Vectors

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Vectors

• Mr. Rodichok
• Regents Physics

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Vectors Ch 6
A variable with magnitude direction

• Definition
• Examples
• Graphical Representation
• Scale
• Example

10 m N 10 m/s W
A vector is represented by an arrow showing its
direction.
The length of the arrow will sometimes represent
the magnitude of the vector.
For each 1 cm represents 5 m/s
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Vector addition

• Resultant Vector
• Range of answers for 2 vectors
• Equilibrant vector

When 2 or more vectors are added including the
direction. Similar to finding net force.
Maximum value vectors at 0º (same direction)
Minimum value vectors at 180º (opposite
direction)
A vector that is equal opposite to the resultant
vector. This vector creates equilibrium.
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Vector Addition

• Example 6-1 Find resultant and equilibrant
  vectors

a) A student walks 3 m West and then continues 4
m North. What it the net displacement of the
student?
b.
c.
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Concurrent Forces
Concurrent Forces Example 6-2 A boat is tied to
a dock by two ropes fastened to its bow. One
rope has a tension of 500 N due North and the
second rope has a tension of 200 N due West.
What is the resultant force and equilibrant force
on the boat?
Two or more forces acting on the same object.
Tip to tail method
Parallelogram method
a2 b2 c2
tan ? b/a
500N2 200N2 c2
tan ? 500 N / 200 N
c 539 N
? 68º
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Vector Addition

• Independence of Vectors (extremely important)
• Example 6-3 A boat is traveling 10 m/s East. It
  is on a river with a current of 5 m/s South.
  What is the boats resultant velocity (magnitude
  and direction) if a) drives upstream, b) drives
  downstream, c) crosses the river.

Vectors are separated into x y when solving
equations.
a) 5 m/s North
b) 15 m/s South
c) 11.2 m/s SE
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Newton the apple

• Newtons 2nd Law in relation to gravity
•  
•  
• Direction
•  
•  Example 5-4

Using Newtons 2nd Law with acceleration due to
gravity weight can be calculated.
Since the acceleration is down (negative) the
force will also be down (negative).
Find the weight of a 35 kg mass.
m 35 kg a g -9.81 m/s2 Fg ?
Fg -343 N
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Newton and the apple (continued)

• Example 5-5
•   

Find the weight of a 35 kg mass is 100 N. What
is the acceleration rate due to gravity in that
location? Is it on the earth?
m 35 kg a g ? Fg 100 N
g 2.86 m/s2
No, this is not on the Earth.
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Changing Speed (continued)

• Example Problems for the 2005 Corvette Z51
• 1.  The corvette can start from rest and reach a
  speed of 27 m/s (60 mph) in 4.3 sec.   
• (a) What was the average acceleration of the car?
  
•  
•  
•  
•  (b) What is the average velocity of the car?

13.5 m/s
14 m/s
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Combined Kinematic Equations

• Uniformly Accelerated Motion
• Combined Kinematic Equations
• Depending on the given information different
  combinations of the following formulas will have
  to be used.
• Old Standbys
• If problem has the following four variables d,
  vi, a, and t as the givens and unknown use the
  following formula

d vi t ½ a t2
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Combined Kinematic Equations

• Example The corvette traveling 40 m/s (100 mph)
  applies its brakes and decelerates at a rate of 6
  m/s2 for 3 seconds after seeing a speed trap. How
  far did it travel while the brakes were applied?

vi 40 m/s d ? a - 6 m/s2 t 3 s
d vi t ½ a t2
d (40 m/s) (3 s) ½ (- 6 m/s2) (3 s)2
d 93 m
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Combined Kinematic Equations

• If problem has the following four variables d,
  vi, vf, and a as the givens and unknown use the
  following formula
• Example The corvette traveling at 30 m/s (70
  mph) has to quickly stop for a squirrel. The
  driver stops the car with an acceleration of -9
  m/s2. Find the distance covered while stopping
  the car.

vf2 vi2 2 a d
vi 30 m/s d ? a - 9 m/s2 vf 0 m/s
vf2 vi2 2 a d
(0 m/s)2 (30 m/s)2 2 (-9 m/s2) d
d 50 m