引力方程

关于万有引力方程的3个问题

1. 三个质量均为 1 kg 的质点位于边长为 1 m 的等边三角形的三个顶点上。每个质点所受到的引力有多大（以 G 为单位）？

解决方案

粒子所受到的引力大小。

F₁₂ = G (m₁（米）₂)/r² = G (1)(1) / 1² = G/1 = G

F₁₃ = G (m₁（米）₃)/r² = G (1)(1) / 1² = G/1 = G

1 点处的合重力：

F₁ = √1²+1² = √1+1 = √2 Newton

2. The figure below depicts three objects m₁ = 6 kg; m₂ = 3 kg 和 m₃ = 4 kg lie on a straight line. Determine the magnitude and direction of the resultant gravitational force experienced by m2! (state in G)

已知：

m₁ = 6公斤

m₂ = 3公斤

m₃ = 4公斤

gravitational constant = G

r₂₁ = 4 m

r₂₃ = 2 m

通缉： F resultant gravity experienced by m₂

解决方案：

The gravitational force between m₂ 和米₃:

F = G (3)(4) / 2² = G 12 / 4 = 3G

The gravitational force between m₂ 和米₁:

F = G (3)(6) / 4² = G 18 / 16 = 1,125G

3. Object A with a mass of 1 kg and object B with a mass of 2 kg are separated by a distance of 2 m from one another. Point P is 2 m from object A and 2 m from object B. How strong is the gravitational field at point P?

已知：

m_A = 1公斤

m_B = 2公斤

r_PA = 2 m

r_PB = 2 m

Gravity constant = G

通缉： E gravity at point P

解决方案：

E_PA = G (m_A)/r² = G (1) / 2² = G/4 = 0,25G

E_PB = G (m_B)/r² = G (2) / 2² = 2G/4 = 0,5G

Resultant gravitational field strength at point P:

E = √0,25G²+0,5G² = √0,0625G²+0,25G² = √0,3125G² = 0,56G N/kg