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GravitationGravity and mass calculation - Example

Projectile motion is analysed in terms of vertical and horizontal components. The gravitational force between objects depends on their mass and the distance between their centres.

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Gravity and mass calculation - Example

The supertankers TI Europe and TI Oceania are two of the largest free-moving objects made by man, how does gravitation affect them?

Each ship has a total mass of \(5\times {10^8}kg\) and they could float alongside each other with their centres separated by 100 metres.

Although they are not spherical objects the gravitational attraction between the two supertankers can be approximately calculated.

To calculate the gravitational attraction between the tankers, Newton's Law of Gravitation can be used:

\({m_1} = {m_2} = 5 \times {10^8}kg\)

\(r = 100m\)

\(G = 6.674 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}\)

\(F = \frac{{G{m_1}{m_2}}}{{{r^2}}}\)

\(F = \frac{{6.674 \times {{10}^{ - 11}} \times 5 \times {{10}^8} \times 5 \times {{10}^8}}}{{{{100}^2}}}\)

\(F = 1670N\)

Although this is quite a big force (possibly over twice your own weight?) you can try calculating what the acceleration of the supertankers would be and how long it would take mutual gravity to move them closer by even a metre assuming no friction due to water resistance.

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