Post

Calculating Gravitational Forces between Masses

Created by @nathanedwards
 at October 31st 2023, 5:10:10 pm.
AP_Physics_1-Questions
#distance
#mass
#gravitational-force

Question:

Two objects, A and B, are located a distance of 1 meter apart. Object A has a mass of 5 kilograms, while object B has a mass of 10 kilograms. The gravitational constant is 6.67 x 10^-11 N(m/kg)^2.

a) Calculate the magnitude of the gravitational force between object A and object B.

b) If the distance between the two objects is tripled, what will be the new magnitude of the gravitational force between them?

c) If object B is then replaced with an object C with a mass of 20 kilograms, and the distance between objects A and C is 2 meters, calculate the magnitude of the new gravitational force between them.

Answer:

a) To calculate the magnitude of the gravitational force between two objects, we can use Newton's Law of Universal Gravitation:

F=G⋅m1⋅m2r2 F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}}

where F is the magnitude of the gravitational force, G is the gravitational constant, m1m_1 and m2m_2 are the masses of the objects, and r is the distance between the objects.

Given: m1=5 kgm_1 = 5 \, \text{kg} m2=10 kgm_2 = 10 \, \text{kg} G = 6.67 \times 10^{-11} \, \text{N(m/kg)^2}

Substituting the given values into the equation, we have:

F = \frac{{(6.67 \times 10^{-11} \, \text{N(m/kg)^2}) \cdot (5 \, \text{kg}) \cdot (10 \, \text{kg})}}{{(1 \, \text{m})^2}}

Calculating this expression gives:

F=3.335×10−10 N F = 3.335 \times 10^{-10} \, \text{N}

Therefore, the magnitude of the gravitational force between object A and object B is 3.335×10−103.335 \times 10^{-10} N.

b) If the distance between the two objects is tripled, the new distance (r') becomes 3 meters. The new magnitude of the gravitational force F′F' can be calculated using the same formula as before:

F′=G⋅m1⋅m2r′2 F' = \frac{{G \cdot m_1 \cdot m_2}}{{r'^2}}

Substituting the given values into the equation, we have:

F' = \frac{{(6.67 \times 10^{-11} \, \text{N(m/kg)^2}) \cdot (5 \, \text{kg}) \cdot (10 \, \text{kg})}}{{(3 \, \text{m})^2}}

Calculating this expression gives:

F′=1.482×10−11 N F' = 1.482 \times 10^{-11} \, \text{N}

Therefore, the new magnitude of the gravitational force between object A and object B, when the distance is tripled, is 1.482×10−111.482 \times 10^{-11} N.

c) If object B is replaced with object C, with a mass of 20 kilograms, and the distance between objects A and C is 2 meters, we can calculate the magnitude of the new gravitational force F′′F'' using the same formula as before:

F′′=G⋅m1⋅m3r′′2 F'' = \frac{{G \cdot m_1 \cdot m_3}}{{r''^2}}

where m3=20 kgm_3 = 20 \, \text{kg} and r′′=2 mr'' = 2 \, \text{m}.

Substituting the given values into the equation, we have:

F'' = \frac{{(6.67 \times 10^{-11} \, \text{N(m/kg)^2}) \cdot (5 \, \text{kg}) \cdot (20 \, \text{kg})}}{{(2 \, \text{m})^2}}

Calculating this expression gives:

F′′=1.6685×10−10 N F'' = 1.6685 \times 10^{-10} \, \text{N}

Therefore, the magnitude of the new gravitational force between object A and object C, when the mass of object B is replaced with object C, is 1.6685×10−101.6685 \times 10^{-10} N.

Chat

Save To Bookmark