Question

Two ocean liners, each with a mass of 42,000 metric tons, are moving on parallel courses, 93 m apart. What is the magnitude of the acceleration of one of the liners toward the other due to their mutual gravitational attraction? Treat the ships as particles.

Answer 1

0.324×10⁻³ m/s²

Step-by-step explanation:

G=Gravitational constant=6.67408×10⁻⁸ m³/kg s

m₁=m₂=Mass of the ships=42000×10³ kg

r=Distance between the ships=93 m

The ships are considered particles

From Newtons Law of Universal Gravitation

`F=G\frac {m_1m_2}{r^2}\\Here\ m_1=m_2\ hence\ m_1* m_2=m_1^2\\\Rightarrow F=G\frac {m_1^2}{r^2}\\\Rightarrow F=(6.67408* 10^(-8)* (42000* 10^3)^2)/(93^2)\\\Rightarrow F=13612.0674\ N\\`

`F=ma\\\Rightarrow 13612.0674=42000* 10^3a\\\Rightarrow a=0.324* 10^(-3)\ m/s^2`

∴Acceleration of one of the liners toward the other due to their mutual gravitational attraction is 0.324×10⁻³