A kite hangs almost still in a steady breeze above a terrace in Ahmedabad on Uttarayan. The string pulls it down and sideways. The Earth pulls it down. The wind pushes it up and back. The kite does not move, so these pushes and pulls must balance. Seeing them all at once is hard. Drawing them one at a time is easy.
Why cut the body free
The second law is about one body: the net force on that body gives that body its acceleration. A real situation has many bodies, a floor, a string, a hand, the Earth. Each of them pushes or pulls on the others. If you draw all of them at once, the forces on the body you care about are lost among the rest. So you draw the one body alone, as if cut out with scissors.
A free-body diagram is a drawing of one body alone, with an arrow for every force that acts on that body and for nothing else.
A free-body diagram has two rules. Every force in it acts on the chosen body. Every force on the chosen body is in it. The forces this body exerts on other bodies belong in their diagrams, not in this one. For a small block, draw the body as a box or simply as a dot, and start every arrow on it.
A book lies on a table. Which force belongs in the free-body diagram of the book?
One force at a time
A fixed order finds every force and invents none. First draw the one non-contact force, the weight \(mg\), straight down. Then go round the edge of the body and look for every point where something touches it. Each touch gives exactly one force, or two if the surface is rough. A surface gives a normal force, and friction if it is rough. A string gives a tension. A spring gives a spring force. A hand gives an applied force.
Step through Fig 4.1 and ask the question at each state: what touches the block? The Earth pulls it without touching, so the weight comes first. The floor touches its base, so a normal force acts upward. The string touches its side, so a tension acts along the string, away from the block. The hand does not touch the block, so the hand's pull appears only through the string. Nothing else touches the block, so the diagram is finished.
The floor in Fig 4.1 is smooth, so there is no friction. On a rough floor a fourth force, friction, would act along the floor against the sliding. It gets its own chapters later in this unit.
Forces that are not there
The most common error is to add a force that has no agent. A ball thrown upward is still rising. Many students draw an upward "force of the throw". But the hand stopped touching the ball the moment it left the hand. After that, nothing touches the ball. The only force is its weight. The ball rises because of its velocity, not because of a force.
The test for every arrow is its agent. Ask of each force, "which body exerts it?". If you cannot name a body, the force does not exist. "Centrifugal force", "the force of motion", and "the force of the throw" all fail this test. A velocity is not a force, and neither is an acceleration. Neither belongs in a free-body diagram.
A cricket ball has left the bowler's hand and is flying towards the batter. Air resistance is neglected. Which forces act on the ball?
A lamp hangs at rest from the ceiling by a single light string. How many forces act on the lamp?
Put the steps for drawing a free-body diagram in order.
Paying off the kite
Draw the kite. The Earth pulls it down with its weight. The string touches it at the bridle, so a tension pulls along the string, down and towards the flier. The wind touches its face, so the air pushes on it. Three agents, three arrows. The flier does not touch the kite, so the flier's hand appears only through the string.
A student draws a box being pushed along a smooth floor and adds an arrow labelled "ma" in the direction of motion. Explain what is wrong with this diagram.
\(ma\) is not a force; it has no agent. The free-body diagram shows only forces, each exerted by a named body: here the weight, the normal force and the push of the hand. The second law says that the sum of these forces equals \(ma\). Drawing \(ma\) as an extra arrow counts the same thing twice.
Before a footbridge is built, an engineer draws a free-body diagram of each beam, each joint and each cable. The loads are the weight of the beam, the crowd and the wind; the contacts are the bolts and supports. The same two questions are asked at every joint: what touches this part, and which way does each touch push or pull? A missing force in the drawing is a missing force in the design.
- Adding a "force of the throw" or a "force of motion".Once the hand lets go, it exerts no force. Every arrow needs an agent that touches the body, or gravity.
- Drawing forces that the body exerts on others.Only forces acting on the chosen body go in its diagram.
- Drawing ma as a force.ma is the result of the forces, not one of them. It goes on the other side of the equation.
- Forgetting the weight because nothing seems to pull down.Draw the weight first, every time. Gravity acts without contact.