Gravitatiounsgläichung

3 Froen iwwer d'Gravitatiounsgläichung

1. Dräi Partikelen mat all enger Mass vun 1 kg sinn an de Spëtze vun engem gläichsäitegen Dräieck, deem seng Säiten 1 m laang sinn. Wéi grouss ass d'Gravitatiounskraaft, déi vun all Punktpartikel erlieft gëtt (a G)?

Léisung

D'Gréisst vun der Gravitatiounskraaft, déi vun engem vun de Partikelen erlieft gëtt.

F₁₂ = G (m₁)(m₂) /r² = G (1)(1) / 1² = G/1 = G

F₁₃ = G (m₁)(m₃) /r² = G (1)(1) / 1² = G/1 = G

Resultant Gravitatiounskraaft um Punkt 1:

F₁ = √1²+1² = √1+1 = √2 Newton

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

Bekannt:

m₁ = 6 kg dir

m₂ = 3 kg dir

m₃ = 4 kg dir

gravitational constant = G

r₂₁ = 4m

r₂₃ = 2m

Gewënscht: F resultant gravity experienced by m₂

Léisung:

The gravitational force between m₂ an m₃:

F = G (3)(4) / 2² = G 12 / 4 = 3G

The gravitational force between m₂ an m₁:

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?

Bekannt:

m_A = 1 kg dir

m_B = 2 kg dir

r_PA = 2m

r_PB = 2m

Gravity constant = G

Gewënscht: E gravity at point P

Léisung:

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