Summary

1. Choose a system and/or subsystems on which to concentrate.
2. Determine the type of forces acting on the system
3. Draw a free-body force diagram of the system.
4. Apply Newton's 2 Second Law to the system.

Which object or group of objects will I take to be a system?
* Any single body can be considered to be a system to which Newton's 2^nd Law can be applied.

* When a problem has several objects connected together somehow, each object could still be considered to be a separate system. In addition, any pair of objects (or all the objects taken together) could also be considered to be a system.

* To make it clear which system you have chosen, sketch the object or group of objects by themselves, isolated from their surroundings. This is part of constructing a free-body diagram.

What are all the forces acting on the system that I have chosen ?
* Decide which forces are acting on the system and which forces are not acting on the system. This is the most difficult part of the process, because you cannot really see force. You can only see the result of the force's action.

* Only those forces that make direct contact with the system will expressly act on the system. It takes some experience to know what forces are acting directly on the system and what forces have an effect on the system but are not acting directly on the system.

* The net force F_net is not a force acting on the system. It is the resulting force due to the action of all the other forces. You could replace the action of all the forces with the net force. However, it is not one of the forces which acts on the system, it is representative of all of them. Likewise, the quantity ma is not a force acting on the system, it is the magnitude of the net force, F_net = ma.

* Sketch all the forces acting on the system, along with their directions, to construct a free-body force diagram.

* Any force that the system exerts on its surroundings is not a force that you should include. However, by Newton's 3^rd Law there is a reaction force that will be acting on the system that you should include.

* An object's velocity-vector is not a force. It surely took a force to give the object a velocity, but once that force is no longer acting on the system it does not somehow transfer its "action" to the object's velocity. Newton's First Law shows that an object does not need any force to keep it moving at a constant speed.

How do I apply Newton's Laws to solve the problem ?
* Choose a frame of reference and sketch its origin on your free-body diagram. It is useful to try to guess which direction the system will move and make that direction the positive axis of one of your coordinate axis.

* Resolve the force-vectors into components to determine the net force along each coordinate direction.

* Write down Newton's 2^nd Law for each coordinate direction. For the horizontal-vertical coordinate system, this will have the form,

* If you have not already done so, express the terms in these Second Law equations using the personal labels you have chosen for the problem.

* Be consistent with the signs you place in front of the forces. Make sure the actual direction of the action of any forces you write down in Newton's 2^nd Law equations is indicated correctly by the sign you use when you write them down. The hardest force to express correctly is the direction of the force of friction.

* Replace any force terms in these Second Law equations with the equations associated with each particular type of force. In particular, any spring force can be replaced with Hook's Law, F_s= -k x, kinetic friction can be replaced with f = m_kn, and the force of gravity can be replaced with W = m g. Rather than replacing them, you can also just write them down along with the Second Law equations.

* Examine the resulting equations to determine what quantities you know and what quantities you do not know. It can be helpful to re-read the problem at this point if you have any doubts. Having already explicitly considered what information is given and what is requested could make this part a snap.

* At this point you may be able to solve the resulting equations for the requested unknowns. If not, reconsider each of the steps you have taken to see if anything is missing or inconsistent with what you know about the behavior of the type of system described in the problem. Check your steps with your intuitive expectations and the facts you are certain of to that point.

* When you do finally get an answer, make sure that it is reasonable with what you expect for this type of process. For example, does the answer indicate that the system is moving in the direction you anticipated ? Are any of the forces you found unreasonably large or small, or in the wrong direction. ?