the piece of iron. Take the universal gravitational constant ๐บ is equal to 6.67 times 10 to the power of negative 11 newton meter squared per kilogram squared.

If we take a look at this question, we can see that it talks about the gravitational force between two bodies. It also mentions the universal gravitational constant ๐บ. So therefore, what we can say that is that weโre gonna use Newtonโs law of universal gravitation to help us solve the problem. And what we have is that ๐น sub ๐บ is equal to capital ๐บ multiplied by ๐ sub one multiplied by ๐ sub two over ๐ squared. And this is where ๐น sub ๐บ is the gravitational force. Then weโve got big ๐บ or capital ๐บ is the universal gravitational constant. And what this is here for is to actually make sure that our units line up when we get our final result if we were looking to find the gravitational force.

Then we have our masses. And these are masses of the bodies. And then we have ๐, which is our separation or distance between them. Now with this type of problem, what we always do first is have a look at the information weโve been given. Well, we know the gravitational force ๐น sub ๐บ is 2.9 times 10 to the power of negative eight newtons. Then we know that the mass of the piece of nickel is 46 kilograms. Then we have the mass of the piece of iron, which weโll call ๐ sub ๐ผ. Well, this is what weโre trying to find out. So weโll put a question mark. Then we have the universal gravitational constant, big ๐บ, which is 6.67 multiplied by 10 to the power of negative 11 newton meters squared per kilogram squared. And then finally, we have ๐, which is our separation or distance between the two pieces of metal. That is 23 centimeters.

However, on inspection, if we look at the other units that weโre using, we can see, in fact, that we want distances to be in meters. So weโre gonna convert 23 centimeters into meters, which is gonna give us 0.23 meters. Okay, great, so we now have all the information we need to substitute into our formula to help us find the mass of the piece of iron. So before we actually substitute our values in, what weโre gonna do is actually rearrange our formula to make the mass of iron the subject. So weโve got ๐น sub ๐บ equals ๐บ multiplied by ๐ sub ๐ผ multiplied by ๐ sub ๐ over ๐ squared.

So first of all, if we multiply through by ๐ squared, weโre gonna get ๐น sub ๐บ ๐ squared is equal to ๐บ multiplied by ๐ sub ๐ผ ๐ sub ๐. So then what we do is divide through by ๐บ ๐ sub ๐. So then what Iโve done here is actually swapped it over so we have the ๐ sub ๐ผ on the left-hand side. So weโve got ๐ sub ๐ผ, so the mass of the iron, is equal to ๐น sub ๐บ ๐ squared over ๐บ multiplied by ๐ sub ๐. Now all weโre left to do is substitute in our values and calculate the mass of the iron.

So when we substitute in our values, we get the mass of the iron is equal to 2.9 times 10 to the power of negative eight multiplied by 0.23 squared divided by 6.67 times 10 to the power of negative 11 multiplied by 46. So then if we calculate this, we get 0.5. So therefore, we can say that the mass of the iron is 0.5 kilograms.