Transcript Slide 1

There are two different ways to
Represent vectors,
Graphically and
Algebraically
A graphical representation of a
Vector is an arrow of
Specified length and direction.
50
An algebraic representation of a
Vector is a boldface letter with
A number and direction.
Like… d = 50m southwest
Two displacement are equal when
The two distances and direction
Are the same.
A resultant vector is equal to the
Sum of two or more vectors.
R
b
a
Adding the vectors like on the
Board only works if the
Vectors are at right angles.
Or by using the Pythagorean
Theorem…
R2 = A2 + B2
If you are adding vectors that
Are not at right angles,
You have to use the law of
Cosines.
R2 = A2 + B2 - 2ABcosθ
Find the magnitude of the sum
Of a 15km displacement and a
25km displacement when the
Angle between them is 135°.
R = 37 km
A car is driven 125 km due west,
Then 65 km due south. What is the
Magnitude of its displacement.
R = 140 km
Multiplying a vector by a scalar
Number changes its length but
Not its direction unless the scalar
Is negative. Then, the vector’s
Direction is negative.
This fact can be used to subtract
Two vectors using the same
Method for adding them.
ΔV = V2 - V1
ΔV = V2 + (-V1)
An airplane flies due north at
150 km/h with respect to the air.
There is a wind blowing at 75 km/h
To the east relative to the ground.
What is the plane’s speed with
Respect to the ground.
170 km/h
By using the trig functions,
You can figure out the components
Of any vector.
We will be dealing with the
Trigonometric functions a lot!!
side oppositeθ
a
sin θ =
=
hypotenuse
c
side adjacent to
b
cos θ =
=
hypotenuse
c
side
opposite
θ
a
tan θ =
=
side adjacent to θ
b
By adjusting the trig functions
We can find the parts of any
Vector.
A
Ay
Ax
Ax = A cos θ
Ay = A sin θ
A bus travels 23.0 km on a
Straight road that is 30° north of
East. What are the east and
North components of its
Displacement.
Ax = 19.9km
Ay = 11.5 km
2
R
= Rx +
2
Tan θ =
2
Ry
Rx2
Ry2
A person attempts to measure the height
Of a building by walking out a distance of
46.0 m from its base and shined a laser
Toward the top. They found that the laser
Was at an angle of 39.0°. How tall
Is the building?
37.3m
There are two types of friction:
Static and Kinetic.
Static friction is the force exerted
On a motionless body by its
Environment to resist
An external force.
Kinetic friction is the force
Exerted on a moving object.
Friction depends on the surfaces
In contact.
This is why we classify them
With the coefficient of friction.
The coefficient of friction is the
Ratio of the force of friction
To the normal force acting
Between two objects.
Fs
µs =
Fn
Fk
µK =
Fn
You push a 25 kg wooden box
Across a wooden floor at a
Constant speed of 1 m/s. How
Mush force do you exert on
The box?
49 N to the right
An object is in equilibrium when
The net force on it is zero.
An equilibrant is a force, that when
Added to others, makes the
Net force of an object zero.
A trunk weighing 562 N is resting
On a plane inclined at 30 above
The horizontal. Find the
Components of the weight force
Parallel and perpendicular
The plane.
FgX = 281N
FgY = 487N
A 62 kg person on skis is going
Down a slope at 37°. The coefficient
Of kinetic friction is 0.15. How fast
Is the skier going 5 s after
Starting from rest?
24 m/s