Download Class examples for adding non-perpendicular

How do you add vectors that are not linear....
and
not perpendicular....
.......you add the perpendicular vector components ! PHY 621 Example Problems for 2­D Vector Addition: Component Method
A car drives 56.8 km [E 49.3o S] and then 83.9 km [W 16.4o N]. What is the resultant displacement of the car?
List knowns:
Find components:
Find total Δdx and total Δdy:
Find Δdx by recombining the total Δdx and total Δdy:
Givens:
optional diagram
(visual aid)
I prefer to use CCW for angles.
Total displacements in each direction are
used to make a right angled triangle that
you can solve easily with trig.
A plane is flying at a velocity of 180 km/h [W 25.8o N] relative to the air. The wind is blowing 52 km/h [E 33.6o N] relative to the ground. What is the velocity of the plane relative to the ground? List knowns:
Find components:
Find the total Vx and the total Vy :
Find VR by recombining the total Vx and total Vy:
Using the CCW for the angles above means
1) you can always associate cosine with the x
component and sine with the y component, and
2) the calculator will always handle the signs for you.
Oop's....final answer got squished into space above
raw answer.
Note that the sig. figs. retained may vary depending on the method you have used. Due to addition in the pythagorean theorem here, I end up with 2 sig. figs. in the magnitude.
As for the angles, we will just remember to keep one decimal place. More Examples of Mathematical Vector Addition
Using Perpendicular Components
Ex. 1 The wind blows 42 km/h [W 35 S] relative to the ground. The plane flies 152 km/h with a heading of [N 35 W] relative to the air. What is the resultant velocity of the plane relative to the ground?
Ans: Vp/g = VR = 158 km/h [W 39.5 N]
Ex. 2 Three students are pushing simultaneously on a cart. Katelyn pushes with 15 N [E 65 N]. Natalie pushes with 16 N [N 45 W]. And, Ellen is pushing with 11 N [W 15 S ]. All forces were applied horizontally.
What is the resultant force pushing the crate?
Ans: FR = 27 N [W 55 N]
Equilibrium
An object in a state of equilibrium has zero net force acting on it.
According to Newton's second law, the acceleration of the object would be zero.
Static equilibrium
occurs when the object is at rest.
Dynamic equilibrium occurs when an object is in motion (at a constant velocity).
An old term (as used in the previous textbook Merrill Physics: Principles and Problems) that can be useful is equilbrant force, FE.
Equilibrant force is a force that when added to pre­existing forces causes an object to obtain equilibirum.
An object that is not in equilibrium is accelerating. The unbalanced forces that cause the acceleration can be added to get a "resultant" force. Applying a new force that is equal in size but opposite in direction to the original resultant force will make the new net force zero newtons.
FR + FE = Fnet
old net resultant
equilibrant
force
force
FE
N
W
E
S
new
FR
force