Question

Three identical very dense masses of 4300 kg each are placed on the x axis. One mass is at x1 = -120 cm , one is at the origin, and one is at x2 = 400 cm .

Part A

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/kg2 .

Express your answer in Newtons.

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of each particle = m = 4300 kg

Position of the first particle on the X-axis = X₁ = -120 cm = -1.2 m

Position of the second particle on the X-axis = X₂ = 400 cm = 4 m

Position of the third particle on the X-axis = X₃ = 0 m

Distance between the first and the third particle = D₁ = X₃ - X₁ = 0 - (-1.2) = 1.2 m

Distance between the second and the third particle = D₂ = X₂ - X₃ = 4 - 0 = 4 m

Gravitational force on the third particle due to the first particle = F₁ (Directed along the negative X-axis)

Gravitational force on the third particle due to the second particle = F₂ (Directed along the positive X-axis)

Net force on the third particle = F_net

F_net = F₂ - F₁

F_net = -7.793 x 10^-4 N

Negative as it is directed along the negative X-axis.

We are asked for the magnitude of the force therefore it will be positive.

A) Magnitude of net gravitational force on the mass at origin due to the other two masses = 7.793 x 10^-4 N