About

7.1 Newton’s Law of Gravitation

Gravitation is a natural phenomenon by which physical bodies attract each other due to their masses. This force occurs whenever masses are present and the two bodies need not to be in contact with each other. It is however the weakest of the fundamental forces of nature.

In 1687, Sir Isaac Newton concluded that this non-contact gravitational force must be as responsible for the falling of the apple from a tree as it is the cause for the rotation of the Moon about the Earth. Hence he published the Newton’s law of gravitation which states that:

“The mutual force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.”

This means that if there are two point masses M and m and they are separated by distance r, the magnitude of the gravitational force attracting them to each other is$|F|=\frac{G{M}_1{M}_2}{r^2}$   where G, the constant of universal gravitation, is $6.\text{67x1}{0}^{-11}\frac{N{m}^2}{k{g}^2}$ (will be given in data & formulae list during tests and examinations).

Note:
1.    r is taken to be the centre to centre distance (i.e. centre of particle to centre of particle). Do not take r to be the radius of orbit!
2.    This formula is an example of the inverse square law.

7.1.1 Inquiry:

  What can you conclude about the two forces in the simulation below?

Answer: Based on the evidences from the simulation triangulated with real life examples, the mutual force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.

7.1.2 Model:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/266

 

Translations

Code	Language		Translator	Run

Credits

This email address is being protected from spambots. You need JavaScript enabled to view it.; Anne Cox; Wolfgang Christian; Francisco Esquembre

 

http://iwant2study.org/lookangejss/02_newtonianmechanics_7gravity/ejss_model_gravity01_0/gravity01_0_Simulation.xhtml

Briefing Doc: 🍎Exploring Gravity and its Simulation

This briefing document reviews key themes and information extracted from excerpts of the webpage "7.1 Gravity Force (Basic) JavaScript HTML5 Applet Simulation Model" hosted on the Open Educational Resources / Open Source Physics @ Singapore website.

Core Themes:

1. Newton's Law of Universal Gravitation: The document emphasizes this fundamental law, stating, "The mutual force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.” This concept is central to understanding the behavior of objects under the influence of gravity.
2. Gravitational Force Formula: The formula |F|= G M1 M2 / r^2 is presented and explained, with G representing the constant of universal gravitation (6.67 x 10^-11 N m^2 kg^2). It's important to note the emphasis on 'r' representing the center-to-center distance between the masses.
3. Interactive Simulation: The webpage highlights an interactive JavaScript simulation designed to illustrate gravitational force. This model allows users to manipulate variables and observe the resulting changes in gravitational attraction. The URL for the embedded simulation is provided for easy access.
4. Educational Applications: The document underscores the educational value of the simulation, particularly for Junior College level Physics education. Sample learning goals are listed, including recalling and applying Newton's law of gravitation.
5. Student Understanding of Gravity: The resource acknowledges common misconceptions students have about gravity and related concepts like Newton's laws of motion. For example, students may incorrectly believe that a force is needed to maintain motion or that heavier objects fall faster.

Key Facts and Ideas:

• Gravitational Field: A region where a mass experiences a force due to gravitational attraction.
• Gravitational Field Strength (g): Defined as the gravitational force per unit mass.
• Inverse Square Law: The gravitational force weakens as the square of the distance between objects increases.
• Center-to-Center Distance: When calculating gravitational force, the distance is measured between the centers of the objects, not their surfaces.

Quotes:

• "Gravitation is a natural phenomenon by which physical bodies attract each other due to their masses."
• "This formula is an example of the inverse square law."
• "The acceleration of free fall for a body near to the Earth is constant and is approximately 10 m/s^2."

Overall Significance:

The webpage provides a valuable resource for understanding and teaching about gravitational forces. The interactive simulation offers a hands-on approach to learning, while the discussion of common student misconceptions can inform teaching strategies. The resource effectively combines theoretical explanation with practical application, enhancing comprehension of this fundamental physics concept.

 

Newton's Law of Gravitation Study Guide

Short Answer Questions

1. Define Newton's Law of Gravitation in your own words.
2. What is the significance of the constant 'G' in Newton's Law of Gravitation? Provide its value and units.
3. How does the distance between two objects affect the gravitational force between them? Explain using the concept of the inverse square law.
4. According to the simulation mentioned in the text, what is the relationship between the masses of two objects and the gravitational force between them?
5. Why is the center-to-center distance crucial when calculating the gravitational force between two objects?
6. Explain why a person's weight can differ at different locations on Earth.
7. Describe one common misconception students have regarding Newton's First Law of Motion.
8. What is the definition of gravitational field strength? How is it related to gravitational force?
9. Explain the concept of 'density' and its relevance to understanding whether objects sink or float.
10. What are some learning difficulties students might face when trying to understand Newton's Third Law of Motion?

Answer Key

1. Newton's Law of Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
2. The constant 'G' is the universal gravitational constant, a fundamental constant that determines the strength of the gravitational force. Its value is 6.67 x 10^-11 N m^2/kg^2.
3. As the distance between two objects increases, the gravitational force between them decreases. This relationship follows the inverse square law, meaning that the force is inversely proportional to the square of the distance. So, if the distance doubles, the force becomes four times weaker.
4. The simulation demonstrates that the gravitational force between two objects is directly proportional to the product of their masses. This means that if the mass of one object doubles, the force doubles. If the masses of both objects double, the force becomes four times stronger.
5. The center-to-center distance is essential because the gravitational force acts as if the entire mass of each object is concentrated at its center. Using this distance ensures accurate calculation of the gravitational force.
6. A person's weight can differ at different locations on Earth due to variations in the Earth's gravitational field strength. Factors like altitude and the Earth's non-uniform density can influence this strength, leading to slight weight differences.
7. One common misconception about Newton's First Law is that a force is required to keep an object in motion. This is incorrect as an object in motion will stay in motion at a constant velocity unless acted upon by an external force.
8. Gravitational field strength (g) is defined as the gravitational force per unit mass experienced by an object in a gravitational field. It is related to gravitational force (F) through the equation: F = mg, where 'm' is the mass of the object.
9. Density is defined as the mass per unit volume of a substance. Objects with a density lower than the fluid they are placed in will float, while objects with a higher density will sink.
10. Students often struggle with the concept of action-reaction pairs in Newton's Third Law. They find it difficult to grasp that forces always exist in pairs and that the two forces in a pair act on different objects with equal magnitude but opposite direction.

Essay Questions

1. Discuss the historical development of Newton's Law of Gravitation, highlighting the contributions of scientists who preceded Newton and how their work influenced his discoveries.
2. Analyze the implications of Newton's Law of Gravitation for our understanding of planetary motion. Explain how this law helps explain Kepler's Laws of Planetary Motion.
3. Critically evaluate the concept of a gravitational field. Discuss its importance in understanding gravitational interactions and its relationship to gravitational potential energy.
4. Compare and contrast Newton's Law of Gravitation with other fundamental forces of nature, such as the electromagnetic force and the strong and weak nuclear forces. Discuss their relative strengths and ranges of influence.
5. Explore the limitations of Newton's Law of Gravitation, particularly in extreme environments like black holes. Discuss how Einstein's theory of general relativity extends and refines our understanding of gravity in such cases.

Glossary of Key Terms

Newton's Law of Gravitation: The law stating that every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Gravitational Constant (G): A fundamental constant in physics that determines the strength of the gravitational force. Its value is approximately 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻².

Inverse Square Law: A principle stating that the intensity of a physical quantity (like gravitational force) is inversely proportional to the square of the distance from the source of that physical quantity.

Center-to-center distance: The distance between the centers of two objects, used in calculating the gravitational force between them.

Gravitational Field: A region of space surrounding a massive object where another massive object experiences a gravitational force.

Gravitational Field Strength (g): The force per unit mass experienced by a test mass placed in a gravitational field.

Density: A measure of how much mass is contained in a given volume. It is calculated by dividing mass by volume.

Newton's First Law of Motion: Also known as the law of inertia, it states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Newton's Third Law of Motion: States that for every action, there is an equal and opposite reaction.

Weight: The force of gravity acting upon an object with mass. It varies depending on the gravitational field strength.

Mass: A measure of the amount of matter in an object. It is a fundamental property of an object and remains constant regardless of location.

Apps

https://play.google.com/store/apps/details?id=com.ionicframework.gravity010app251517&hl=en

Sample Learning Goals

1. recall and use Newton's law of gravitation in the form \( |F| = \frac{M_{1}M_{2}}{r^{2}} \)

Research 6.5 Gravitational field: Map of key concepts and ideas covered at upper secondary level Newton’s law of universal gravitation Key inquiry question:

How can we express the gravitational interaction between objects in the Universe?

1. Gravitational field

• A gravitational field is a region in which a mass experiences a force due to gravitational attraction.

• Gravitational field strength, g of a field is defined as the gravitational force per unit mass.

2. Field near to the surface of the Earth

• The acceleration of free fall for a body near to the Earth is constant and is approximately 10 m/s2 .

Students’ prior knowledge of Dynamics and Gravitational field

Primary level:

Students learn about mass (a measure of the amount of matter in a body) and volume (the amount of space that a body occupies) and the use of appropriate apparatus to measure these quantities (e.g. use of a lever balance, an electronic balance, a measuring cylinder, a syringe, and a measuring jug). However, the concept of density is not introduced although students do simple experiments to investigate the ability of objects of different materials (plastics, wood, rubber and metals) to float/sink in water.

Students recognize that objects have weight because of the gravitational force between them and the Earth and that weight is different at different places, and can be measured using a spring balance or a weighing scale.

Lower secondary level:

Students learn that:

• the density of a substance is the mass of the substance per unit volume, and can be used to predict whether objects sink or float.

• gravity exists between any two objects (e.g. ball and Earth). The weight of an object depends on the force of gravity pulling on that object. Students’ common misconceptions and learning difficulties in Dynamics and Gravitational field

Newton’s first law:

Students often think that:

• a force is required to maintain an object in its motion;

• if there is no motion, there is no force acting;

• constant speed results from a constant force;

• friction (instead of inertia) causes objects to resist a change in its state of rest or motion.

Newton’s second law:

Students often think that:

• a larger velocity means a larger resultant force;

• acceleration implies increasing force;

• greater mass implies greater force;

• a force cannot move an object unless it is greater than the object’s weight;

• heavier objects fall faster than light objects.

 Newton’s third law:

Students often think that force is a single physical quantity associated with a single object rather than as an interaction between two objects which must therefore exist as an action reaction pair. They have difficulty in understanding that:

• two objects of greatly differing masses (e.g. Earth and us) exert forces of equal magnitude on each other;

• the normal force on an object and the weight of the object do not always have equal magnitudes;

• gravity acts on an object all the time (not just when it is falling).

Video

 by lookang lawrence wee

 7.1 Gravity Force Model (Basic) JavaScript by lookang lawrence wee

 Version:

1. http://weelookang.blogspot.sg/2016/03/a-comparison-of-phet-and-osp-gravity-lab.html refreshed version
2. http://weelookang.blogspot.sg/2015/04/ejss-gravity-022.html?q=gravity earilest post by lookang
3. http://www.opensourcephysics.org/items/detail.cfm?ID=9683 based on Coulomb's Law and Electric Field Package by Anne Cox, Wolfgang Christian, and Francisco Esquembre

Other Resources

1. http://www.physicsclassroom.com/Physics-Interactives/Circular-and-Satellite-Motion/Gravitational-Fields/Gravitational-Fields-Interactive by physics classroom
2. https://phet.colorado.edu/en/simulation/gravity-force-lab by PhET

Gravity Force FAQ

1. What is gravitation?

Gravitation is a fundamental force of nature that causes all objects with mass to attract each other. It's a non-contact force, meaning the objects do not need to be touching for the force to exist. While universal, gravity is the weakest of the fundamental forces.

2. What is Newton's Law of Gravitation?

Newton's Law of Gravitation states that the force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, this can be expressed as:

• F = G(_M_₁_M_₂)/_r_²

where:

* _F_ is the force of gravity

* _G_ is the universal gravitational constant (6.67 x 10⁻¹¹ N m²/kg²)

* _M_₁ and _M_₂ are the masses of the two objects

* _r_ is the distance between the centers of the two objects

3. How does the distance between objects affect the force of gravity?

The force of gravity is inversely proportional to the square of the distance between the centers of the objects. This means if the distance between two objects is doubled, the force of gravity between them is reduced to one-fourth of its original value.

4. What is the significance of the 'center to center' distance in calculating gravitational force?

The distance (r) used in Newton's Law of Gravitation refers to the distance between the centers of the two masses. This is important because it assumes that the mass of each object is concentrated at a single point at its center.

5. What is a gravitational field?

A gravitational field is a region of space surrounding a mass where another mass will experience a gravitational force. The strength of the gravitational field depends on the mass of the object creating the field and the distance from that object.

6. What is gravitational field strength?

Gravitational field strength (g) is defined as the gravitational force per unit mass. It is a vector quantity and its direction is always towards the center of the mass producing the field.

7. How does the concept of gravitational fields relate to the acceleration of free fall near the Earth's surface?

The acceleration of free fall (g) for an object near the Earth's surface is approximately 9.8 m/s². This value is relatively constant because it's determined by the Earth's mass and radius. Essentially, the Earth's mass creates a gravitational field that pulls objects towards its center, causing them to accelerate downwards.

8. What are some common misconceptions about gravity?

• A force is required to maintain an object in motion: This is incorrect as per Newton's first law. Objects in motion will stay in motion at a constant velocity unless acted upon by an external force.
• Heavier objects fall faster than lighter objects: In a vacuum, all objects fall at the same rate regardless of their mass. The difference in fall rates we sometimes observe is due to air resistance.
• Gravity only acts on falling objects: Gravity acts on all objects all the time, regardless of whether they are falling or not. Gravity is what keeps us on the ground and what keeps the planets in orbit around the sun.