Tension Forces

Tension forces are the same as any other forces...except that they don't "push"...they only pull. There are some typical aspects to solutions to tension problems that should be remembered, however:

1. When there is a tension joining TWO objects, the tension at one end of the string/cord is equal and opposite to the tension at the other end (even if the cord is "bent" around a pulley).

***Note: this is only true for "massless" strings...we will only use massless strings in this course.

2. If the tension forces are NOT known, the acceleration of the whole system must be known before one may calculate the tension force. This requires a free body diagram of the WHOLE system, considering ALL forces.
3. Newton's Second law and the Fnet definition can be used to find the acceleration of the system.

***Note: the two tension forces are equal and opposite...so they cancel each other in the net force calculation (F_net = F_g + F_tension - F_tension+ F_f + ... (all forces that apply in the problem).

4. Once the acceleration of the system is known, a SINGLE object in the system can be studied using Newton's Second Law and the net force definition to find the force of tension in the cord:

F_net = ma

F_net = F_g + F_tension

OR

F_net = ma

F_net = F_friction + F_tension

5. Solve for the tension force variable in each case. BOTH solutions should be completed to VERIFY that the correct solution has been obtained. When the solutions do not produce the same tension values, a LIKELY suspect value is the SYSTEM acceleration or the NET FORCE value that is being used in the single object equation.

***Note: gravity may or may not be used a tension problem; it has been used here as it applies to the image above.

As always...be SURE that you are not MEMORIZING solutions to other problems and applying them to NEW situations. Every problem can be seen as similar to a previous one...but EVERY solution is unique in terms of directions, and variables used.

As discussed in class, we are following a convention that considers VARIABLES as "containers" that main "contain" positive or negative values. As such the equations above show ALL variables as positive; it is important to be sure to not POSITIVE and NEGATIVE directions so that the values substituted in these equations reflect appropriate direction relative to the acceleration of the object.