PHYS 1111 - Introductory Physics I
Free Body Diagram Supplement

1. Introduction. A free body diagram is a picture of the forces which act on an object and is the first (and perhaps the most important) step in solving force problems. This supplement is designed to improve your understanding of free body diagrams.

2. Purpose. The purpose of the free body diagram (FBD) is to help you identify and analyze the forces that act on a particular object or body. This supplement first covers those types of forces that are candidates to be included on a FBD. Then, a step-by-step method for constructing FBDs is presented. Finally, a few FBD examples are provided.

3. Types of Forces. The types of forces normally encountered in classical mechanics are:

WEIGHT

APPLIED

NORMAL

TENSION

FRICTION

Additional types of forces that can appear on FBDs will be encountered in Introductory Physics II.

a. WEIGHT: Weight is the gravitational force exerted on a object by the Earth or any other celestial body. If an object is near the Earth's surface and has mass, then the object has a weight. The magnitude of its weight is w = mg and its direction is toward the center of the Earth.

b. APPLIED FORCE: Applied forces usually result from things physically touching and acting on a body. By this definition, normal, tension and friction forces are applied forces, but we usually categorize them separately. In our context, applied forces include such phenomena as pushing an object or the force exerted by a spring on an object.

c. NORMAL FORCE: The normal force is due to contact of an external surface on an object. The surface supplies the normal force to the object. If two objects are in contact, normal forces exist. The direction of the normal force is perpendicular to the surfaces in contact and directed toward the body under consideration. The magnitude of the normal force can only be determined by analyzing all forces acting on the body.

d. TENSION FORCE: A tension force is a force applied to a body by a rope or string. Ropes and strings are incapable of pushing a body; they always must pull a body. Tension forces are directed away from the body being pulled and along the direction of the rope or string.

e. FRICTION FORCES: Friction forces occur because of surface adhesion between two objects in contact. The friction force is always parallel to the surfaces in contact (perpendicular to the normal force). The friction force acts in the opposite direction of impending motion or opposite the motion of the body. The magnitude of the friction force is f_s £ m_sn, if there is no sliding; and f_k = m_kn, if there is sliding ( m_s is the coefficient of static friction; m_k is the coefficient of kinetic friction; and n is the magnitude of the normal force). If motion is not impending, the only way to calculate the magnitude of f_s is by using Newton's 2nd Law.

4. Drawing a FBD. In summary, the steps (discussed in more detail below) for drawing a FBD are:

1 Isolate the body.

2 Draw and label all forces acting on the body.

3 Choose a coordinate axes and a direction for positive torque.

4 Include critical angles and dimensions.

a. Isolate the body. This step requires that you separate the body (block, wheel, cart, etc.) that you are investigating from everything else and draw it.

b. Draw and label all forces acting on the body. This is the most difficult step. Here is a suggested method to use:

1) List the possible types of forces. A handy mnemonic is WANT FORCES:

W W eight

A A pplied

N N ormal

T T ension

Forces F riction

2) Answer the following questions about the types of forces:

a) Does the body have mass? If it does, weight must be included.

b) Is there an applied force described in the problem?

c) Is there a normal force? Does the body touch another surface? If so, there must be a normal force.

d) Is there a rope or string attached to the body? If so, there is a tension force directed in such a way as to pull the body.

e) Is there a friction force? If the surface is frictionless or smooth, then no friction force is present. Otherwise a friction force is present and is directed parallel to the surface and opposing motion or impending motion.

3) Determine where to draw the forces on the FBD. At this point in the course, the positions of the force vectors on the diagram will not affect our analysis, but later, when we discuss rotational motion, position will become important. Use the following rules:

a) Identify the point of application of the force.

1)) For a homogeneous mass, the weight acts at the geometric center of the object.

2)) The point of application of applied and tension forces is normally specified in the problem statement.

3)) Normal and friction forces involve areas of surfaces in contact. By convention we will choose the center of the surface in contact as the point of application of these two forces.

4)) The normal force is drawn perpendicular to the surface of contact through the center of the body.

5)) The friction force is drawn parallel to the contact surface.

b) The line of action for a force is defined as a straight line in the direction of the force and passing through the point of application.

c) The principle of transmissibility states that the motion of an object remains unchanged when a force acting at a point on a body is replaced by another equal force which lies anywhere along the line of action of the original force. As a result, we can draw our forces anywhere along their lines of action.

c. Choose a coordinate axes and direction of positive torque. Virtually any coordinate axes can be used in a problem; however, certain selections will make the application of Newton's 2d Law much easier mathematically. Some rules to find a good set of axes:

1) Object experiencing acceleration. Choose one axis along the direction of acceleration. Choose the other axis perpendicular to the first.

2) Object moving a constant velocity. Choose one axis along the direction of motion. Choose the other axis perpendicular to the first.

3) Object at rest. Choose one axis parallel to the surface upon which the object rests. Choose the other axis perpendicular to the first.

The direction of positive torque will be discussed later in the course when we cover rotational motion. At this stage in the course, we need not concern ourselves with torque.

d. Include critical angles and dimensions. In many cases, it will be necessary to break force vectors into their components. Identifying critical angles allows the simple application of trigonometric relationships.

5. Examples. We are now ready to try a few examples as homework problems.

a. A block of mass, m, sitting on a level table.

b. A block of mass, m, sitting on an inclined plane. The block does not move.

c. Two blocks of masses, m₁ and m₂, attached by a string which runs over a massless, frictionless pulley, with one block (m₁) on a smooth inclined plane.

d. A block of mass, m, being pushed up an inclined plane by a horizontally directed force.

This supplement is a modification of a supplement long in use at the Department of Physics of the United States Military Academy (USMA) at West Point, New York. Dr. John Campbell, the instructor of this course and once a member of the faculty at USMA, was only one of many contributors to the development of the West Point version of the Free Body Diagram supplement.

Last update: June 15, 2006