Determining Net Force
What is Net Force?

Net Force is the
vector sum of all of
the forces on an
object.

In other words, it’s
the “total” of all
forces.
So, can’t we just add them up?

Its not that simple. You must use the
free-body diagram of the forces to
decide what type of math to do to total
up the forces.
Same Direction…

Only if the forces are in
the same direction can
you add.

Since Fa and Ft are
both upward, we can
add them.

Fa + Ft = 2 + 4 = 6N
Fa = 2N
Ft = 4N
Fg = 6N
Opposite direction….

If forces are in the
opposite direction, you
must subtract them
from each other.

Since Ft and Fg are
opposite, we subtract.

Ft – Fg = 4 –6 = -2N.

The negative sign
indicates a net force
that is downward.
Ft = 4N
Fg = 6N
Let’s sum up the forces in both
directions.


Fa + Ft= 9 + 7 =
16N, upward.
Fa = 9N
Ft = 7N
Fg = 20 N,
downward.
Fg= 20N
Simplified…..

16N upward and 20N
downward.

Since these are
opposites we subtract.

16 – 20 = -4N
downward.

Remember the minus
sign just tells us that the
net force is downward.
Once you simplify,
draw the new FBD.
Fnet = 4N, downward
What about left and right?

The same rules still apply.
Same direction = add
 Opposite direction = subtract

What happens if you have forces
that are horizontal and vertical?

Simplify in each plane
first using the rules for
same and opposite
directions.

Then, draw the new
FBD. You should have
one force in each plane.

Notice that the vectors
are PERPENDICULAR
now.
What happens if you have forces
that are horizontal and vertical?
Once you have
perpendicular vectors, you
must continue to simplify.

a
How? See the triangle?
The hypotenuse is the
Fnet!
c

Now
since we have the
lengths of both sides we
just have to use
Pythagoreans Theorem!
b
Using Pythagorean’s Theorem

a2 + b2 = c 2
We
want to find c (net
force)

42 + 3 2 = c 2

16 + 9 = c2
 25

= c2
c = 5N (up and right)
4N
3N
Finding Fnet in Summary…

Simplify in both planes:
– Same direction = add
– Opposite direction = subtract

Draw the simplified FBD then use
Pythagoreans theorem IF the new
vectors are PERPENDICULAR.
Classwork/Homework….

Get started on Forces: Worksheet 2.

This is due tomorrow!