Solving Newton's Second Law Problems

Our physics class has been spending the past few days perfecting the art of solving problems that apply Newton's second law of motion. These problems use the formula: F=ma, or the net force acting on an object is equal to its mass multiplied by its acceleration. This formula can be used to solve problems involving Newton's second law.
Follow these simple steps to solve F=ma problems:

1. Draw a free body diagram (FBD) with the information given to you in the question. Depending on the type of question, you might have to draw more than one FBD in order to solve the question. For example, pulley and train type questions require multiple FBDs.
2. Create your list of assumptions. Is there any friction? Is there air resistance? How many FBDs do I use? Is there acceleration? Which way is positive? Are the x and y axes tilted? These are some of the questions that must be answered before solving the problem. Drafting a list of assumptions will answer these questions and allow you to solve the problem without it becoming unnecessarily difficult to solve. The following is a list of assumptions for each of the four types of second law problems:

• Equilibrium problems:
• no friction
• a = 0
• Incline problems (static):
• fs = µsFn
• a = 0
• x and y axes are tilted to line up with the ramp's surface
• (+) in direction of a
• no air resistance
• µ = tan θ
• Fn is perpendicular to surface of incline
• Incline problems (kinetic):
• fk = µkFn
• ax ≠ 0, ay = 0
• (+) in direction of a
• no air resistance
• Fn is perpendicular to surface of incline
• Pulley problems:
• frictionless pulleys + rope
• no air resistance
• multiple FBDs
• (+) in direction of a
• T1 = T2
• a of system is the same
• Train problems:
• 1 FBD for a
• 3 FBDs for T1 and T2
• ay = 0
• a is consistent
• no air resistance
• weightless cables
• (+) in direction of a

3. Once you have your list of assumptions, you are ready to solve the problem. Split each of the FBDs into the x and y axis. Then solve for Fx = max and Fy = may for each of the FBDs. You will likely get two separate equations that you can then sub into each other to solve for the missing variable.


Congratulations! You have just solved a problem using Newton's second law of motion.


Some pictures:

An example of a free-body diagram.

Another example of a free-body diagram.