Transcript Aim: How can we add two vectors together acting on a point?

Review Components
Do Now:
Draw a vector that is 40 m/s at 40° North of
West
 What is the x component of the velocity and the
y component of the velocity?
 Solve both graphically (with an appropriate
scale) and by using trig
Quick Experiment
► If
two forces act on an object, how can the
forces be arranged to get the maximum
force? The minimum force? A force in
between the maximum and the minimum?
 Work with your partner. Choose an object on
your desk. Each partner applies a force with
your force producer (finger). Figure answer.
Resultant
►A
single vector that represents the same
affect as the addition of 2 or more vectors
► Represented as a dashed line
Two Vectors in the Same Direction
Mathematically
► 0°
angle between them
► Add the magnitudes of the vectors together
► The resultant is the maximum value possible
Aim: How can we add two vectors
together acting on a point?
A girl walks 200 m East and then walks
another 400 m East. Draw a scaled
representation.
Scale:
1 cm = 100 m
Resultant = 600 m
Two Vectors in Opposite Directions
Mathematically
► 180°
angle between the vectors
► Subtract the magnitude of the two vectors
► The direction of the resultant is the same as
the direction of the larger vector
► The resultant is the minimum value possible
A boy runs 50 m West and then runs 20 m
East.
What distance did the boy run?
70 m
What is the boy’s resultant displacement?
Scale:
1 cm = 10 m
Resultant = 30 m
Range of Possible Values
► When
two vectors are added together, the
resultant can be between the maximum
value (when the angle is 0°) and the
minimum value (when the angle is 180°)
► Example: Is 9 N a possible value when the
forces of 30 N and 20 N act concurrently on
an object?
 No: the range of values is 50 N maximum and
10 N minimum. 9 N falls outside of that range.
A 5 N force directed North and a 3 N force
directed East act concurrently (acts on the
same point at the same time)
Draw the two vectors (Hint: start with a set of axes)
Scale:
N
1 cm = 1 N
E
W
S
► Make
N
W
S
a parallelogram
► The resultant is
constructed from the
origin of the two vectors
to the opposite corner
► Measure the magnitude
with the ruler and the
angle with the
protractor
5.7 cm = 5.7 N
59° North of East
Adding Two Vectors at Right Angles
Mathematically
► Magnitude
is obtained through the
Pythagorean Theorem
a2 + b2 = R2
(3 N)2 + (5 N)2 = R2
9 N2+ 25 N2 = R2
34 N2 = R2
R = 5.8 N
N
5N
W
S
3N
► The
angle is obtained through SOHCAHTOA
opp
tan 
adj
N
5N
tan  
3N
5N
θ
W
S
3N
tan   1.67
  59o North of East
Solve the following problems mathematically
and graphically using an appropriate scale
A moterboat can move with a velocity of 4
m/s. What is the resultant velocity if:
 The boat is traveling with a current of 2.5 m/s
south?
 The boat is traveling against a current of 2.5
m/s south?
 The boat is trying to move perpendicularly
(west) across a stream that is flowing south
with a current of 2.5 m/s?