Two tankers of equal mass attract each other with a force of 3.5 x 103 N. If their centres are 85 m apart, find the mass of each tanker.



Answer :

ANSWER

6.15 · 10⁸ kg

EXPLANATION

Given:

• The force of attraction between the two tankers, F = 3.5x10³N

,

• The distance between their centers of mass, r = 85m

,

• The two tankers have equal masses, m₁ = m₂ = m

Known:

• The gravitational constant, G = 6.67 x 10⁻¹¹ Nm²/kg²

Unknown

• The mass of each tanker, m

By Newton's law of universal gravitation, we have that the force of attraction between two objects of masses, m₁, and m₂, separated by a distance r is,

[tex]F=G\cdot\frac{m_1m_2}{r^2}[/tex]

In this case, both masses are equal,

[tex]F=G\cdot\frac{m^2}{r^2}[/tex]

Solving for m,

[tex]m=r\sqrt[]{\frac{F}{G}}[/tex]

Replace with the values,

[tex]m=85m\cdot\sqrt[]{\frac{3.5\times10^3N}{6.67\times10^{-11}Nm^2/\operatorname{kg}}}\approx6.15\times10^8\operatorname{kg}[/tex]

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