You thought you were done with Pythagoras,
didn’t you?
 What
is the difference between
mass and weight?

What is a vector?


Example of a vector

A quantity that has
both magnitude (a
size) and direction
Velocity! Velocity is
speed (which has a
size) with a
direction (+ or -)

Other examples of
vectors



Is mass a vector?

Force – force can be
applied in a direction
Acceleration – we can
have + or –
acceleration
No! Mass only has a
size, not a direction
so it is scalar (only
has magnitude).

Is weight a vector?

Yes! Weight is a
specific force, so it
is also a vector.

Two people are
pushing on a desk.
One applies a force
of 30N and another
applies a force of
40. What is the
total force on the
desk.

Since the force is in
the same direction,
you simply add the
forces together.
◦ 30N+40N = 70N

Suppose the same
two people are now
on opposite sides
of the desk. One
pushes right with a
force of 30N and
the other pushes
left with a force of
40 N. What is the
total force on the
desk?

Since they are in
opposite directions,
one of the forces is
negative. Let left
be the negative
direction.
◦ 30N+(-40N) = -10N

Suppose Kevin kicks
the soccer ball
towards the goal with
a force of 30N and the
defender on the other
team kicks the ball at
the same time with a
force of 40 N. What is
the total force on the
ball?


How do you find
the resulting force
vector?
What does a vector
diagram of this
look like?

Using the
Pythagorean
theorem.

What is the
Pythagorean
Theorem?
a b  c
2
2
2
a = one of the legs of the
right triangle
b = the other leg of the right
triangle
c = the hypotenuse of the
right triangle

In our example,
what are the parts
of the triangle?
c
b
a

How do we solve
for the resulting
force?
Given: a = 30N, b = 40N
Unknown: c = ?
Tool: a2+b2=c2

How do we solve for Solution:
the resulting force? ◦ (30N)2+(40N)2=c2
◦ 900N2+1600N2=c2
◦ 2500N2=c2
◦ Take the square root of both
sides
◦ 50N = c
This means that the soccer
ball moved with a force of
50N in an angled direction.

What is the
resulting force from
player A and B?

Let North be + and
South be –
◦ -70N+40N = -30N
◦ This means the
resulting force is 30N
in the South
direction.

What is the
resultant force of
all three players?

We know in the up
down direction, we
have a force of 30N
in the South
Direction. This
makes our actual
diagram look like
30 N
South

What is the resultant
force of all three
players?
30 N
40 N West
South

Resulting
Force = ?
Given:
◦ 30 N South
◦ 40 N West

Unknown:
◦ Resulting Force

Tool: a2+b2=c2

What is the resultant
force of all three
players?
30 N
40 N West
South

Solution:
Resulting
Force = ?
◦ (30N)2+(40N)2=c2
◦ 900N2+1600N2=c2
◦ 2500N2=c2
◦ 50N = c
The resulting force is 50
N in the South-west
direction
Vector Addition Worksheet