Physics

Physics

Problem

Mass m1=2.0 kgm_1 = 2.0\,\text{kg} is located at point A(0, 0, 0)A(0,\,0,\,0) and mass m2=3.0 kgm_2 = 3.0\,\text{kg} is located at point B(0.30 m, 0.40 m, 0.00 m)B(0.30\,\text{m},\,0.40\,\text{m},\,0.00\,\text{m}) in a Cartesian coordinate system. (i) Determine the position vector r12\mathbf r_{12} from m1m_1 to m2m_2 and its magnitude rr. (ii) Hence calculate the gravitational force vector F12\mathbf F_{12} acting on m1m_1 due to m2m_2 in unit-vector notation. (iii) Write the gravitational force vector acting on m2m_2 due to m1m_1 and verify that the two forces are equal in magnitude and opposite in direction.
Intuitive explanation

The core concept here is gravitational force between point masses and Newton's third law. Start by finding the displacement vector between the masses—this direction tells you where the force points—then use Newton's law of universal gravitation F=Gm1m2r2F = \frac{Gm_1m_2}{r^2} to find the magnitude, and finally scale a unit vector in that direction to get the full force vector. The key insight is that the two forces must be equal and opposite by Newton's third law, so you're really just checking your arithmetic and understanding that gravity always acts along the line joining the masses.

Intuitive explanation

The core concept here is gravitational force between point masses and Newton's third law. Start by finding the displacement vector between the masses—this direction tells you where the force points—then use Newton's law of universal gravitation F=Gm1m2r2F = \frac{Gm_1m_2}{r^2} to find the magnitude, and finally scale a unit vector in that direction to get the full force vector. The key insight is that the two forces must be equal and opposite by Newton's third law, so you're really just checking your arithmetic and understanding that gravity always acts along the line joining the masses.

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