3 questions about Gravity equation
1. Three particles each with a mass of 1 kg are at the vertices of an equilateral triangle whose sides are 1 m long. How large is the gravitational force experienced by each point particle (in G)?
Solution
The magnitude of the gravitational force experienced by one of the particles.
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 gravitational force at point 1:
F1 = √12+12 = √1+1 = √2 Newton
2. The figure below depicts three objects m1 = 6 kg; m2 = 3 kg and m3 = 4 kg lie on a straight line. Determine the magnitude and direction of the resultant gravitational force experienced by m2! (state in G)
Known:
m1 = 6 kg
m2 = 3 kg
m3 = 4 kg
gravitational constant = G
r21 = 4 m
r23 = 2 m
Wanted: F resultant gravity experienced by m2
Solution:
The gravitational force between m2 and m3:
F = G (3)(4) / 22 = G 12 / 4 = 3G
The gravitational force between m2 and 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?
Known:
mA = 1 kg
mB = 2 kg
rPA = 2 m
rPB = 2 m
Gravity constant = G
Wanted: E gravity at point P
Solution:
EPA = G (mA) / r2 = G (1) / 22 = G/4 = 0,25G
EPB = G (mB) / 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
4. Problem: Determine the gravitational force between two objects with masses 5 kg and 10 kg that are 2 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (5 kg x 10 kg) / (2 m)² = 8.343875 x 10⁻¹¹ N.
5. Problem: Determine the gravitational force between two objects with masses 1 kg each that are 1 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (1 kg x 1 kg) / (1 m)² = 6.67430 x 10⁻¹¹ N.
6. Problem: Determine the gravitational force between two objects with masses 1000 kg and 2000 kg that are 3 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (1000 kg x 2000 kg) / (3 m)² = 1.48206 x 10⁻⁸ N.
7. Problem: Determine the gravitational force between two objects with masses 500 kg and 500 kg that are 1 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (500 kg x 500 kg) / (1 m)² = 1.668575 x 10⁻⁸ N.
8. Problem: Determine the gravitational force between two objects with masses 700 kg and 800 kg that are 2 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (700 kg x 800 kg) / (2 m)² = 1.334860 x 10⁻⁸ N.
9. Problem: Determine the gravitational force between two objects with masses 5 kg and 10 kg that are 2 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (5 kg x 10 kg) / (2 m)² = 8.343875 x 10⁻¹¹ N.
10. Problem: An object with a mass of 10 kg is dropped from a height. What is the acceleration due to gravity? Solution: The acceleration due to gravity is approximately 9.8 m/s² on Earth. It does not depend on the mass of the object.
11. Problem: Determine the gravitational force between two objects with masses 1 kg each that are 1 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (1 kg x 1 kg) / (1 m)² = 6.67430 x 10⁻¹¹ N.
12. Problem: An object with a mass of 500 kg is dropped from a height. What is the acceleration due to gravity? Solution: The acceleration due to gravity is approximately 9.8 m/s² on Earth. It does not depend on the mass of the object.
13. Problem: Determine the gravitational force between two objects with masses 700 kg and 800 kg that are 2 m apart. Solution: F = G x (m₁m₂) / r² = 6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻² x (700 kg x 800 kg) / (2 m)² = 1.334860 x 10⁻⁸ N.