## Introduction

Recall that a force is something that causes an object to accelerate. This means that a force has been applied when the magnitude of speed and/or direction of an object has changed. Typically there are five categories of forces to consider.

## Units

Since force is the product of mass and acceleration, the units for force are the product of those units. Mass is measured in kilograms and acceleration in m/s2, thus the unit for force can be expressed as kg×m/s2. However, this unit is bulky and time consuming to write and pronounce. Fortunately, this derived unit is also represented as the newton (N), in honor of Isaac Newton. Hence a m/s2 is equivalent to a newton.

## Weight

Unlike the other forces mentioned on this page, weight is present in every situation. This is because weight is the force on an object that is the consequence of its gravitational attraction to some celestial body. Unless otherwise stated, one can assume this is Earth. Its direction is oriented vertically downward to the Earth.

Since the value for g, acceleration due to gravity, does not differ significantly across the surface of the Earth, weight is uniform for an object at any location on or near the surface. Usng the equation F = ma, and considering a to be equivalent to g, weight can be found using a modified F = mg. For this reason, an object's weight can be estimated by multiplying its mass in kilograms by 10. For a more accurate (but usually not significantly different result), multiplying an object's mass by 9.8 gives the true value.

## Normal Force

The normal force is a "support" exerted by a surface on the body resting on the surface. In the situation of a book resting on a table, the book's weight is exerted downward on the table. The table exerts a force upward on the book. The normal force is always oriented upward from perpendicular to the surface. For this reason, it is incorrect to assume the magnitude of the normal force will be equal to the magnitude of an object's weight. This is only true if the object rests on a flat surface. If an object rests on an incline, as shown in the picture below, the normal force is not equal and opposite to the object's weight. Note that it is perpendicular to the surface if the incline.

## Tension

Tension, like normal force, can be a "support" that acts in opposition to weight. Only objects that are suspended in some way (and not resting on a surface) can exhibit a force of tension. An example of tension acting in opposition to weight can be shown with a hanging flower pot. In the diagram below, a force vector for the flower pot's weight is directed downward and labeled with a W. The force that is equal and opposite this force is supplied by the tension in the three rods that support the pot. It is shown with a force vector pointing upward and labeled with a T.

Tension can also exist in opposition to an applied force. This can be visualized in a tug of war battle. However, it is not the opposing team that supplies the force of tension. There is a tension in the rope in opposition to each team's pull. In the diagram below, the two applied forces, or "pulls" are represented with a P. The corresponding tension in the rope from each pull is represented with a T. Note that for each pair, the magnitude of P and T are equal and opposite. If this is not true, the rope will break. The reason why the rope may slide through one team's hands, or the team will be pulled in some way is due to the two different pulls not being equal (they are however still opposite). Thus a team wins tug of war by supplying a large pull (P) than the other team, not because of the tension in the rope.

## Friction

Friction exists when one surface is moving across the surface of another object. The direction of the force is opposite the direction of motion of the object. While sometimes the magnitude of friction can be determined from the other forces acting on an object, it can also be determined independently using the formula Ffriction = μ×Fnormal where μ represents a constant called the coefficient of friction. The coefficient of friction value is different for surfaces of different materials. Surfaces that are rough and more likely to induce friction have larger values for μ.

## Applied Force

An applied force is generally considered to be any push or pull that a person applies on an object in order to change its motion. The pull of a sled or push of a box across a floor are examples of applied forces.