Force Diagrams (Free-body Diagrams)

Types of forces typically used:

Force Symbol Magnitude Direction
Gravity (weight) F(G)  = mobject*g        (9.8 m/s2) Downward
Normal (surface) F(N) any (up to breaking load) perpendicular to surface
Tension  F(T) any (up to breaking load) along string/rope/chain
Friction F(fr) not slipping:  between zero and ms*F(N)
slipping: = mk*F(N)
Direction opposing relative motion.

Drawing a Force Diagram

A force diagram is simply a diagram showing all the forces acting on an object, the force's direction and its magnitude.  It is a simplification of the picture that shows just the forces.  In the example below, the first image is a picture of a climber on the side of a cliff.  The second image shows just the object of interest (the climber) and has vectors drawn representing the different forces on the climber, which are labeled with everyday language.  The third image is a force diagram; the object of interest is simply represented by a dot, and the vectors are labeled by the type of force, the object exerting the force, and the object receiving that force.

Steps for drawing a force diagram:

  1. Identify the object you will draw a diagram for.  (If there are multiple objects of interest, you will need to draw multiple diagrams.)
  2. Identify all the forces acting directly on the object and the object exerting them.  With the exception of gravity and certain other forces rarely used in first semester physics (magnetism, electric force), the two objects will be in direct contact.  Do not include forces by an object acting through another object--only include the force due to the intermediate object.
  3. Draw a dot to represent the object of interest.
  4. Draw a vector to represent each force.  Draw it in the direction the force is being exerted, and label it by (a) the type of force, (b) the object exerting the force, and (c) the object receiving the force (which will be you object of interest).  It will have the form F(type)exerting object -> object of interest
  5. If the object is stationary or is moving at a constant velocity, the vectors should graphically add up to zero.  If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration.

Writing down the sum of the forces

  1. Identify direction of every force and of acceleration.
  2. Pick a coordinate system to minimize the number of things (forces and acceleration) that must be broken into components, especially unknown values
  3. Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle that is given (or being looked for).
  4. Pick one direction and write down all the forces or components of forces in that direction, using positive and negative signs to identify those in the positive and negative directions.
  5. Set the sum of the forces in that direction as equal to the mass multiplied by the acceleration in that direction.  (If not moving or moving at a constant velocity in that direction, acceleration will be zero.)
  6. Repeat for the other direction.