## Key Idea: Gravitational potential energy is associated with the distance an object is above a reference point, such as the center of the earth, and the mass of the object.

*Students are expected to know that:*

- The gravitational potential energy of an object depends on both the distance an object is above the center of the earth and the mass of the object and that
gravitational potential energy depends
*only*on these two factors. Gravitational potential energy does not depend on other factors such as speed, size, shape, material the object is made of, or the path the object took to get to the distance above the center of the earth. - Objects that have the same mass and are equal distances from the center of the earth have the same amount of gravitational potential energy.
- Increasing the distance an object is from the center of the earth will increase the gravitational potential energy of the object (assuming the mass of the object does not change) and decreasing the distance an object is from the center of the earth will decrease the gravitational potential energy of the object (assuming the mass of the object does not change).
- If the gravitational potential energy of an object increases, the distance the object is from the center of the earth must have increased (assuming the mass of the object does not change) and if the gravitational potential energy of an object decreases, the distance the object is from the center of the earth must have decreased (assuming the mass of the object does not change).
- For objects that have the same mass, the object farthest from the center of the earth will have the most gravitational potential energy and the object closest to the center of the earth will have the least gravitational potential energy.
- For objects that have the same mass, the object with the greatest gravitational potential energy is the farthest from the center of the earth, and the object with the least gravitational potential energy is the closest to the center of the earth.
- For objects that are equal distances from the center of the earth (greater than zero), the object with the greatest mass will have the most gravitational potential energy and the object with the least mass will have the least gravitational potential energy.
- For objects that are equal distances from the center of the earth (greater than zero), the object with the greatest gravitational potential energy has the greatest mass and the object with the least gravitational potential energy has the least mass.
- For objects that have the same amount of gravitational potential energy, the object with the greatest mass is closest to the center of the earth and the object with the least mass is the farthest from the center of the earth.
- For objects that have the same amount of gravitational potential energy, the object that is the farthest from the center of the earth will have the least mass and the object that is the closest to the center of the earth will have the greatest mass.

*Boundaries:*

- Students are not expected to know the meaning of the term “potential.”
- Students are not expected to know or use formulas associated with gravitational potential energy, such as mass x gravitational constant x height/distance (mgh). The sub-ideas above describe qualitative relationships.
- As a result, students are not expected to compare situations where both the mass and distance vary. In assessment items, either the mass or the distance will be held constant while the other varies so that both variables will not be changed at the same time.
- Additionally, the distance used in the assessment items will be the distance above the center of the earth unless a substitute reference plane, such as the floor, is explicitly stated in the assessment item. When this is the case, the reference plane will be the lowest plane in the context so that there will be only positive values for the distance.
- Note: The students are not expected to know the difference between “weight” and “mass.” All of the context used in the assessment items will be ones where “mass” and “weight” are proportional to each other. The earth will be used as the context for all assessment items.
- Note: Any plane on which all points are essentially equidistant from the center of the earth, such as the floor of a room, can be used as a substitute for the center of the earth in determining the amount of gravitational potential energy an object has. Because all points on this reference plane are considered to be equidistant from the center of the earth, all objects on the plane can be considered to have zero gravitational potential energy. (There will be only one reference plane that applies to all objects in the situation.) In assessment items the “reference plane” will be referred to as a “reference point.”

Item ID Number |
Knowledge Being Assessed | Grades 6–8 |
Grades 9–12 |
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The mass of a rock will affect the gravitational potential energy of a rock on top of a cliff. | See the Original Project | |||

For two books on a table, the book that weighs more has more gravitational potential energy. | See the Original Project | |||

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Misconception |
Student Misconception |
Grades 6–8 |
Grades 9–12 |
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Frequency of selecting a misconception was calculated by dividing the total number of times a misconception was chosen by the number of times it could have been chosen, averaged over the number of students answering the questions within this particular idea.

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