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Free Body Diagrams

How to Draw Free Body Diagrams

Free body diagrams are used to gain an understanding of the forces (or sometimes the fields) acting on an object. This is a good first step when solving problems involving two or more forces, or forces that are not in line with the motion of an object. (For examples, see the questions and answers below)

To draw a free body diagram show the relative magnitude and direction of all forces acting on a body:

  1. Draw a dot to represent the center of gravity of the object.
  2. Draw and label arrows extending outward from the dot to represent the forces acting on the object. Drawing the arrows at least approximately to scale and correct angles helps.
  3. Draw a reference frame (x and y axes) with the motion along one of the axes.
  4. Dotted lines are drawn along x and y directions to represent the orthogonal components of the forces if necessary.

The relative lengths of the arrows in the diagram imply the direction of net force (and therefore, acceleration). If the acceleration of the object is zero, all forces cancel; if the object is accelerating, the net force is in the direction of the acceleration.

Commonly used forces in free body diagrams are weight (Fg), friction including air resistance (Ff), normal force supplied by a surface (FN), and applied force (Fa).

Components of forces are often labeled (Fx) or (Fy).

Free Body Diagram Problems

(See bottom of page for answers.)

1. Draw a free body diagram of a parachutist who
a. has just stepped out of the airplane, and is accelerating toward the ground.
b. has opened her parachute and is traveling downward with constant velocity.

2. Draw a free body diagram of a brick
a. at rest on a table.
b. being pushed to the right and having a constant velocity along a rough horizontal surface.
c. being pushed and speeding up to the right along a rough horizontal surface.
d. sliding freely to the right along a rough horizontal surface and slowing down.

3. Draw a free body diagram of a brick on a rough sloped surface and
a. at rest.
b. accelerating down the slope.

4. A 2.8-kg book resting on a surface inclined at 32º above the horizontal. Find the normal force exerted on the book.

5. A child on a sled accelerates down an icy slope at 3.38 m/s/s. If friction can be ignored, what is the angle of the slope to the horizontal?

6. A carton is resting on a ramp. As slope increases, the carton remains in place until the incline reaches a value of 32.7° from horizontal. At this angle, the carton begins to slide down the slope.
a. What is the coefficient of static friction between the carton and the ramp surface.
b. If the coefficient of kinetic friction between the carton and the ramp is 0.330, what would be the acceleration of the moving carton at this angle?

7. A package hangs from the ceiling of a freight car by a long string. The freight car, whose wheels are in contact with the earth, is accelerating in its forward direction. Draw free-body diagrams of the package, and the string. Indicate the pairs of action-reaction forces.

8. A 250 kg chest accelerates down a 25 degree incline at 0.70 m/s/s. What should the incline be for the chest to slide down at a constant speed?

9. A weightlifter held a 253 kg barbell overhead. The weightlifter's mass was 133kg. Draw a free body diagram for this situation and calculate the normal force exerted on each of the weightlifter's feet.

Answers to Free Body Diagram Problems

Selected solutions are printed below.
For solutions to all the problems on this page click here.

1. a

Free body diagram showing drag (friction from the air) and weight.

1. b

Air resistance can be represented as friction on a falling body.
Vertical normal force offsets weight.

2. a

2. b

Free body diagram showing opposing forces cancelling out
Free body diagram showing the applied force is only partially cancelled by friction.

2. c

Friction, normal force and weight act on a body.

2. d

For solutions to all the problems on this page click here.

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