Two objects are placed so their centers are 1.65 meters apart, and the force between them is 8.09 x 10-10 newtons. What is the mass of each object if one has twice the mass of the other? Include units

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asked Nov 16, 2023 80.5k views

2 votes

Physics
college

Aidanjacobson asked

by Aidanjacobson

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1 Answer

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Using Newton's law of universal gravitation:

$F=G\cdot(m1\cdot m2)/(r^2)$

Where:

$\begin{gathered} G=6.674*10^(-11)\cdot\frac{m^3}{\operatorname{kg}\cdot s^2} \\ r=1.65m \\ F=8.09*10^(-10)N \\ m2=2m1 \end{gathered}$

So:

$F=2G\cdot(m1^2)/(r^2)$

Solve for m1:

$\begin{gathered} m1=\sqrt[]{(F\cdot r^2)/(2G)} \\ m1=\sqrt[]{(8.09*10^(-10)\cdot(1.65)^2)/(2\cdot6.674*10^(-11))} \\ m1=4.06\operatorname{kg} \end{gathered}$

So:

$m2=8.12\operatorname{kg}$

Answer:

4.06kg and 8.12kg

Nij answered Nov 23, 2023

by Nij

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