Free-Body Diagrams: Introduction
Description: Contains several conceptual questions asking the students various questions about free-body diagrams and highlighting their role in the solution process.
Learning Goal: To learn to draw free-body diagrams for various real-life situations.

Imagine that you are given a description of a real-life situation and are asked to analyze the motion of the objects involved. Frequently, that analysis would involve finding the acceleration of the objects. That, in turn, requires that you find the net force.

To find the net force, you must first identify all of the forces involved and then add them as vectors. Such a procedure is not always trivial. It is helpful to replace the sketch of the situation by the drawing of the object (represented as a particle) and all the forces applied to it. Such a drawing is called a free-body diagram. This problem will walk you through several examples of free-body diagrams and will demonstrate some of the possible pitfalls.

Here is the general strategy for drawing free-body diagrams:
  • Identify the object of interest. This may not always be easy: A sketch of the situation may contain many objects, each of which has a different set of forces acting on it. Including forces acting on different objects in the same diagram will lead to confusion and a wrong solution.
  • Draw the object as a dot. Draw and clearly label all the forces acting on the object of interest. The forces should be shown as vectors originating from the dot representing the object of interest. There are two possible difficulites here: omitting some forces and drawing the forces that either don't exist at all or are applied to other objects. To avoid these two pitfalls, remember that every force must be applied to the object of interest by some other object--or, as some like to say, "every force must have a source."
  • Once all of the forces are drawn, draw the coordinate system. The origin should coincide with the dot representing the object of interest and the axes should be chosen so that the subsequent calculations of vector components of the forces will be relatively simple. That is, as many forces as possible must be either parallel or perpendicular to one of the axes.

It should come as good news that, even though real life can present us with a wide variety of situations, we will be mostly dealing with a very small number of forces. Here are the principal ones of interest:

  • Weight, or the force due to gravity. Weight acts on every object and is directed straight down unless we are considering a problem involving the nonflat earth (e.g., satellites).
  • Normal force. The normal force exists between two surfaces that are pressed against each other; it is always perpendicular to the surfaces.
  • Force of tension. Tension exists in strings, springs, and other objects of finite length. It is directed along the string or a spring. Keep in mind that a spring can be either compressed or stretched whereas a string can only be stretched.
  • Force of friction. A friction force exists between two surfaces that either move or have a tendency to move relative to each other. Sometimes, the force of air drag, similar in some ways to the force of friction, may come into play. These forces are directed so that they resist the relative motion of the surfaces.

The following examples should help you learn to draw free-body diagrams. We will start with relatively simple situations in which the object of interest is either explicitly suggested or fairly obvious.

Part A  
A hockey puck slides along a horizontal, smooth icy surface at a constant velocity as shown.

Draw a free-body diagram for the puck. Which of the following forces are acting on the puck?
  1. weight
  2. friction
  3. force of velocity
  4. force of push
  5. normal force
  6. air drag
  7. acceleration
Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 AE 
There is no such thing as "the force of velocity." If the puck is not being pushed, there are no horizontal forces acting on it. Of course, some horizontal force must have acted on it before, to impart the velocity--however, in the situation described, no such "force of push" exists. Also, the air drag in such cases is assumed to be negligible. Finally, the word "smooth" usually implies negligible surface friction. Your free-body diagram should look like the one shown here.
Part B  

Consider a block pulled by a horizontal rope along a horizontal surface at a constant velocity as shown. The tension in the rope is nonzero.

Draw a free-body diagram for the block. Which of the following forces are acting on the block?

  1. weight
  2. friction
  3. force of velocity
  4. force of tension
  5. normal force
  6. air drag
  7. acceleration


Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 ABDE 
Because the velocity is constant, there must be a force of friction opposing the force of tension. Since the block is moving, it is kinetic friction. Your free-body diagram should look like that shown here.
Part C  

Now consider a block resting on a slope as shown.

Which of the following forces are acting on the block?
  1. weight
  2. kinetic friction
  3. static friction
  4. force of push
  5. normal force
Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 ACE 
Part D  
What is the direction of the force due to gravity acting on the block?
ANSWER:
vertically upward
vertically downward
perpendicular to the slope
upward along the slope
downward along the slope
Part E  
What is the direction of the normal force acting on the block?
Hint E.1 Concept of normal force
As the name suggests, the normal force on an object from the surface it is resting on or against acts normal to the plane of the surface and is equal to any force that the object exerts on the surface. This is because, under the assumption that the surface does not buckle, the acceleration of the object "into the surface" has to be zero.
ANSWER:
vertically upward
vertically downward
perpendicular to the slope
upward along the slope
downward along the slope
Part F  
Draw the free-body diagram for the block. What is the direction of the force of friction acting on the block?
ANSWER:
vertically upward
vertically downward
perpendicular to the slope
upward along the slope
downward along the slope
Without friction, the block would slide down the slope; so the force of static friction must oppose such a motion and be directed upward along the slope. Your free-body diagram should look like that shown here.
Part G  

Now consider a block sliding up a rough slope after having been given a quick push as shown.

Which of the following forces are acting on the block?

  1. weight
  2. kinetic friction
  3. static friction
  4. force of push
  5. normal force
  6. the force of velocity
Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 ABE 
The word "rough" implies the presence of friction. Since the block is in motion, it is kinetic friction. Once again, there is no such thing as "the force of velocity." However, it seems a tempting choice to some students since the block is going up.
Part H  
Draw the free-body diagram for the block. What is the direction of the force of friction acting on the block?
ANSWER:
vertically upward
vertically downward
perpendicular to the slope
upward along the slope
downward along the slope
The force of kinetic friction opposes the upward motion of the block. Your free-body diagram should look like the one shown here.
Part I  

Now consider a block being pushed up a smooth slope. The force pushing the block is parallel to the slope.

Which of the following forces are acting on the block?
  1. weight
  2. kinetic friction
  3. static friction
  4. force of push
  5. normal force
Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 ADE 

Your free-body diagram should look like the one shown here.

The force of push is the normal force exerted, possibly, by the palm of the hand of the person pushing the block.

In all the previous situations just described, the object of interest was explicitly given. Let us consider a situation where choosing the objects for which to draw the free-body diagrams is up to you.
Part J  
Two blocks of masses m_1 and m_2 are connected by a light string that goes over a light frictionless pulley. The block of mass m_1 is sliding to the right on a rough horizontal surface of a lab table.

To solve for the acceleration of the blocks, you will have to draw the free-body diagrams for which objects?

  1. the block of mass m_1
  2. the block of mass m_2
  3. the connecting string
  4. the pulley
  5. the table
  6. the earth
Type the letters corresponding to all the correct answers in alphabetical order. Do not use commas. For instance, if you think that only answers C and D are correct, type CD.
ANSWER:
 AB 
Part K  
Draw the free-body diagram for the block of mass m_1. How many forces are exerted on this block?
ANSWER:
none
one
two
three
four
Your free-body diagram should look like that shown here.
Part L  
Draw the free-body diagram for the block of mass m_2. How many forces are exerted on this block?
ANSWER:
none
one
two
three
four
Your free-body diagram should look like that shown here.
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