Physics students, and even professional physicists, often don't know how to start when solving a problem. The more complex the problem, the harder it is for physics students to know where to start. For problems involving forces, physicists always start by drawing a free body diagram of the forces in the problem. Even when the problem solver does not know how to proceed, the free body diagram will often help physics students see what to do next.
What Is a Free Body Diagram?
A free body diagram is a drawing of the forces involved in a physics problem. A free body diagram does not however show all the forces at work. Rather a free body diagram shows all the forces acting on one specific object involved in the problem. In a free body diagram, the shape of an object is not important. It is usually best to simply represent the object as a point and the forces as arrows roughly proportional to the strength of the force.
For example if a woman is sitting in a chair, the free body diagram of the woman would show the gravitational force pulling her down and the normal force of the chair pushing her up. The free body diagram of the woman would not show the gravitational force that she exerts on the Earth, or the downward normal force she exerts on the chair.
Notice that the free body diagram of an object shows the forces acting on the object not the forces exerted by the object.
Forces and Newton's Third Law
As an aside, if the woman is not accelerating, the two forces acting on her from the chair and Earth are equal and opposite forces. They are not, however, the action reaction pair dictated by Newton's third law. The reaction force to Earth's gravity pulling down on the woman is her gravity pulling up on Earth. The reaction force to the chair pushing the woman up is the woman pushing the chair down. Both of these action reaction pairs are equal and opposite forces.
Using Free Body Diagrams
To solve a physics force problem draw the free body diagram. After identifying and visualizing all the forces acting on the object of interest in the problem, apply Newton's second law, F=ma. The vector sum, F, of all the forces acting on an object is the object's mass, m, multiplied by its acceleration, a.
Because the force and acceleration are both vector quantities, they must be divided into components parallel to the x, y, and z axes. Apply the formula for Newton's second law separately along each axis.
If the object of interest is not accelerating, the problem becomes a little simpler. Set the acceleration equal to zero and the sum of the force also equals zero. In either case solve the equation or equations for the unknown quantity or quantities in the problem.
Free body diagrams are an essential tool for solving physics force problems.
Further Reading
Knight, R.D., Physics for Scientists and Engineers, Pearson, 2004.
Paul A. Heckert - I have a Ph.D. in astrophysics, over 30 years experience teaching physics and astronomy, and over 60 published research articles.
