Two Masses Are 109 M Apart. Mass 1 Is 227 Kg, And Mass 2 Is 231 Kg. What Is The Gravitational Force Between The Two Masses?$\vec{F} = [?] \times 10^{[?]} \, \text{N}$

Introduction

The gravitational force between two masses is a fundamental concept in physics, governed by the law of universal gravitation. This law, formulated by Sir Isaac Newton, describes the attractive force between two objects with mass. In this article, we will calculate the gravitational force between two masses, given their distances and masses.

The Law of Universal Gravitation

The law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. Mathematically, this can be expressed as:

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

where:

• $F$ is the gravitational force between the two masses
• $G$ is the gravitational constant, approximately equal to $6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$
• $m_1$ and $m_2$ are the masses of the two objects
• $r$ is the distance between the centers of the two objects

Given Values

We are given the following values:

• Distance between the two masses: $r = 109 \, \text{m}$
• Mass of mass 1: $m_1 = 227 \, \text{kg}$
• Mass of mass 2: $m_2 = 231 \, \text{kg}$

Calculating the Gravitational Force

Using the law of universal gravitation, we can calculate the gravitational force between the two masses:

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

Substituting the given values, we get:

$$F = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \times \frac{227 \, \text{kg} \times 231 \, \text{kg}}{(109 \, \text{m})^2}$$

Simplifying the expression, we get:

$$F = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \times \frac{52307 \, \text{kg}^2}{11921 \, \text{m}^2}$$

$$F = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \times 4.373 \, \text{kg/m}^2$$

$$F = 2.913 \times 10^{-10} \, \text{N}$$

Therefore, the gravitational force between the two masses is approximately $2.913 \times 10^{-10} \, \text{N}$.

Conclusion

In this article, we calculated the gravitational force between two masses using the law of universal gravitation. We found that the gravitational force between the two masses is approximately $2.913 \times 10^{-10} \, \text{N}$. This calculation demonstrates the fundamental concept of gravitational force and its dependence on the masses and distance between objects.

References

• Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.

Further Reading

• Gravitational force and its applications
• Newton's law of universal gravitation
• Gravitational constant and its value
• Mass and its units
• Distance and its units
  Gravitational Force Between Two Masses: Q&A =============================================

Introduction

In our previous article, we calculated the gravitational force between two masses using the law of universal gravitation. In this article, we will answer some frequently asked questions related to gravitational force and its applications.

Q: What is the gravitational force between two objects?

A: The gravitational force between two objects is a fundamental concept in physics, governed by the law of universal gravitation. It is the attractive force between two objects with mass, and it depends on the masses and distance between the objects.

Q: What is the formula for calculating the gravitational force?

A: The formula for calculating the gravitational force is:

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

where:

• $F$ is the gravitational force between the two masses
• $G$ is the gravitational constant, approximately equal to $6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$
• $m_1$ and $m_2$ are the masses of the two objects
• $r$ is the distance between the centers of the two objects

Q: What is the gravitational constant, and why is it important?

A: The gravitational constant, denoted by $G$, is a fundamental constant in physics that describes the strength of the gravitational force between two objects. It is approximately equal to $6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$. The gravitational constant is important because it allows us to calculate the gravitational force between two objects using the formula above.

Q: What are some examples of gravitational force in everyday life?

A: Gravitational force is present in many everyday situations, including:

• The force of gravity that keeps you on the ground
• The force of gravity that pulls objects towards the center of the Earth
• The force of gravity that causes objects to fall towards the ground
• The force of gravity that holds planets in orbit around their stars

Q: Can gravitational force be used to lift objects?

A: No, gravitational force cannot be used to lift objects. Gravitational force is an attractive force that pulls objects towards each other, and it cannot be used to lift objects against the force of gravity.

Q: Can gravitational force be used to propel objects?

A: Yes, gravitational force can be used to propel objects. For example, a rocket uses the force of gravity to propel itself into space. The rocket's engines work by expelling hot gases out of the back of the rocket, which creates a reaction force that propels the rocket forward.

Q: What are some applications of gravitational force in science and technology?

A: Gravitational force has many applications in science and technology, including:

• Space exploration: Gravitational force is used to propel spacecraft into orbit and beyond.
• Geophysics: Gravitational force is used to study the Earth's interior and to understand the movement of tectonic plates.
• Astronomy: Gravitational force is used to study the motion of celestial objects and to understand the behavior of galaxies.
• Engineering: Gravitational force is used to design and build structures such as bridges and buildings.

Conclusion

In this article, we answered some frequently asked questions related to gravitational force and its applications. We hope that this article has provided a better understanding of the concept of gravitational force and its importance in science and technology.

References

• Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.

Further Reading

• Gravitational force and its applications
• Newton's law of universal gravitation
• Gravitational constant and its value
• Mass and its units
• Distance and its units