Determine the gravitational force between two identical balls each of mass 3.01 kilograms, given that the distance between their centres is 15.05 centimetres, and the universal gravitational constant is 6.67 multiplied by 10 to the minus 11 newton metres squared per kilogram squared.
So, what we have to solve this problem is a formula. And that formula is that 𝐹 is equal to 𝐺𝑚 one 𝑚 two over 𝑠 squared, where 𝐹 is the gravitational force. Capital 𝐺 is gravitational constant, not to be confused with small 𝑔 which is what we use for acceleration due to gravity. 𝑚 one and 𝑚 two are our masses. And 𝑠 is our distance. Okay, great. So, now, we know this, let’s use this formula to work out our problem and determine the gravitational force.
Well, the first thing I do with any problem like this is list out our variables. Well, we know 𝑚 one and 𝑚 two are both equal to 3.01. And the reason they’re 3.01 is because we’re told that the two balls are identical. So, these are both 3.01 kilograms. Now, what I’d also do is check the units. We can see that they’re both kilograms. And we can also see that part of the units for our gravitational constant are kilograms. So, that’s great! We’re working in the same units here. So, now, let’s move on to what else we know.
Well, we know that capital 𝐺, our gravitational constant, is 6.67 times 10 to the power of negative 11. And then, we know that 𝑠 is equal to 15.05 centimetres. However, again, if we take a look at the units that are used in our gravitational constant, we could see that 𝑚 appears here, so metres. However, our distance is in centimetres. So, what we need to do is convert. So, as there are 100 centimetres in a metre, we’re gonna divide by 100. And when we do that, we get 0.1505 metres. And that’s because all we do is we move each of the digits two place values to the right. So therefore, we can say that our value of 𝑠 is 0.1505.
Okay, great. So, now, all we need to do is plug this into our formula. And when we do that, what we’re gonna get is 𝐹 is equal to 6.67 multiplied by 10 to the power of negative 11 multiplied by 3.01 squared. And it’s 3.01 squared cause it’s 3.01 multiplied by 3.01 cause, as we said, they’re identical balls. And this is all divided by 0.1505 squared. Which would give us an answer for 𝐹 of 2.668 multiplied by 10 to the power of negative eight.
Now, we’re gonna think, well, what’s the units going to be? Well, as we’re looking at a force, we should know that unit’s going to be newtons. However, what we can do is double check this by checking our units. Well, if we take a look at our units, we’ve got newton metres squared per kilogram squared multiplied by kilogram squared over metre squared.
Well, on the numerator, we can cancel out our kilogram squared cause we divide by kilogram squared and we multiplied by kilograms squared. So, these units will cancel. So, then, we’re left with newton metres squared over metre squared. So, then, our metre squared also cancel. So, we’re left with newtons. So, this is what we had. So, we can confirm that the gravitational force is 2.668 multiplied by 10 to the power of negative eight newtons.