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Newton 3 & Vectors
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Action/Reaction• When you
lean against a wall, you exert a force on the wall.
• The wall simultaneously exerts an equal and opposite force on you.
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You Can OnlyTouch as Hard as You Are Touched
• He can hit the massive bag with considerable force.
• But with the same punch he can exert only a tiny force on the tissue paper in midair.
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Newton’s Cradle
• The impact forces between the blue and yellow balls move the yellow ball and stop the blue ball.
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Naming Action & Reaction
• When action is “A exerts force on B,”
• Reaction is then simply “B exerts force on A.”
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Vectors• A Vector has 2
aspects– Magnitude (r) (size)– Direction (sign or angle)
()Vectors can be represented by arrows
Length represents the magnitude
The angle represents the direction
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Reference Systems
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Vector Quantities
• Displacement• Velocity• Acceleration• Force• Momentum• (3 m, N) or (3 m,
90o)
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Vector Addition Finding the Resultant
Head to Tail Method
Parallelogram Method
Resultant
Resultant
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A Simple Right Angle Example
Your teacher walks 3 squares south and then 3 squares west. What is her displacement from her original position?
This asks a compound question: how far has she walked AND in what direction has she walked?
E
N
W
S
3 squares
3 squares
Resultant
Problem can be solved using the Pythagorean theorem and some knowledge of right triangles.4.2 squares, 225o
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:1 20Scale cm m
(136 ,56 )oA m
(64 ,305 )oW m
A W
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Getting the Answer
Resultant
1. Measure the length of the resultant (the diagonal). (6.4 cm)
2. Convert the length using the scale. (128 m)
3. Measure the direction counter-clockwise from the x-axis. (28o)
(128 ,28 )oA W m
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Boat in River Velocity
, , ,boat shore boat water water shorev v v
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Airplane Velocity Vectors
, , ,plane ground plane air air groundv v v
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Rope Tensions
• Nellie Newton hangs motionless by one hand from a clothesline. If the line is on the verge of breaking, which side is most likely to break?
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Where is Tension Greater?
• (a) Nellie is in equilibrium – weight is balanced by vector sum of tensions
• (b) Dashed vector is vector sum of two tensions • (c) Tension is greater in the right rope, the one
most likely to break
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Vector Components
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Resolving into Components
• A vector can be broken up into 2 perpendicular vectors called components.
• Often these are in the x and y direction.
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Components Diagram 1
E
N
W
S
A = (50 m/s,60o)
Resolve A into x and y components.
1. Draw the coordinate system.2. Select a scale.
3. Draw the vector to scale.
60o
Let 1 cm = 10 m/s
5 cm
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Components Diagram 2
E
N
W
S
A = (50 m/s, 60o) Resolve A into x and y components. 4. Complete the rectangle
a. Draw a line from the head of the vector perpendicular to the x-axis.
b. Draw a line from the head of the vector perpendicular to the y-axis.
5. Draw the components along the axes.
6. Measure components and apply scale.
Let 1 cm = 10 m/s
Ax = 25 m/s
Ay = 43 m/s
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Vector ComponentsVertical Component
Ay= A sin
Horizontal Component
Ax= A cos
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Signs of Components
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(x,y) to (R,)• Sketch the x and y components
in the proper direction emanating from the origin of the coordinate system.
• Use the Pythagorean theorem to compute the magnitude.
• Use the absolute values of the components to compute angle -- the acute angle the resultant makes with the x-axis
• Calculate based on the quadrant
22yx DDD
x
y
D
D1tan
o360