Construct a diagram of the problem. This assists in visualization and reduces the chance of confusing the facts. For a running example, consider a simple pulley system where a rope is run between a pulley with weights hanging on either end. You would draw this exact setup and write the known variables, such as the mass of each object.
Calculate the acceleration of the weights. If the two weights possess different masses, the larger one will pull the smaller one upwards at an increasing speed, i.e. it accelerates. If the masses are identical, neither weight would move and acceleration would be zero. The formula to determine acceleration is: a = g * [(m2 - m1) / (m1 + m2)]
Where: "a" is acceleration, "g" is gravity, "m1" is the mass of the first weight and "m2" is the mass of the second weight.
Let's say the weights' masses are 1.0 kg and 2.0 kg, corresponding to m1 and m2, respectively. "g" is a constant measured at 9.8 m/s/s, read "9.8 meters per second per second" or "meters per second squared". Therefore:
a = 9.8 * [(2.0 - 1.0) / (1.0+ 2.0)]
a = 9.8 * (1.0 / 3.0)
a= 3.3, rounded, with the units "m/s/s".
Calculate the tension in the system, using acceleration as a variable in the formula: T = m1 * (g + a)
Where T is tension, and the other variables are referenced as before. One thing you will notice is if "a" is zero, then the tension is simply the force of gravity on the weight, i.e., m1 * g. This is because there is no additional force exerted to the first weight by the movement upwards. In the example, there is acceleration which acts to increase the tension on the rope, such that:
T = 1.0 * (9.8 + 3.3)
T = 1.0 * 13
T = 13, with the units kg*m/s/s, or Newtons
T = 13 N