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3.5 Inertial vs. Gravitational Mass

4 min readjanuary 19, 2023

Peter Apps

Peter Apps

Kashvi Panjolia

Kashvi Panjolia

Peter Apps

Peter Apps

Kashvi Panjolia

Kashvi Panjolia

Learning Targets

is the property of an object or a system that determines the strength of the gravitational interaction with other objects, systems, or gravitational fields.

  • a. The of an object determines the amount of force exerted on the object by a gravitational field.

  • b. Near Earth’s surface, all objects fall (in a vacuum) with the same acceleration, regardless of their .

Inertial Mass

and are two different ways of measuring the amount of matter in an object. is determined by measuring the force required to accelerate an object. This is described by , which states that the force required to accelerate an object is equal to the product of the object's mass and acceleration (). The greater the of an object, the greater the force required to accelerate it. For example, a bowling ball has a larger than a feather, so a greater force is required to accelerate the bowling ball than the feather. When you try to lift the bowling bowl, it is harder to lift than a feather. 🪶

Gravitational Mass

, on the other hand, is determined by measuring the strength of the gravitational force exerted by an object on other objects. The gravitational force exerted by an object is determined by its and the distance between it and the other object(s). The strength of the gravitational force is described by Newton's law of universal gravitation, which states that the gravitational force exerted by an object is proportional to the product of the gravitational masses of the two objects and inversely proportional to the square of the distance between them (inverse-square relationship). For example, the Earth has a larger than a bowling ball, so the Earth exerts a greater gravitational force on the bowling ball than the bowling ball exerts on the Earth. The Earth has an even larger than a feather, and this is why, when you drop a bowling ball and a feather on the surface of the Earth, the bowling ball will hit the ground faster. 🌎

https://cdn.vox-cdn.com/uploads/chorus_asset/file/2428646/bowling_ball_2.0.gif

GIF courtesy of Vox.

Gravitational Mass vs. Inertial Mass

The value for the and are always found to be equal for all objects. This is because and are two different ways of measuring the amount of matter in an object. One such experiment demonstrating their equivalence was the famous conducted by astronaut David Scott on the surface of the Moon. Because there is no atmosphere on the Moon, Scott was able to drop a feather and a hammer at the same time and show that they landed at the same time, proving that in the absence of air resistance, all objects fall at the same rate -- the .

https://64.media.tumblr.com/525c3667271a44e25bd9a6b6e78ff0d7/tumblr_nejuzwN6Lw1tlppcdo1_400.gif

In a vacuum chamber, all objects reach the ground at the same time. GIF courtesy of EducationalGifs.

We can use this experiment to make the statement that all objects near Earth's surface fall with the same acceleration, regardless of their .

It is important to note that the is different from the gravitational force. While the is the same for all objects, the gravitational force is not. The gravitational force is calculated using F=Gm1m2/r^2, which is . As derived in the previous guide, however, the is not dependent on the mass of the object being dropped -- only the mass of the planet. The equation for the is g=GM/r^2, where M is the mass of the planet. As you can see, there is no mention of the mass of the object being dropped in this equation, so the is constant for all objects at a certain distance away from the center of the planet.

The idea that inertial and satisfy conservation principles means that the total amount of matter in a closed system remains constant and is conserved, regardless of the forces acting on it. This is known as the Conservation of Mass.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-13%20at%2011.49.49%20AM.png?alt=media&token=9b73d258-1299-48da-a7ed-72d3629cb152

Image courtesy of quickmeme.com.

🎥Watch: AP Physics 1- Unit 3 Streams

Key Terms to Review (8)

Acceleration due to gravity

: The acceleration due to gravity is the rate at which an object falls towards the Earth under the influence of gravity. It is approximately 9.8 meters per second squared (m/s^2) near the surface of the Earth.

Apollo 15 experiment

: The Apollo 15 experiment was conducted during NASA's Apollo 15 mission in 1971. Astronauts David Scott and James Irwin performed a demonstration on the Moon's surface where they dropped a feather and a hammer simultaneously, proving that objects fall at the same rate regardless of their mass in a vacuum environment.

F=ma

: F=ma is Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

Gravitational Mass

: Gravitational mass refers to the measure of an object's response to the force of gravity. It determines how strongly an object is attracted towards another object due to gravity.

Inertial Mass

: Inertial mass refers to the measure of an object's resistance to changes in its motion. It determines how difficult it is for an external force to accelerate or decelerate an object.

Newton's Second Law of Motion

: Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its inertial mass. In simpler terms, it explains how forces affect an object's motion.

Newton's Universal Law of Gravitation

: Newton's Universal Law of Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Vacuum chamber

: A vacuum chamber is a sealed container from which air and other gases have been removed, creating a low-pressure environment. It is used for various purposes such as scientific experiments, testing equipment, and simulating space conditions.

3.5 Inertial vs. Gravitational Mass

4 min readjanuary 19, 2023

Peter Apps

Peter Apps

Kashvi Panjolia

Kashvi Panjolia

Peter Apps

Peter Apps

Kashvi Panjolia

Kashvi Panjolia

Learning Targets

is the property of an object or a system that determines the strength of the gravitational interaction with other objects, systems, or gravitational fields.

  • a. The of an object determines the amount of force exerted on the object by a gravitational field.

  • b. Near Earth’s surface, all objects fall (in a vacuum) with the same acceleration, regardless of their .

Inertial Mass

and are two different ways of measuring the amount of matter in an object. is determined by measuring the force required to accelerate an object. This is described by , which states that the force required to accelerate an object is equal to the product of the object's mass and acceleration (). The greater the of an object, the greater the force required to accelerate it. For example, a bowling ball has a larger than a feather, so a greater force is required to accelerate the bowling ball than the feather. When you try to lift the bowling bowl, it is harder to lift than a feather. 🪶

Gravitational Mass

, on the other hand, is determined by measuring the strength of the gravitational force exerted by an object on other objects. The gravitational force exerted by an object is determined by its and the distance between it and the other object(s). The strength of the gravitational force is described by Newton's law of universal gravitation, which states that the gravitational force exerted by an object is proportional to the product of the gravitational masses of the two objects and inversely proportional to the square of the distance between them (inverse-square relationship). For example, the Earth has a larger than a bowling ball, so the Earth exerts a greater gravitational force on the bowling ball than the bowling ball exerts on the Earth. The Earth has an even larger than a feather, and this is why, when you drop a bowling ball and a feather on the surface of the Earth, the bowling ball will hit the ground faster. 🌎

https://cdn.vox-cdn.com/uploads/chorus_asset/file/2428646/bowling_ball_2.0.gif

GIF courtesy of Vox.

Gravitational Mass vs. Inertial Mass

The value for the and are always found to be equal for all objects. This is because and are two different ways of measuring the amount of matter in an object. One such experiment demonstrating their equivalence was the famous conducted by astronaut David Scott on the surface of the Moon. Because there is no atmosphere on the Moon, Scott was able to drop a feather and a hammer at the same time and show that they landed at the same time, proving that in the absence of air resistance, all objects fall at the same rate -- the .

https://64.media.tumblr.com/525c3667271a44e25bd9a6b6e78ff0d7/tumblr_nejuzwN6Lw1tlppcdo1_400.gif

In a vacuum chamber, all objects reach the ground at the same time. GIF courtesy of EducationalGifs.

We can use this experiment to make the statement that all objects near Earth's surface fall with the same acceleration, regardless of their .

It is important to note that the is different from the gravitational force. While the is the same for all objects, the gravitational force is not. The gravitational force is calculated using F=Gm1m2/r^2, which is . As derived in the previous guide, however, the is not dependent on the mass of the object being dropped -- only the mass of the planet. The equation for the is g=GM/r^2, where M is the mass of the planet. As you can see, there is no mention of the mass of the object being dropped in this equation, so the is constant for all objects at a certain distance away from the center of the planet.

The idea that inertial and satisfy conservation principles means that the total amount of matter in a closed system remains constant and is conserved, regardless of the forces acting on it. This is known as the Conservation of Mass.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-13%20at%2011.49.49%20AM.png?alt=media&token=9b73d258-1299-48da-a7ed-72d3629cb152

Image courtesy of quickmeme.com.

🎥Watch: AP Physics 1- Unit 3 Streams

Key Terms to Review (8)

Acceleration due to gravity

: The acceleration due to gravity is the rate at which an object falls towards the Earth under the influence of gravity. It is approximately 9.8 meters per second squared (m/s^2) near the surface of the Earth.

Apollo 15 experiment

: The Apollo 15 experiment was conducted during NASA's Apollo 15 mission in 1971. Astronauts David Scott and James Irwin performed a demonstration on the Moon's surface where they dropped a feather and a hammer simultaneously, proving that objects fall at the same rate regardless of their mass in a vacuum environment.

F=ma

: F=ma is Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

Gravitational Mass

: Gravitational mass refers to the measure of an object's response to the force of gravity. It determines how strongly an object is attracted towards another object due to gravity.

Inertial Mass

: Inertial mass refers to the measure of an object's resistance to changes in its motion. It determines how difficult it is for an external force to accelerate or decelerate an object.

Newton's Second Law of Motion

: Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its inertial mass. In simpler terms, it explains how forces affect an object's motion.

Newton's Universal Law of Gravitation

: Newton's Universal Law of Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Vacuum chamber

: A vacuum chamber is a sealed container from which air and other gases have been removed, creating a low-pressure environment. It is used for various purposes such as scientific experiments, testing equipment, and simulating space conditions.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.