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Force Diagrams

Already in this chapter we have seen a number of force diagrams. In this section we discuss some rules for drawing force diagrams. There are two types of force diagrams:
  • a diagram in which all the objects appear and the forces come in third-law pairs, and
  • a diagram featuring one object and all its forces (or maybe several objects, but not all the objects in the situation).
  • In most problems we will want the second type, but it is important to know how to draw both, and knowing diagrams of the first type will help with the second type.
To draw the first type of diagram, we ask four questions:
  1. What gravitational forces are important?
  2. What things are touching? (These give contact forces.)
  3. Does the problem mention any specific forces?
  4. Do the net forces in the diagram conform to expectation?
For each force we draw an arrow whose tail lies on the object on which the force acts. This may seem unnatural at first, but it makes things easier in the end. For some examples, look at the diagrams we drew in Section C.
 
Example

A girl jumps horizontally from a boat in the water. Draw all the forces on the boat, the girl, and the Earth. Ignore the tiny gravitational force between the girl and the boat, and ignore the drag force of the water on the boat.

 

Solution

First we add the gravitational forces in pairs (Figure 3-11).

 

Image

Figure 3-11
 

Then we add the forces due to the boat and girl touching (Fbg and Fgb) and the contact force between the Earth and the bat (Neb and NbE). See Figure 3-12.

 

Image

Figure 3-12
 

The net forces on the boat indicate that it accelerates backwards, which seems right. The net force on the girl indicates she would accelerate forward and down, which seems right. It is difficult to tell what is going on with the Earth.
 

 

Example

A vase sits on a table, which sits on the Earth. List all pairs of forces. Do this example on your own before you look at the solution.

 

Solution

See Figure 3-13.

 

Image

Figure 3-13
 

FEv = gravitational force of Earth on the vase,

 

FvE = gravitational force of vase on the Earth,

 

FEt = gravitational force of Earth on the table,

 

FtE = gravitational force of table on the Earth,

 

Ntv = contact force of table on vase,

 

Nvt = contact force of vase on table,

 

NEt = contact force of Earth on table,

 

NtE = contact force of table on Earth.

 

Drawing a diagram of the second type is easier, but you have to be careful not to leave out any forces nor to add any ghost forces.
 

 

Example

A roller skate is rolling frictionlessly on level ground to the left. Draw all the forces on the roller skate. STOP! Try doing this problem before looking at the solution.

 

Solution

Gravity is pulling down (question 1). And the ground is touching the skate, pushing up (question 2). There is no friction, nor any other forces, so the force diagram is Figure 3-14.

 

Image

Figure 3-14
 

Image

Figure 3-15


Did your diagram look like Figure 3-15 A or B? If so, you have not yet tuned your intuition about the first law of motion. Just because the skate is going to the left does not mean there is a force to the left. Only if the skate were speeding up to the left would we be forced to conclude that there was a force to the left.
 

  • In this chapter we studied Newton’s laws of motion. In a sense, the first law of motion is the most subtle. If an object is moving at a constant velocity, then the forces on the object add to zero, and if the vector sum of the force vectors for an object is zero, then the object moves at constant velocity. Constant velocity means constant speed in a straight path. No force is required to keep an object moving.
  • In this chapter we studied Newton’s laws of motion. In a sense, the first law of motion is the most subtle. If an object is moving at a constant velocity, then the forces on the object add to zero, and if the vector sum of the force vectors for an object is zero, then the object moves at constant velocity. Constant velocity means constant speed in a straight path. No force is required to keep an object moving.
  • The second law of motion concerns objects whose force vectors’ sum is not zero: The acceleration of such an object is in the same direction as the total force, proportional to its magnitude and inversely proportional to the object’s mass. That is a = Fnet/m. Do you see why we use equations?
  • The third law states that forces come in pairs: If object 1 pushes object 2, then object 2 pushes object 1 in the opposite direction.
Pay especial attention to Section D on force diagrams. In solving problems, we are always interested in the forces on an object at a given instant in time. These include gravity, usually, and forces due to things touching the object at that moment. No other forces need to be included. In particular, do not include a force in a direction just because the object in moving in that direction.




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