## Newton's Third Law, Action and Reaction

Based on the previous two laws, motion still can not be completely explained. Sometime, over objects, there is not a clear external force acting on the object; like for example, a person standing on the middle of a room, alone. If the person choose to walk out of the room. Where is the net external force need for accelerating the person coming from? Originally, the person is at rest (zero velocity) and later the person is moving with a given velocity; thus, the acceleration is not zero. What does apply the net external force to the person? The answer to this question is provided by Newton's third law, Action and Reaction.

If body A applies a net external force on body B (action), FBA, body B reacts by applying a force of the same magnitude but opposite direction on body A (reaction), FAB. These pair of forces is called an action and reaction pair.

### Characteristics of action and reaction pairs:

1. The action and reaction forces have the same magnitude:
2. The action and reaction forces are opposite to each other:
3. These two forces, action and reaction, act on different objects; therefore, the two forces do not cancel each other. In fact on body A, there is only one force acting on it:

 As an example of action and reaction, consider a person pushing a block as illustrated in the figure. The action is the force applied by the woman on the block. To this action, there is a reaction force exerted by the block and acting over the arms of the woman. The body of the person transmit this force all the way to the feet, blue vector. In the absence of friction (see below), the woman will slide back because of the reaction force acting on her. Static friction prevents sliding of the feet. On the figure, the friction between the floor and the block is not represented even when it is present. In most cases, the force that the woman exerts over the block is such that the block can be pushed at constant velocity (excepts when it just starts the motion where the push must also accelerate the block from rest). Depending on the friction between the different surfaces, the result of this action and reaction pair can be (starting from rest): Static friction between floor and shoes and between block and floor are greater than the force applied by the woman. Neither the block nor the woman move. Static friction between floor and shoes greater than force applied by the woman. However, static friction between floor and block is smaller than the force applied by woman. Block starts sliding forward. Woman must maintain an applied force in order to over come the kinetic friction (see below) between the block and the floor. Static friction between block and floor greater than applied force by the woman. In this case, the static friction between the floor and the shoes is smaller than the reaction force. Woman will slide back without being able to push the block. Static friction between the two pairs of surfaces is smaller than the force applied by the woman (imagine the floor is iced) both the woman and the block will slide in opposite directions. Woman to the left, and block to the right.

### Using Newton's third law, the change in the state of motion for a person can be explained.

 Over the player there are only two forces acting, the weight and the reaction of the floor to the pushing of the player against the ground. The reaction force of the floor, acting on the player, can be decomposed into vertical and horizontal components, V and H. Between this vertical component of the reaction force and the weight of the player, the resultant force in the vertical direction is zero (in average when the player is allowed to jump while running). However, the horizontal component of the reaction force is unbalance.
 Therefore, there is a net external force acting over the player. This force produces the acceleration of the player.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com