Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Video: Determining the Net Force Due to Gravitation Acting on Two Identical Bodies

Ed Burdette

Evaluate the magnitude of gravitational force between two 5.0 kg mass spherical steel balls separated by a center-to-center distance of 15 cm.

02:48

Video Transcript

Evaluate the magnitude of gravitational force between two 5.0-kilogram mass spherical steel balls separated by a center-to-center distance of 15 centimeters.

In this problem, weโ€™ll assume that capital ๐บ, the universal gravitational constant, is exactly 6.67 times 10 to the negative 11th meters cubed per kilogram second squared.

Letโ€™s start by highlighting some of the vital information given to us. Weโ€™re told the mass of each of the spherical steel balls, which is 5.0 kilograms.

Weโ€™re also told that they have a center-to-center distance of 15 centimeters. We want to solve for the magnitude of the gravitational force between them. Weโ€™ll call this ๐น sub ๐‘”.

To begin, letโ€™s recall the relationship telling us the gravitational force magnitude between two masses, called ๐‘š sub one and ๐‘š sub two. The gravitational force magnitude between two masses is equal to ๐บ, the gravitational constant, multiplied by the product of the masses, ๐‘š one times ๐‘š two, divided by the distance between them squared.

Recall that capital ๐บ is equal to 6.67 times 10 to the negative 11th meters cubed per kilogram second squared. Letโ€™s apply this equation for gravitational force to our scenario. The problem statement tells us that ๐‘š one and ๐‘š two are the same, that they both equal 5.0 kilograms.

Weโ€™re also told that the distance between the centers of the spherical steel balls is 15 centimeters, which is equal to 0.15 meters.

We can now enter in the values for ๐บ, ๐‘š one, ๐‘š two, and ๐‘Ÿ into this equation for force magnitude. And we find an equation that reads the gravitational force magnitude is equal to 6.67 times 10 to the negative 11th meters cubed per kilogram second squared multiplied by 5.0 kilograms times 5.0 kilograms divided by 0.15 meters squared.

When we calculate this value, we find it equal to 7.4 times 10 to the negative 8th newtons. This is the gravitational force magnitude between these two masses.