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Section learning objectives

By the end of this section, you will be able to:

  • Describe Newton's Second Law both verbally and mathematically
  • Use Newton's Second Law to solve problems

The Learning Objectives in this section will help your students master the following TEKS:

  • (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to:
    • (4D) : calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects
Section key terms
freefall Newton's second law of motion weight

Describing newton's second law of motion

[BL] [OL] Review the concepts of inertia and Newton’s first law. Explain that, according to Newton’s First Law, a change in motion is caused by an external force. For instance, a ball that is pitched changes its speed and direction when it is hit by a bat.

[BL] [OL] [AL] Write the equation for Newton’s Second Law and show how it can be solved for all three variables, F, m, and a. Explain the practical implications for each case. Ask students how the other two variables would behave if one quantity is held constant.

Students might confuse the terms “equal” and “proportional.”

Newton’s first law considered bodies at rest or bodies in motion at constant velocity. The other state of motion to consider is when an object is moving with a changing velocity, which means a change in either the speed and/or the direction of motion. This type of motion is addressed by Newton’s second law of motion    , which states how force causes changes in motion. Newton’s second law of motion is used to calculate what happens in situations involving forces and motion, and it shows the mathematical relationship between force, mass, and acceleration. Mathematically, the second law is most often written as

F n e t = m a
where F net (or ∑F) is the net external force, m is the mass of the system, and a is the acceleration. Note that F net and ∑F are the same because the net external force is the sum of all of the external forces acting on the system.

First, what do we mean by “a change in motion”? A change in motion is simply a change in velocity: the velocity of an object can get bigger or smaller, its direction can change, or both. A change in velocity means, by definition, that an acceleration has occurred. Newton’s first law says that only a nonzero net external force can cause a change in motion, so a net external force must cause an acceleration. Note that “acceleration” can refer to slowing down or to speeding up. Acceleration can also refer to a change in the direction of motion with no change in speed, because acceleration is the change in velocity divided by the time it takes for that change to occur, and velocity is defined by speed and direction.

The equation F n e t = m a or F = m a can be used for:

  1. Speed
    1. a = F n e t m or a = F m
    2. a F n e t
  2. Direction
  3. Velocity

From the equation F net =ma, we see that force is directly proportional to both mass and acceleration, which makes sense. To accelerate two objects from rest to the same velocity, you would expect more force to be required to accelerate the more massive object. Likewise, for two objects of the same mass, applying a greater force to one would accelerate it to a greater velocity.

Practice Key Terms 3

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Source:  OpenStax, Updated tutor hs physics content - legacy. OpenStax CNX. Mar 16, 2015 Download for free at https://legacy.cnx.org/content/col11768/1.4
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