Drawing a Free Body Diagram.

In most cases, it is a simple task to determine which forces are acting on a body, which way they point, and which way the acceleration points. A free body diagram (FBD) is simply a sketch of this information. What we usually don't know is the magnitude of one or more of the forces acting on the body or the acceleration. If we apply Newton's Second Law to the FBD we normally find a set of equations that can be solved to find those magnitudes. In this note we summarize how to decide which forces act on a body, which way they point, and which way the object is accelerating.

You will need to draw one FBD for each object you are interested in. How can you tell which objects you are interested in? Normally those are the ones for which you are trying to find an acceleration or a force that acts on it or for which you are told something about such as the object's mass.

FBDs are drawn for a single instant in time. It is for this instant that you indicate the forces acting on the body and its acceleration. For instance, imagine you will push a massive block across a table. You could draw free body diagram for the block before you start to push, while you are pushing but the object is not yet moving, or while the block is sliding. The question should indicate when you are interested in the object.

There are only a few forces that can be acting on simple objects such as a block. A problem may tell you someone or something is pushing an object, however you won't be told about the rest of the forces acting. These are the ones that you are always expected to know about even if they are not mentioned in a problem. Here are the most common ones.

Weight

• Objects which have mass feel a gravitational pull toward the centre of the earth.
• In free-body drawings, the earth is always at the bottom of the page. So draw an arrow pointing straight down.
• Label weight W or mg in your diagram.
• Note weight is the one force for which we know both direction and magnitude.

Normal forces

• When an object touches a surface or another inanimate object, it experiences a normal force. This force is easily overlooked because we don't usually think of tables as exerting forces on whatever is placed on them but they must if the weight of the object is to be balanced out.
• Normal forces point from the surface through the object of interest. The normal force is always normal (perpendicular) to flat surfaces.
• An object may be touching several surfaces or other objects, and thus may have multiple normal forces acting on it.
• Normal forces are usually labeled N or F_N.
• The normal force from the surface an object is sitting on, e.g. a tabletop, a floor, a weigh scale, is often called the apparent weight.

Tension

• Whenever a taut string pulls an object, it experiences a tension.
• The tension points from the object along the string.
• Tension can never push.
• In an ideal string, the tension is the same all along the string. Two blocks connected by the same string will experience the same tension although in different directions.
• Label the force with T or F_T.

Friction

• Occurs whenever an object is on a rough surface.
• When the object slides or slips on a surface, there is kinetic friction f_k acting.
• Kinetic friction opposes the sliding of the object.
• When there is no motion of the object relative to the surface, static friction f_s may be acting.
• Static friction varies from zero to f_s^MAX.
• Static friction is a resistance. It tries to prevent the object from slipping or sliding. If the other forces acting on the object, including weight, are trying to make the object slide one way, f_s acts in the opposite direction.
• If there is no net force trying to make the object slide, there will be no f_s.
• You must be explicitly told that the object is about to slip to use f_s^MAX in a FBD.

Note that when two different forces of the same type act on a body or you are drawing the FBD for two objects, you distinguish them by the use of subscripts. For example, if two strings are tied to an object one would be denoted T₁ and the other T₂. If you had two objects, the weight of one would be m₁g and m₂g for the other.

Acceleration

• When an object is speeding up, the acceleration is in the same direction as the velocity.
• When an object is slowing down, the acceleration is in the opposite direction to the velocity.
• When an object is turning around, the acceleration is in the direction it is turning.
• When an object has constant velocity, it is not accelerating.
• When an object moves in a curve, it has a centripetal acceleration which points from the object to the centre of the curve.

Note that a FBD diagram like

is impossible since Newton's Second Law, , says that the acceleration of the object is in the same direction as the net force.