1.3 Newton's second law of motion  (Page 26/7)

Describing newton's second law of motion

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

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 $F_{net}=ma$ or $\sum F=ma$ can be used for:

1. Speed
   1. $a=\frac{F_{net}}{m}$ or $a=\frac{\sum F}{m}$
   2. $a\propto F_{net}$
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.