RaySix

Post

Gravitational Forces and Acceleration Between Two Planets

Created by @nathanedwards

at October 31st 2023, 9:29:06 pm.

AP_Physics_1-Questions

#gravitational-force

#newtons-law-of-universal-gravitation

#acceleration-due-to-gravity

Question:

Two planets, A and B, have masses of 3 × 10^24 kg and 5 × 10^24 kg, respectively. The distance between the centers of the planets is 6 × 10^8 meters.

a) Calculate the gravitational force between planets A and B.

b) If planet A experiences an acceleration due to gravity of 4 m/s², calculate the acceleration due to gravity experienced by planet B.

Answer:

a) To calculate the gravitational force between two objects, we can use Newton's law of universal gravitation:

F = G \cdot \frac{m_1 \cdot m_2}{r^2}

where F is the gravitational force, G is the gravitational constant (approximately equal to 6.67 × 10^(-11) N·m²/kg²), m₁ and m₂ are the masses of the objects, and r is the distance between their centers.

For planet A and B, m₁ = 3 × 10^24 kg, m₂ = 5 × 10^24 kg, and r = 6 × 10^8 m. Plugging these values into the equation, we get:

F = (6.67 \times 10^{-11} \, \text{N·m²/kg²}) \times \frac{(3 \times 10^{24} \, \text{kg}) \times (5 \times 10^{24} \, \text{kg})}{(6 \times 10^{8} \, \text{m})^2}

Simplifying,

F = (6.67 \times 10^{-11} \, \text{N·m²/kg²}) \times \frac{15 \times 10^{48} \, \text{kg²}}{36 \times 10^{16} \, \text{m²}}

Dividing and cancelling units,

F = 2.778 \times 10^{14} \, \text{N}

Therefore, the gravitational force between planets A and B is approximately 2.778 × 10^14 N.

b) The acceleration due to gravity experienced by an object can be calculated using the formula:

g = \frac{F}{m}

where g is the acceleration due to gravity, F is the gravitational force, and m is the mass of the object.

For planet B, the gravitational force F is the same as the calculated value in part (a), while the mass m of planet B is 5 × 10^24 kg. Plugging these values into the equation, we have:

g = \frac{2.778 \times 10^{14} \, \text{N}}{5 \times 10^{24} \, \text{kg}}

Simplifying,

g = \frac{2.778}{5} \times 10^{-10} \, \text{m/s²}

Therefore, the acceleration due to gravity experienced by planet B is approximately 5.556 × 10^(-11) m/s².