There are two types of forces: contact and field. Forces are vector quantities. When you add two or more forces together, you get a resultant vector called the net force.
The forces acting on an object are vectors, which have magnitude and direction. These vectors can be depicted in a force diagram using arrows that point in the direction the force is acting. Scientists usually use right as positive and left as negative.
Look at the forces in the diagram above. One person pulls on an object with a 100 N force to the left, and another person pulls on the same object with a 70 N force to the right.
Find the net force acting on the object.
Add the two vectors together, and the resultant is -30 N. That means my net force is -30 N, or 30 N to the left.
Some of the forces that you will see in diagrams have special names. The most common are weight, friction, tension, applied force, and normal force.
It is often useful to analyze forces acting on an object by the use of a free-body diagram. A free-body diagram is different from a force diagram because the free-body diagram only shows the object in the problem and arrows representing the forces acting on the object. Free-body diagrams do not include other objects such as wall or floors; other vectors such as displacement, velocity, or acceleration; or any reaction forces from the object.
Let's draw a free-body diagram of you sitting in your chair.
When your weight acts down, the normal force of the chair acts up.
Your weight, W, acts down; the normal force acts up. These are the only two forces acting on you in this diagram, so the free-body diagram is complete.
Notice that in the final diagram above, you do not see the chair, and you do not see the reaction force of you pushing back on the chair.
In the previous example, the normal force balanced the weight. This is not always true. If you are sitting in your chair and someone pushes down on your shoulders, the normal force increases and is greater than your weight. If someone lifts you up as you sit, the normal force is less than your weight.
Let's look at an example with a force applied at an angle.
The following image shows the force diagram for a box being pulled across a rough floor using a rope that makes a 30° angle.
Force Diagram:
Examine the free-body diagram below. Since the rope pulls up on the box at the angle, the tension has a y component, Ty that pulls up. Ty and the normal force share the job of supporting the box's weight, and therefore, the normal force decreases. It is now less than the weight.
Free-Body Diagram:
Similarly, if you push down on the box at the angle, like you would with a lawnmower handle or on a shopping cart, the normal force increases because the y component of the push force P pushes down on it.
Force Diagram:
Now when you look at the free body diagram, you see that the normal force has to balance both the weight and Py.
Free-Body Diagram:
