Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by...
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Transcript of Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by...
![Page 1: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/1.jpg)
Vectors
Pearland ISD Physics
![Page 2: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/2.jpg)
Scalars and Vectors
• A scalar quantity is one that can be described by a single number:– Examples:
• temperature, speed, mass
• A vector quantity deals inherently with both magnitude and direction:– Examples:
• Acceleration, velocity, force, displacement
![Page 3: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/3.jpg)
Identify the following as scalars or vectors – not in your notes
• The acceleration of an airplane as it takes off
• The number of passengers and crew on the airplane
• The duration of the flight• The displacement of the flight• The amount of fuel required for the
flight scalar
vector
scalarscalar
vector
![Page 4: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/4.jpg)
Representing vectors
• Vectors can be represented graphically.– The direction of the arrow is the direction of
the vector. – The length of the arrow tells the magnitude
• Vectors can be moved parallel to themselves and still be the same vector.– Vectors only tell magnitude (amount) and
direction, so a vector can starts anywhere
4 N 8 N
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Adding vectors
• The sum of two vectors is called the resultant.
• To add vectors graphically, draw each vector to scale.
• Place the tail of the second vector at the tip of the first vector. (tip-to-tail method)
• Vectors can be added in any order.• To subtract a vector, add its opposite.
![Page 6: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/6.jpg)
Vector Addition and Subtraction
• Often it is necessary to add one vector to another.
![Page 7: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/7.jpg)
Vector Addition and Subtraction
5 m 3 m
8 m
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Adding Vector Problem
A parachutist jumps from a plane. He has not pulled is parachute yet. His weight or force is 800 N downward. The wind is applying a small drag force of 50 N upward. What is the vector sum of the forces acting on him?
750 N downward
![Page 9: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/9.jpg)
Adding perpendicular vectors
• Perpendicular vectors can be easily added and we use the Pythagorean theorem to find the magnitude of the resultant.
• Use the tangent function to find the direction of the resultant.
![Page 10: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/10.jpg)
Vector Addition and Subtraction
![Page 11: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/11.jpg)
1.6 Vector Addition and Subtraction
2.00 m
6.00 m
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Vector Addition and Subtraction
2.00 m
6.00 m
222 m 00.6m 00.2 R
R
m32.6m 00.6m 00.2 22 R
4.180.6
0.2tan 1
![Page 13: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/13.jpg)
Adding perpendicular Vectors – this slide is not in your notes
Note: in this example, In order to use the tip-to-tail Method, Vector B must be moved.
![Page 14: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/14.jpg)
Vector Addition and Subtraction This slide is not in your notes
When a vector is multiplied by -1, the magnitude of the vector remains the same, but the direction of the vector is reversed.
YOU MAY WANT TO MAKE A NOTE OF THIS!!
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Multiplying Vectors
• A vector multiplied or divided by a scalar results in a new vector.– Multiplying by a positive number changes
the magnitude of the vector but not the direction.
– Multiplying by a negative number changes the magnitude and reverses the direction.
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Resolving vectors into components.• Any vector can be resolved, that is,
broken up, into two vectors, one that lies on the x-axis and one on the y-axis.
![Page 17: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/17.jpg)
1.7 The Components of a Vector
. ofcomponent vector theand
component vector thecalled are and
r
yx
y
x
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1.7 The Components of a Vector
.AAA
AA
A
yx
that soy vectoriall together add and
axes, and the toparallel are that and vectors
larperpendicu twoare of components vector The
yxyx
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Calculate the following: Practice!!
• A roller coaster moves 85 meters horizontally, then travels 45 meters at an angle of 30.0° above the horizontal. What is its displacement from its starting point?
• A pilot sets a plane’s controls, thinking the plane will fly at 2.50 X 102 km/hr to the north. If the wind blows at 75 km/hr toward the southeast, what is the plane’s resultant velocity?
![Page 20: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/20.jpg)
RELATIVE VELOCITYSECTION: 4
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Relative Motion
• The motion of an object can be expressed from different points of view
• These points of view are known as “frames of reference”
• Depending on the frame of reference used, the description of the motion of the object may change
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Relative Velocity (motion of objects is independent of each other)
• Velocity of A relative to B: using the ground as a reference frame
• The LanguagevAG : v of A with respect to G (ground) = 40 m/svBG : v of B with respect to G = 30 m/svAB : v of A with respect to B:
BGAGAB vvv
smsmAB /30/40 v
smAB /10v
![Page 23: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/23.jpg)
Example 1
• The white speed boat has a velocity of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both with respect to the ground. What is the relative velocity of the white boat with respect to the yellow boat?
YGWGWY vvv
hkmhkmWY /25/30 v
hkmWY /5v
![Page 24: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/24.jpg)
Example 2- The Bus Ride Lets do this together
A passenger is seated on a bus that is
traveling with a velocity of 5 m/s, North.
If the passenger remains in her seat,
what is her velocity:
a) with respect to the ground?
b) with respect to the bus?
![Page 25: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/25.jpg)
Example 2 –continuedLets do this together
The passenger decides to approach the driver with a velocity of 1 m/s, N, with respect to the bus, while the bus is moving at 5m/s, N.
What is the velocity of the passenger with respect to the ground?
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Resultant Velocity (motion of objects is dependent on each other)
The resultant velocity is the net velocity
of an object with respect to a reference
frame.
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Example 3- Airplane and Wind - relative to the groundAn airplane has a velocity of 40 m/s, N, in still air. It is facing a headwind of 5m/s with respect to the ground.
What is the resultant velocity of the airplane?
WGPGPG vvv
smsmPG /5/40 v
smPG /35v
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Frame of reference
• What is this guy’s velocity?
• What about now?
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Frame of reference
• What about now?
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Relative Velocity:Example 4: Crossing a River
The engine of a boat drives it across a river that is 1800m wide.The velocity of the boat relative to the water is 4.0m/s directed perpendicular to the current. The velocity of the water relativeto the shore is 2.0m/s.
A)What is the velocity of the boat relative to the shore?
B) How long does it take for the boat to cross the river?
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Relative Velocity
• G: • U: • E: (Pythagorean Theorem)
• S:
• S:
2222 sm0.2sm0.4 WSBWBS vvv
WSBWBS vvv
63/0.2
/0.4tan 1
sm
sm
sm /0.4BWv sm /0.2WSv
?BSv
sm5.4
![Page 32: Vectors Pearland ISD Physics. Scalars and Vectors A scalar quantity is one that can be described by a single number: –Examples: temperature, speed, mass.](https://reader034.fdocuments.us/reader034/viewer/2022051316/5697bff21a28abf838cbbf2c/html5/thumbnails/32.jpg)
Relative Velocity
• G: • U:
• E: (Kinematics)
• S:
• S: s 450sm4.0
m 1800t
?t
t
x
v
v
xt