Question

Two ships of equal mass are 109 m apart. What is the acceleration of either ship due to the gravitational attraction of the other? Treat the ships as particles and assume each has a mass of 39,000 metric tons. (Give the magnitude of your answer in m/s2.)

Answer 1

The acceleration is
`a = 2.190 *10^(-7) \ m/s^2`

Step-by-step explanation:

From the question we are told that

The distance of separation of the ship is
`r= 109 \ m`

The mass of each ship is
`M = 39,000 \ metric\ tons =39,000 * 1000 = 3.9 *10^(7)\ kg`

The gravitational force of attraction exerted on each other is mathematically represented as

`F_g = ( GMM)/(r^2)`

Where G is the gravitational constant with value

substituting values

`F_g = ( 6.674 30 * 10^(-11) (3.9 *10^(7))^2)/(109^2)`

`F_g = 8.54 \ N`

This force can also be mathematically represented as

`F_g = M * a`

=>
`a = (F_g)/(M)`

substituting values

`a = (8.544)/(3.9 *10^(7))`

`a = 2.190 *10^(-7) \ m/s^2`