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Where:
– F is the gravitational force of attraction
– G is the gravitational constant (6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2})
– m_1 and m_2 are the masses of the two objects
– r is the distance between the centers of the two objects
Gravitational force of attraction is the force between two objects due to their mass and their separation distance. The formula for calculating gravitational force is given by Newton's law of universal gravitation:
F = G \frac{m_1 \cdot m_2}{r^2}
where:
- F is the gravitational force,
- G is the gravitational constant (6.67430 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2}),
- m_1 and m_2 are the masses of the two objects, and
- r is the distance between the centers of the two objects.
The units of gravitational force can be derived by substituting the units of mass (\text{kg}), distance (\text{m}), and the gravitational constant into the formula. Therefore, the unit of gravitational force is:
\left(6.67430 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2}\right) \cdot \left(\text{kg} \cdot \text{kg}\right) \cdot \left(\text{m}^{-2}\right) = \text{m}\text{kg}\text{s}^{-2} = \text{N}
Thus, the gravitational force is typically measured in Newtons (N), which is the unit of force in the International System of Units (SI).
Mass
One of the key factors influencing gravitational force is the mass of the objects involved.
As we can see from the formula, the gravitational force is directly proportional to the product of the masses of the objects. This means that the force of attraction between two objects will increase as the masses of the objects increase.
Gravitational force between objects
Another factor that affects gravitational force is the distance between the objects. The force of attraction decreases with increasing distance between the objects.
The experiment involves setting up two masses at different distances and measuring the gravitational force between them using a spring scale. By analyzing the collected data, we can confirm the relationship between mass, distance, and gravitational force and gain insights into how these factors affect the strength of gravitational force between objects.the gravitational force.
An experiment can be conducted to demonstrate the impact of varying masses and distances on gravitational force. The experiment involves setting up two masses at different distances and measuring the gravitational force between them using a spring scale. By analyzing the collected data, we can confirm the relationship between mass, distance, and gravitational force and gain insights into how these factors affect the strength of gravitational force between objects.
Gravity is a fundamental force that influences the motion of objects both on Earth and in space. On Earth, gravity causes objects to fall towards the ground when dropped, and it determines the weight of an object based on its mass and the acceleration due to gravity, F = ma.
In space, gravity plays a crucial role in keeping objects in orbit around larger bodies. When an object is in orbit, it is constantly falling towards the larger body due to gravity, but its horizontal velocity is enough to keep it moving tangentially to the gravitational pull. This balance between the force of gravity and the object's velocity results in a stable orbit.
One example of an object in orbit due to gravitational force is the International Space Station (ISS) orbiting around Earth. The gravitational force between the Earth and the ISS keeps it in a stable orbit, allowing astronauts to conduct research, experiments, and live aboard the space station.
Another example is the Moon orbiting around Earth. The gravitational force between the Earth and the Moon keeps the Moon in its orbit, causing the tides on Earth and influencing the planet's rotation.
Gravity influences the motion of objects on Earth and in space by exerting a force of attraction between masses. This force of gravity keeps objects in orbit around larger bodies, such as the ISS orbiting Earth and the Moon orbiting Earth. The mathematical expression for gravitational force can be used to calculate the strength of the gravitational pull between objects.
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Question: Calculate the gravitational force of attraction between two objects with masses 5 kg and 10 kg separated by a distance of 2 meters. (Given: Gravitational constant G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 )
Solution:
Step 1: Identify the given values
Mass of object 1, m_1 = 5 \, \text{kg}
Mass of object 2, m_2 = 10 \, \text{kg}
Distance between objects, r = 2 \, \text{m}
Gravitational constant, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2
Step 2: Calculate the gravitational force of attraction using the formula
F = \frac{G \times m_1 \times m_2}{r^2}
Step 3: Plug in the values
F = \frac{6.674 \times 10^{-11} \times 5 \times 10}{2^2}
F = \frac{6.674 \times 10^{-10} \times 5}{4}
F = \frac{33.370\times 10^{-10}}{4}
F = 8.3425\times 10^{-10} \, \text{N}
Therefore, the gravitational force of attraction between the two objects is 8.3425\times 10^{-10} \, \text{N} .
2. Question: If the masses of two objects are 8 kg and 12 kg respectively, and the gravitational force of attraction between them is 3.6 N, calculate the distance between the two objects. (Given: Gravitational constant G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 )
Solution:
Step 1: Identify the given values
Mass of object 1, m_1 = 8 \, \text{kg}
Mass of object 2, m_2 = 12 \, \text{kg}
Gravitational force of attraction, F = 3.6 \, \text{N}
Gravitational constant, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2
Step 2: Use the formula for gravitational force to find the distance
F = \frac{G \times m_1 \times m_2}{r^2}
Step 3: Rearrange the formula to solve for distance, r
r = \sqrt{\frac{G \times m_1 \times m_2}{F}}
r = \sqrt{\frac{6.674 \times 10^{-11} \times 8 \times 12}{3.6}}
r = \sqrt{\frac{6.674 \times 10^{-11} \times 96}{3.6}}
r = \sqrt{\frac{6.40944 \times 100}{3.6}}
r = \sqrt{640.944}
r \approx 25.3 \, \text{m}
Therefore, the distance between the two objects is approximately 25.3 \, \text{m} .
3. Question: Two objects with masses 2 kg and 4 kg are placed 3 meters apart. Calculate the gravitational force of attraction between them. (Given: Gravitational constant G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 )
Solution:
Step 1: Identify the given values
Mass of object 1, m_1 = 2 \, \text{kg}
Mass of object 2, m_2 = 4 \, \text{kg}
Distance between objects, r = 3 \, \text{m}
Gravitational constant, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2
Step 2: Use the formula for gravitational force to find the force
F = \frac{G \times m_1 \times m_2}{r^2}
Step 3: Calculate the force
F = \frac{6.674 \times 10^{-11} \times 2 \times 4}{3^2}
F = \frac{6.674 \times 10^{-11} \times 8}{9}
F = \frac{5.3392 \times 10^{-10}}{9}
F = 5.9324 \times 10^{-11} \, \text{N}
Hence, the gravitational force of attraction between the two objects is 5.9324 \times 10^{-11} \, \text{N} .
Question: If the gravitational force of attraction between two objects is 8 N and the masses of the objects are 6 kg and 12 kg respectively, find the value of the gravitational constant. (Given: Distance between objects is 4 meters)
Solution:
Step 1: Identify the given values
Gravitational force of attraction, F = 8 \, \text{N}
Mass of object 1, m_1 = 6 \, \text{kg}
Mass of object 2, m_2 = 12 \, \text{kg}
Distance between objects, r = 4 \, \text{m}
Step 2: Use the formula for gravitational force in terms of the gravitational constant
F = \frac{G \times m_1 \times m_2}{r^2}
Step 3: Rearrange the formula to solve for the gravitational constant, G
G = \frac{F \times r^2}{m_1 \times m_2}
G = \frac{8 \times 4^2}{6 \times 12}
G = \frac{8 \times 16}{72}
G = \frac{128}{72}
G \approx 1.7778 \, \times 10^{-11} \, \text{Nm}^2/\text{kg}^2
Therefore, the value of the gravitational constant is approximately 1.7778 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 .
Question: Two objects of 10 kg and 15 kg are separated by a distance of 5 meters. Calculate the gravitational force between them. (Given: Gravitational constant G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 )
Solution:
Step 1: Identify the given values
Mass of object 1, m_1 = 10 \, \text{kg}
Mass of object 2, m_2 = 15 \, \text{kg}
Distance between objects, r = 5 \, \text{m}
Gravitational constant, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2
Step 2: Use the formula for gravitational force of attraction
F = \frac{G \times m_1 \times m_2}{r^2}
Step 3: Calculate the force
F = \frac{6.674 \times 10^{-11} \times 10 \times 15}{5^2}
F = \frac{6.674 \times 10^{-11} \times 150}{25}
F = \frac{1.0011 \times 10^{-8}}{25}
F \approx 4.0044 \times 10^{-10} \, \text{N}
Therefore, the gravitational force of attraction between the two objects is approximately 4.0044 \times 10^{-10} \, \text{N} .
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1. What is the formula to calculate the gravitational force between two objects of masses m1 and m2 separated by a distance r?
2. Calculate the gravitational force between two masses of 5 kg and 10 kg separated by a distance of 2 meters.
3. If the gravitational force between two objects is 50 N and the masses are 2 kg and 4 kg, what is the distance between them?
4. If the distance between two masses is doubled, how does the gravitational force between them change?
5. If the mass of one object is tripled and the distance between the objects is halved, how does the gravitational force change?
6. What is the value of the gravitational constant G in the equation for gravitational force?
7. Calculate the gravitational force between two masses of 6 kg and 8 kg that are 3 meters apart.
8. If the masses of two objects are doubled, how does the gravitational force between them change?
9. How does the gravitational force between two objects change if the distance between them is tripled?
10. Calculate the gravitational force between two masses of 10 kg and 12 kg separated by a distance of 4 meters.
11. If the gravitational force between two objects is 80 N and the distance between them is 2 meters, what are the masses of the objects?
12. If the distance between two masses is quadrupled, how does the gravitational force between them change?
13. If the mass of one object is halved and the distance between the objects is doubled, how does the gravitational force change?
14. Calculate the gravitational force between two masses of 3 kg and 5 kg that are 6 meters apart.
15. If the masses of two objects are tripled and the distance between them is halved, how does the gravitational force change?
1. F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}}
2. F = \frac{{6.67 \times 10^{-11} \cdot 5 \cdot 10}}{{2^2}} = 8.34 \times 10^{-10} \, N
3. 50 = \frac{{G \cdot 2 \cdot 4}}{{r^2}}
  r = \sqrt{\frac{{G \cdot 2 \cdot 4}}{{50}}}
  r = 1.26 \, m
4. The gravitational force decreases by a factor of 4 if the distance between two masses is doubled.
5. The gravitational force remains the same if the mass of one object is tripled and the distance between the objects is halved.
6. G = 6.67 \times 10^{-11} \, N \cdot m^2/kg^2
7. F = \frac{{6.67 \times 10^{-11} \cdot 6 \cdot 8}}{{3^2}} = 2.67 \times 10^{-10} \, N
8. If the masses of two objects are doubled, the gravitational force between them is quadrupled.
9. The gravitational force between two objects decreases by a factor of 9 if the distance between them is tripled.
10. F = \frac{{6.67 \times 10^{-11} \cdot 10 \cdot 12}}{{4^2}} = 5.001 \times 10^{-10} \, N
11. 80 = \frac{{6.67 \times 10^{-11} \cdot m_1 \cdot m_2}}{{2^2}}
m_1 \cdot m_2 = \frac{{80 \cdot 4}}{6.67 \times 10^{-11}} = 4.79 \times 10^{11} \, kg^2
The masses of the objects are approximately 21.9 kg and 21.9 kg.
12. The gravitational force between two masses decreases by a factor of 16 if the distance between them is quadrupled.
13. The gravitational force decreases by a factor of 4 if the mass of one object is halved and the distance between the objects is doubled.
14. F = \frac{{6.67 \times 10^{-11} \cdot 3 \cdot 5}}{{6^2}} = 5 \times 10^{-11} \, N
15. The gravitational force between two objects increases by a factor of 9 if the masses are tripled and the distance between them is halved.
