Circular Motion - Detailed Help

Assignment CG7: The Acceleration of Gravity

Objectives:
  • The student should be able to define the acceleration of gravity and identify the variables which effect its value.
  • The student should be able to predict the effect of alterations in strategic variables upon the acceleration of gravity.

 

Reading:

The Physics Classroom - Circular Motion Unit, Lesson 3, Part d

 

 

The acceleration of gravity (g) refers to the ____. List all that apply ... .


Definition of the Acceleration of Gravity:

The acceleration of gravity is the acceleration value experienced by an object upon which the only force is gravity. It is the acceleration caused by gravity alone.


It is not uncommon for students to become terribly confused about the meaning of the symbol g. The symbol g stands for the acceleration of gravity - a quantity whose value on Earth's surface is 9.8 m/s/s. Students often shorten the phrase acceleration of gravity to simply gravity and then think that g stands for gravity. But don't be fooled! The symbol g represents the acceleration of gravity and should never be confused with another quantity known as the force of gravity. The force of gravity is just that - a force. It is not an acceleration and its value could never be 9.8 m/s/s since the unit m/s/s is not a unit of force.


What is meant by the acceleration of gravity?

 

 

The acceleration of gravity (g) value for an object of mass 'm' located on the surface of some planet of mass 'M' and radius 'R' is ____ related to the ____. List the two that apply ... .


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. The force of gravity would be the net force and the acceleration would be the force of gravity divided by the object's mass.

g = Fgrav / mobject

Substituting Newton's expression for gravitational force into the numerator would result in a new equation for the acceleration of gravity which is applicable to locations other than on Earth's surface:

g = ( G • mobject • Mplanet / d2 ) / mobject

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


Many students are under the conception that the acceleration of an object acted upon by gravity is dependent upon the object's mass. After all, the acceleration is calculated as the ratio of net force to mass. But don't be fooled. In the case of a free-falling object, the net force is also dependent upon mass. As shown in the derivation in the Formula Fix section above, the mass of the object cancels from numerator and denominator. The acceleration of gravity value is independent of the object's mass. All objects free fall at the same rate of acceleration.


What is meant by the acceleration of gravity?

What quantities effect the acceleration of gravity of an object?

 

 

The acceleration of gravity on the surface of the Earth is 9.8 m/s/s. As one moves increasingly further from the surface of the Earth, the acceleration of gravity value ____.


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


As stated in the Physics Rules section and as expressed in the Formula Fix section, the value of g is inversely proportional to the square of the distance between an object and the center of the planet. To say that two quantities are inversely proportional is to mean that an increase in one quantity would lead to a decrease in the other quantity.


What effect does separation distance have upon the acceleration of gravity of an object?

 

 

An astronaut is on the orbiting Space Shuttle, approximately 60 miles (~100 000 meters) above the surface of the Earth. (The Earth's radius is ~6 360 000 meters and its mass is ~5.98 x 10^24 kg.) At this location, one might predict the acceleration of gravity to be ____.


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


The gravitational acceleration experienced by a person is inversely related to the separation distance between the person and the Earth's center. As objects get further from Earth' surface, the gravitational acceleration decreases. A distance of 60 miles above the Earth's surface is a very small distance compared to the distance from Earth's center to Earth's surface. The values in this question are provided, so the math can be pondered. At 60 miles up, an astronaut is about 6460000 meters from Earth's center compared to the 6360000 meters when on Earth's surface. This is a 1.6% increase in the distance from Earth's center. Using the inverse square law, this increase in distance would lead to a 2.5% decrease in the gravitational acceleration.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


How can the inverse square law be applied the acceleration of gravity of an object?

 

 

The acceleration of gravity upon Earth's surface is 9.80 m/s/s. At a location of 'R' above Earth's surface (where 'R' is the radius of the Earth), the acceleration of gravity is closest to ____ m/s/s.

Note: The numerical values in your question were randomly selected and may differ from those shown above.


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


This question targets the relationship between separation distance and the acceleration of gravity. Placing an object a distance R above a planet's surface is comparable to doubling the distance of the object from the planet's center. Gravitational acceleration is inversely proportional to the square of the separation distance. The inverse nature of the law means that if the distance is increased, then the gravitational acceleration will be decreased. The inverse square nature of the law means the acceleration value will be decreased by the square of the factor by which the separation distance is increased. So if the separation distance becomes two times bigger, then the gravitational acceleration will become four times (22) smaller. The new gravitational acceleration would be one-fourth the original value. If the separation distance becomes three times bigger, then the gravitational acceleration will become nine times (32) smaller. The new gravitational acceleration would be one-ninth the original value.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


How can the inverse square law be applied the acceleration of gravity of an object?

 

 

The acceleration of gravity upon Earth's surface is 9.80 m/s/s. At a location of '2R' above Earth's surface (where 'R' is the radius of the Earth), the acceleration of gravity is closest to ____ m/s/s.

Note: The numerical values in your question were randomly selected and may differ from those shown above.


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


This question targets the relationship between separation distance and the acceleration of gravity. Placing an object a distance 2R above a planet's surface is comparable to tripling the distance of the object from the planet's center. Gravitational acceleration is inversely proportional to the square of the separation distance. The inverse nature of the law means that if the distance is increased, then the gravitational acceleration will be decreased. The inverse square nature of the law means the acceleration value will be decreased by the square of the factor by which the separation distance is increased. So if the separation distance becomes two times bigger, then the gravitational acceleration will become four times (22) smaller. The new gravitational acceleration would be one-fourth the original value. If the separation distance becomes three times bigger, then the gravitational acceleration will become nine times (32) smaller. The new gravitational acceleration would be one-ninth the original value.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


How can the inverse square law be applied the acceleration of gravity of an object?

 

 

An object of mass 'm' is located a distance 'R' from the center of a planet with mass 'M.' The acceleration of gravity of the mass 'm' at this location is 12 m/s/s. Suppose that the mass of the object is doubled to '2m' and the separation distance is halved to '0.5R.' The new acceleration of gravity value for the mass and the new location would be ____ m/s/s.

Note: The numerical values in your question were randomly selected and may differ from those shown above.


Acceleration of Gravity or Gravitational Field Strength:

The acceleration of gravity at any given location near or above a planet's surface is often referred to as the gravitational field constant of that planet. Such acceleration values are directly proportional to the planet's mass and inversely proportional to the square of the distance from the planet's center.


This question explores the affect of changing object mass and changing separation distance upon the acceleration of gravity. The acceleration of gravity is dependent upon an object's location and would be affected by changes in its distance from a planet's center. But don't be fooled! The acceleration of gravity of an object is not affected by the mass of the object.


This question targets the relationship between separation distance and the acceleration of gravity. Gravitational acceleration is inversely proportional to the square of the separation distance. The inverse nature of the law means that if the distance is increased, then the gravitational acceleration will be decreased. The inverse square nature of the law means the acceleration value will be decreased by the square of the factor by which the separation distance is increased. So if the separation distance becomes two times bigger, then the gravitational acceleration will become four times (22) smaller. The new gravitational acceleration would be one-fourth the original value. If the separation distance becomes three times bigger, then the gravitational acceleration will become nine times (32) smaller. The new gravitational acceleration would be one-ninth the original value. If the separation distance becomes one-half the size, then the gravitational acceleration will be four times (22) large. The new gravitational acceleration would be four times the original value.


How can the inverse square law be applied the acceleration of gravity of an object?

What effect does object mass have upon the acceleration of gravity of an object?

 

 

Four different planets with different masses are depicted below. A location about the planet is also indicated. Rank the four locations in increasing order of their acceleration of gravity value, beginning with the lowest. Enter your four answers in increasing order with no spaces or commas between letters.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


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This is a very difficult question which explores the relationship between the acceleration of gravity, the distance from a planet's center and the mass of the planet. As demonstrated by the equation in the Formula Fix section above, the acceleration of gravity is dependent upon the Mplanet / d2 ratio. You will need to find this ratio for the stated location about each planet. Take your time and write down some results in an organized fashion. If the indicated location is a distance R above the planet's surface, then the separation distance (d) is 2•R. Once you have found this important ratio for each planet, rank the locations in order of increasing acceleration of gravity values with the smallest ratio coming first.


What quantities effect the acceleration of gravity of an object?

How can the inverse square law be applied the acceleration of gravity of an object?

 

 

Two objects are located at different locations about two planets with distinctly different masses. Compared to location A, the acceleration of gravity value at location B is ____.


The acceleration of gravity (g) is the acceleration an object experiences when the only force acting upon it is gravity. According to Newton's universal gravitation law, its value can be predicted by the following equation:

g = G • Mplanet / d2

where Mplanet represents the planet's mass and d represents the distance that the object is from the planet's center.


This is a very difficult question which explores the relationship between the acceleration of gravity, the distance from a planet's center and the mass of the planet. As demonstrated by the equation in the Formula Fix section above, the acceleration of gravity is dependent upon the Mplanet / d2 ratio. You will need to find this ratio for locations A and B. Take your time and write down the results. If one of the locations is a distance R above the planet's surface, then the separation distance (d) is 2•R. Once you have found this important ratio for both locations, you will be ready to answer the question.


What quantities effect the acceleration of gravity of an object?

How can the inverse square law be applied the acceleration of gravity of an object?