Video: Determining the Gravitational Force between Two Spheres

Determine the gravitational force between two balls of masses 5.9 kg and 10 kg, given that the distance between their centers is 10 cm and the universal gravitational constant is 6.67 × 10⁻¹¹ N⋅m²/kg².

03:35

Video Transcript

Determine the gravitational force between two balls of masses 5.9 kilograms and 10 kilograms, given that the distance between their centers is 10 centimeters and the universal gravitational constant is 6.67 times 10 to the power of negative 11 newton meters squared per kilogram squared.

So, in this question, we’re told about the universal gravitational constant. So what this tells us is that this question is a question about Newton’s universal law of gravitation. And when we’re looking at Newton’s law of universal gravitation, there are a couple of formulae that can help us. And in this problem, we’re gonna use the one that’s based around the gravitational force between two masses. And this formula tells us that 𝐹 sub 𝐺 is equal to capital 𝐺 multiplied by 𝑚 sub one multiplied by 𝑚 sub two over 𝑟 squared. And this is where 𝐹 sub 𝐺 is the gravitational force, capital 𝐺 is the universal gravitational constant, 𝑚 sub one and 𝑚 sub two are the masses of our two balls, and then 𝑟 is the distance between their centers.

So now, we have this formula. What we can do is use it to help us find what we’re asked to find in this question, which is the gravitational force between two balls. Well, what we want to do first is look through the question to see what information we have been given. First of all, we know the masses of the two balls. So we’ve got 𝑚 sub one is 5.9 kilograms and 𝑚 sub two is 10 kilograms. We know that 𝑟, the distance between our centers, is 10 centimeters.

However, if we check the units of our universal gravitational constant, we can see that it’s newton meters squared per kilogram squared. So therefore, our length measurement is in fact in meters. So what we need to do is convert 𝑟, distance between their centers, from centimeters to meters. And because there are 100 centimeters in a meter, to do this, all we do is divide by 100. So when we do that, we get a distance of 0.1 meters. So we can say that the distance between the centers is 0.1 meters.

Then finally, we’re told that the universal gravitational constant is 6.67 times 10 to the power of negative 11 newton meters squared per kilogram squared. Okay, great, we have all the information we need now to find our gravitational force 𝐹 sub 𝐺. So when we substitute our values into the formula that we looked at at the beginning, then what we’re gonna get is 𝐹 sub 𝐺, our gravitational force, is equal to 6.67 times 10 to the power of negative 11 multiplied by 5.9 multiplied by 10 all over 0.1 squared.

So now if we calculate this, what we’re going to get is 𝐹 sub 𝐺 is equal to 3.935 times 10 to the power of negative seven newtons. So therefore, we can say that the gravitational force between two balls of masses 5.9 kilograms and 10 kilograms, given that the distance between their centers is 10 centimeters, is 3.935 times 10 to the power of negative seven newtons.

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