Two cars each have a mass of 1050 kg. lf the gravitational force between them is #2.27 times 10^-7# N, how far apart are they if G = #6.67 times 10^-11 # N*(m/kg)^2?

1 Answer
Surya K.
Feb 4, 2018

The two cars are #1799.86m# apart.

Explanation:

Let's use Newton's Law of Gravitation, which states that the gravitational force between two masses, #m_1# and #m_2#. The distance between the two objects is #d#, and the force's notation is #F#.

Newton put this all into one equation:

#F=(Gm_1m_2)/d^2#

In our case, #m_1# and #m_2# are #1050kg# each. The gravitational force, #F#, is #2.27*10^-7N#.

We must rearrange the equation to make #d# the subject:

#d=+-sqrt((Gm_1m_2)/F)#

Now, since distance can't be negative, the equation is just:

#d=sqrt((Gm_1m_2)/F)#

Now we can input:

#d=sqrt((6.67*10^-11*1050*1050)/(2.27*10^-7))#

#d=sqrt((0.0000735)/(2.27*10^-7))#

#d=sqrt(3239504.405)#

#d~~1799.86m# is the distance between the two cars.

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