This unit is called
quantitative dynamics
because we will begin analyzing why objects move
the particular way that they do.
The key issue is to quantitatively analyze forces.
FreeBody Diagrams and Vectors
A freebody diagram is a dot (or simple picture)
with arrows emanating from it.
The dot represents one object.
Each arrow represents one force acting on that object.
Here is an example of a quantitative freebody diagram:
This freebody diagram includes two forces:

A force of 100 Newtons to the right.

A force of 60 Newtons to the left.
Because force is a vector,
each force has both a magnitude and direction.
In a quantitative freebody diagram,
each force is represented by an arrow and a number.
The direction is given by the direction of the arrow,
and the magnitude is given by the number next to the arrow.
The unit for force is Newtons (N),
so each number has this unit.

Write the magnitude and the direction of this force:

Write the magnitude and the direction of this force:

What does the letter "N" stand for in these diagrams?

What is the name of a diagram of all of the forces acting on an object,
each represented by an arrow?
Finding Net Force of Two Forces
To find the net force
acting on an object,
use the freebody diagrams.

If two forces (arrows) are in the same direction,
ADD.

If two forces (arrows) are in opposite direction,
SUBTRACT.
The direction of net force is in the direction that had greater magnitude.

Find the net force (Magnitude and direction).

Find the net force (Magnitude and direction).

Find the net force (Magnitude and direction).

Find the net force (Magnitude and direction).
Finding Net Force of More than Two Forces
To find the net force from a free body diagram with more than
two forces, follow these steps:

Add all of the forces on the left side.

Add all of the forces on the right side.

Subtract the sums of each side.

The direction of net force is the direction
that had more force.

Find the net force (Magnitude and direction).

Find the net force (Magnitude and direction).

Find the net force (Magnitude and direction).
Drawing a freebody diagram and finding net force.
Sometimes,
a freebody diagram is not given to you in a problem,
but you have to draw your own freebody diagram first,
then find the net force acting on an object.
(In all problems below, please ignore any forces
not explicitly stated.)
Also know this:
If the net force is zero, then the net force has no direction!

Two forces act on an object.

It is pushed with a force of 50 N to the right.

Friction resists with a force of 20 N to the left.

Draw a freebody diagram showing these two forces.

Find the net force (Magnitude and direction).

A rocket ship is experiencing three forces.

An upward thrust of 500 N.

A weight of 200 N. The direction of weight is always downward.

An air resistance of 20 N downward.

Draw a freebody diagram showing these three forces.

Find the net force (Magnitude and direction).

A book is lying on a table. There are two forces acting on the book.

It has a weight of 102 N.
The direction of weight is always downward.

There is an upward normal force of 102 N.

Draw a freebody diagram showing these three forces.

Find the net force (Magnitude and direction).
Answers