Question

problem 1
two spaceships are headed to colonize mars. find the approximate gravitational force of attraction between the two spaceships in space, separated by a distance of r = 10, 000 m. one spaceship has a mass of m₁ = 10, 000 kg, and the other one has a mass of m₂ = 7, 000 kg. make sure to follow the following steps: 1) draw a free body diagram 2) write down the expression for the force 3) plug in the numbers.

Explanation:

Step1: Draw a free - body diagram

Draw two circles representing the spaceships. Label them with their masses \(m_1 = 10000\space kg\) and \(m_2=7000\space kg\). Draw an arrow between them representing the gravitational force \(F\). The distance between the centers of the two circles is \(r = 10000\space m\).

Step2: Write down the expression for the force

The gravitational force formula is \(F=G\frac{m_1m_2}{r^{2}}\), where \(G = 6.67\times10^{- 11}\space N\cdot m^{2}/kg^{2}\) (the gravitational constant).

Step3: Plug in the numbers

Substitute \(m_1 = 10000\space kg\), \(m_2 = 7000\space kg\), \(r = 10000\space m\) and \(G=6.67\times 10^{-11}\space N\cdot m^{2}/kg^{2}\) into the formula:

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Answer:

The gravitational force of attraction between the two spaceships is approximately \(4.67\times 10^{-11}\space N\)