Acceleration due to Gravity

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Concept Map

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Additional resources

  1. The Value of "g". This is a good resource to study the variation of “g” at various distances above the Earth's atmosphere.
  2. This article examines the Galileo experiment and discusses if there are other possible explanations.

Concept #1 - Gravitational force due to the Earth produces an acceleration

  1. Gravitational force due to the Earth produces an acceleration in the objects. This is the force acting on a freely falling object.
  2. The value of acceleration is not dependent on the mass.
  3. All freely falling bodies gain same acceleration.

Learning objectives

  1. To understand what causes an object to fall - the force and the acceleration
  2. Calculating the value of "g"

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes. Free fall and acceleration due to gravity A freely falling body undergoes acceleration. This acceleration is caused by the gravitational force exerted by the larger mass of the Earth. This is referred to as acceleration due to gravity. The Earth also undergoes an acceleration due to the gravitational force exerted by the object. We do not notice it because of the mass of the Earth. This is represented by "g" and has the value of 9.8 m/s^2.

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

How do we perceive this weight?

When you stand on a surface, the force of the Earth's gravity is acting upon you downwards and there is a normal force exerted by the surface on which you stand. Since you stand on a firm surface and there is no acceleration, the normal force is equal to the gravitational force and this is equal to mg. If an object is suspended from a spring, the gravitational force will be balanced by the tension force in the string.

Weight is that supporting force felt by an object in equilibrium; this opposes and balances the gravitational pull of the Earth. Thus, humans experience their own body weight as a result of this supporting force, which results in a normal force applied to a person by the surface of a supporting object, on which the person is standing or sitting. In the absence of this force, a person would be in free-fall, and would experience weightlessness. It is the transmission of this reaction force through the human body, and the resultant compression and tension of the body's tissues, that results in the sensation of weight.

When an object is in equilibrium, it only experiences the gravitational and restoring force/ Weight is mass multiplied by the acceleration due t gravity.

Measured weight can change:

  1. when acceleration due to gravity changes
  2. when the object is accelerating (non-inertial frame)

When used to mean force, magnitude of weight (a scalar quantity), often denoted by an italic letter W, is the product of the mass, m, of the object and the magnitude of the local gravitational acceleration g;. thus: W = mg. When considered a vector, weight is often denoted by a bold letter W. The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton.

For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, about one-sixth as much on the Moon, and very nearly zero when in deep space far away from all bodies imparting gravitational influence.

Earlier concepts of weight

Concepts of heaviness (weight) and lightness (levity) date back to the ancient Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire and water. He ascribed absolute weight to earth and absolute levity to fire. Archimedes saw weight as a quality opposed to buoyancy, with the conflict between the two determining if an object sinks or floats. The first operational definition of weight was given by Euclid, who defined weight as: "weight is the heaviness or lightness of one thing, compared to another, as measured by a balance.".

Satellites and weightlessness

It is a very common misconception that when astronauts are in orbit they are weightless because they are somehow far enough from the earth that the force of earth's gravity does not pull on them. This is totally incorrect. If they were that far away, earth's gravity would not pull on the shuttle either and it would be impossible for it to be in orbit around the earth.

Gravity (a force we call weight) is actually responsible for keeping the space craft and the astronaut in orbit around the earth. Gravity is still pulling on the astronaut. The feeling of weight;ess is no differenet than when in ree fall. What they are not experiencing is the normal force, which is the opposing force. When that force is gone, we feel say we feel "weightless." In fact, whenever a person is in freefall they feel weightless even though gravity is still causing them to have weight. While in orbit, the space shuttle does not have to push on the astronaut (or anything else in the cabin) to keep him up. The space shuttle and the astronaut are in a constant state of freefall around the earth.

For further details and derivation click here.

Activities

Observe a freely falling body and watch this short video Apollo-shot.png
Hammer and feather drop: Click here to see Apollo 15 astronaut David Scott on the Moon recreating Galileo's famous gravity experiment.


Concept #2 - How does gravitation cause acceleration

Learning objectives

  1. Every object will continue in its state of rest or motion unless acted upon by a force
  2. This force can be provided by gravitation


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