Key Idea: The magnitude of two forces can be added together.

Students are expected to know that:

  1. Arrows can be used to represent forces acting on an object. The length of the arrows represents the strength of the forces, and the direction of the arrows represents the direction of the forces.
  2. Two forces acting on an object in the same direction at the same time are equivalent to a single force that is stronger than either of the two individual forces and is in the same direction as the two individual forces.
  3. Two forces acting on an object in opposite directions at the same time are equivalent to a single force that is weaker than the stronger of the two individual forces and is in the same direction as the stronger of the two individual forces.
  4. Two forces of the same strength acting on an object in opposite directions at the same time will cancel one another.

Boundaries:

  1. Students are expected to analyze situations involving no more than two forces acting on an object at the same time, that act along the object’s line of motion.
  2. Students are expected to combine forces qualitatively, but they are not expected to calculate net force.
Percent of students answering correctly (click on the item ID number to view the item and additional data)
Item ID
Number
Knowledge Being Assessed Grades
6–8
Grades
9–12
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FM075004

The length and direction of force arrows on an object can be used to determine the total force on the object.

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FM074005

The length of force arrows pointing on an object from opposite directions can be used to determine the total force on the object.

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Frequency of selecting a misconception

Misconception
ID Number

Student Misconception

Grades
6–8
Grades
9–12

FMM116

When force arrows are used to represent opposing forces, students think the greater force wins so that the total force is equal to the value of the greater force (AAAS Project 2061, n.d.).

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FMM115

Students add forces without considering the direction of the forces, i.e., they add absolute values of the forces (AAAS Project 2061, n.d.).

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FMM094

Two forces in opposite directions will cancel each other no matter what their strengths are (diSessa, 1993).

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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.