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Free Body Diagrams and Weight Forces

In order to be able to analyze forces and their consequences it is often necessary to draw pictures. The essential aspects of these pictures are the forces and where they act. Such pictures eliminate everything unimportant. The pictures are called free-body diagrams.

In order to make sense of them we need to first find a common nomenclature, a way to label everything. We will start with the forces. Forces are distinguished by the way they act on the object. We have contact and non-contact forces.

 Non-contact forces do not require the objects to have contact for the interaction to occur. The most important non-contact force is gravitational force, which gives rise to the weight of every object and is therefore labeled with a W for weight. Other non-contact forces of interest in this course are the magnetic force and the electric force. Contact forces are separated into pushes and pulls for obvious reasons. The pull force is called tension, just so we can label it T and not P for push. Tension forces only act when strings, ropes, chains or your hair is involved. Push forces depend on the angle at which the force is applied. If it is applied perpendicular (or normal) t the surface they are called Normal forces. If they are applied parallel to the surface they are friction forces. Friction is labeled with a lower case f, to distinguish them from the force label “F”. The net force is not a force found on the free-body digram. It is the sum of all the forces that act on the object, not a seperate force.

 These forces are then put onto the object. The force vectors always start at the object. So, even if the two guys are pushing to the right on the left side of the car, their forces appear on the right of the car. Make it a habit to always start with the weight force. Every object that we will be dealing with will have weight force. Most of the time the normal force of the ground pushing up will counter this force. Then figure out the rest of the forces. Friction in most cases resists the motion or the attempt to move something.

Once the free-body diagram is drawn your task will most likely always be to rank the forces on the diagram. For this you use Newton’s Second and Third law. The Second Law compares two forces on the same free-body diagram. For instance for the car example above, the weight force has to equal the normal force. This is because the car does not accelerate up or down. No acceleration results in a zero net force, which in turn means these two forces have to cancel out.  Looking at the horizontal forces you can actually find the net force in the above example and then figure out the acceleration.

You use the Third law if you want to compare forces on two different diagrams. You use it, so to speak, to jump from one free body diagram to another, in order to make a connection. This can also be done with tension, because there is only one tension in any one string or rope.

Consider the example below: a sled being pulled by a force at an angle. The angled tension force can be broken down into its two components, the horizontal and vertical component. This uses trigonometry so don’t worry too much about it. Once its broken down into the two components T(x) and T(y) you put these in the diagram instead of the angled tension force. That means that you have two forces up and one down (N, T(y) and W), as well as one force each left and right (T(x) and f).

Now you have to use Newton’s Second Law to figure out the Normal force. The weight of the sled is 150N. Since the tension T(y) is 60N (trigonometry) that leaves the normal force to be 90N. This is because there is no net force acting on the sled vertically. No net force means all forces cancel out (right side of the picture)

Horizontally you have two forces that are not equal: friction f=50N and tension T(x) = 80N. That gives a net force of 30N to the right. (right side of the picture). With this net force one can then figure out the acceleration of the sled: F = ma gives a= 2 m/s/s.

Imagine now you had to maintain such an acceleration for the sled. That would mean that after only five seconds of your speed would be 10m/s, which is faster than you can run.

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