# Forces in different directions relationship

### Equal & Opposite Reactions: Newton's Third Law of Motion If two forces of equal strength act on an object in opposite directions, the forces In Newton's second law of motion, he described the relationship of force, mass. In general, an object can be acted on by several forces at the same time. A force is a vector quantity which means that it has both a magnitude and a direction. If two vectors have the same magnitude (size) and the same direction, then we call them equal to each other. For example, if we have two forces, \(\vec{F_{1}}.

### Balanced and Unbalanced Forces

What happens to the body from which that external force is being applied? That situation is described by Newton's Third Law of Motion. It states, "For every action, there is an equal and opposite reaction. Newton expanded upon the earlier work of Galileo Galileiwho developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon.

Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass. Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature intwo years after Newton was born. Pushback Forces always occur in pairs; when one body pushes against another, the second body pushes back just as hard. For example, when you push a cart, the cart pushes back against you; when you pull on a rope, the rope pulls back against you; and when gravity pulls you down against the ground, the ground pushes up against your feet.

## Balanced and Unbalanced Forces

The simplified version of this phenomenon has been expressed as, "You cannot touch without being touched. The minus sign indicates that the forces are in opposite directions. Often FAB and FBA are referred to as the action force and the reaction force; however, the choice of which is which is completely arbitrary. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Balanced Forces But what exactly is meant by the phrase unbalanced force? What is an unbalanced force?

### Vectors and Forces in Two-Dimensions

In pursuit of an answer, we will first consider a physics book at rest on a tabletop. There are two forces acting upon the book. One force - the Earth's gravitational pull - exerts a downward force. The other force - the push of the table on the book sometimes referred to as a normal force - pushes upward on the book. Since these two forces are of equal magnitude and in opposite directions, they balance each other.

The book is said to be at equilibrium. There is no unbalanced force acting upon the book and thus the book maintains its state of motion. When all the forces acting upon an object balance each other, the object will be at equilibrium; it will not accelerate. Consider another example involving balanced forces - a person standing on the floor.

There are two forces acting upon the person. In such instances, the gravity force plus the vertical component of the applied force is equal to the upward normal force. In this case, the vertical forces sum to zero; the remaining horizontal forces will sum together to equal the net force. If friction is present, a vertical force analysis is used to determine the normal force; and the normal force is used to determine the friction force. Then the net force can be computed using the above equation. Finally, the acceleration can be found using Newton's second law of motion. The Hanging of Signs and Other Objects at Equilibrium Several of the problems in this set target your ability to analyze objects which are suspended at equilibrium by two or more wires, cables, or strings. In each problem, the object is attached by a wire, cable or string which makes an angle to the horizontal. As such, there are two or more tension forces which have both a horizontal and a vertical components. The horizontal and vertical components of these tension forces is related to the angle and the tension force value by a trigonometric function see above. Since the object is at equilibrium, the vector sum of all horizontal force components must add to zero and the vector sum of all vertical force components must add to zero.

In the case of the vertical analysis, there is typically one downward force - the force of gravity - which is related to the mass of the object. There are two or more upward force components which are the result of the tension forces. The sum of these upward force components is equal to the downward force of gravity. The unknown quantity to be solved for could be the tension, the weight or the mass of the object; the angle is usually known. The graphic above illustrates the relationship between these quantities.

Detailed information and examples of equilibrium problems is available online at The Physics Classroom Tutorial. Inclined Plane Problems Several problems in this set of problems will target your ability to analyze objects positioned on inclined planes, either accelerating along the incline or at equilibrium. As in all problems in this set, the analysis begins with the construction of a free-body diagram in which forces acting upon the object are drawn.

This is shown below on the left. Note that the force of friction is directed parallel to the incline, the normal force is directed perpendicular to the incline, and the gravity force is neither parallel nor perpendicular to the incline.

On horizontal surfaces, we would look at all horizontal forces separate from those which are vertical. But on inclined surfaces, we would analyze the forces parallel to the incline along the axis of acceleration separate from those which are perpendicular to the incline.

Since the force of gravity is neither parallel nor perpendicular to the inclined plane, it is imperative that it be resolved into two components of force which are directed parallel and perpendicular to the incline.

## Equal & Opposite Reactions: Newton's Third Law of Motion

This is shown on the diagram below in the middle. The formulas for determining the components of the gravity force parallel and perpendicular to the inclined plane have an incline angle of theta are: The net force is determined by adding all the forces as vectors. The forces directed perpendicular to the incline balance each other and add to zero. For the more common cases in which there are only two forces perpendicular to the incline, one might write this as: As always, the net force is found by adding the forces in the direction of acceleration and subtracting the forces directed opposite of the acceleration.