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PHYSICS 10 VECTORS

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Page 1: Vectors

PHYSICS 10 VECTORS

Page 2: Vectors

SCALARS AND VECTORS

Scalar – a physical property that can be completely described by a single number with a unit. Time, temperature, mass, volume, speed, etc.

Vector – a physical property that has both magnitude (“how big”) and direction. Force, velocity, acceleration, linear momentum etc.

Page 3: Vectors

DISPLACEMENT

Page 4: Vectors

DISPLACEMENT

Fig. 4 DisplacementFig. 5 The displacement depends on P1 and P2

But not on the path taken

Fig. 6 If the particle makes a roundtripThe displacement it zero

A displacement will always be straight line segment directed from the starting point to the ending point

Page 5: Vectors

A

B

BAC B

A

ABC

Page 6: Vectors

PARALLELOGRAM METHOD

A

B

Page 7: Vectors

VECTOR ADDITION

Suppose a particle undergoes a displacement A and followed by a second displacement B. How should the resultant vector look like?

Figs. 7 & 8 Displacement by placing them head to tail Fig. 9 Parallelogram Method

Page 8: Vectors

VECTOR ADDITION

Only when to vectors A and B are parallel does the magnitude of the sum equal to the sum of their magnitudes: C = A + B. Fig.10

When vectors A and B are anti parallel, the magnitude of their sum is equal to the difference of their magnitude. C = | A – B |. Fig 11.

Fig. 10 The sum of two parallel vectors Fig. 11 The sum of two anti-parallel vectors

Page 9: Vectors

VECTOR ADDITION

Example: Find the sum of these three vectors.

Page 10: Vectors

VECTOR ADDITION

Solutions

Page 11: Vectors
Page 12: Vectors

VECTOR MULTIPLICATIONMultiplying vectors by a positive scalar and

negative scalar quantity

Fig. 12 A vector multiplied by a positive scalar quantity

Fig. 12 A vector multiplied by a negative scalar quantity

Page 13: Vectors

PROBLEM

A cross-country skier skis 1.00 km N and 2.00 km E on a horizontal snow field. How far and in what direction is she from the starting point?

Page 14: Vectors

The distance from the starting and ending position is the length of the hypotenuse

22yx AA 22 )00.2(00.1 kmkm

km

km

00.1

00.2tan

Page 15: Vectors

COMPONENTS OF VECTORS

We can represent any vectors lying in the xy-plane as the sum of the vector Parallel to the x-axis and vector parallel to the y-axis

Page 16: Vectors

COMPONENTS OF VECTORS

What are the x- and y-components of vector D. The magnitude of the vector is D=3.00m and the angle α=45.°.What are the x- and y- components of vector E. The magnitude of the vector E =4.50 m and the angle β= 37.0°

Page 17: Vectors

SOLUTION

Page 18: Vectors
Page 19: Vectors

NORTH

SOUTH

EASTWEST

Page 20: Vectors

PROBLEM

Page 21: Vectors
Page 22: Vectors
Page 23: Vectors

SUMMARY

Quantities in physics have direction associated with them and cannot be described by a single number

When a physical quantity is described by a single number, we call it scalar quantity

Vector Quantities have magnitude (how big) and direction in space

When adding vectors, place them head to tail

We can add then by Parallelogram construction

The displacement depends on the starting and ending positions.

Page 24: Vectors

EXERCISE Consider the following vectors:

A = 5.00 m, 45° above +x

B = 6.00 m, towards –y

C = 2.50 m, 15° to the left of +y

D = 3.25 m, 30° to the right of –y

E = 6.00 m, towards +y

F = 2.50 m, 75° below +x

G = 5.00 m, 45° below –x

H = 3.25 m, 60° above –x

Determine the resultant vector.

Page 25: Vectors

LONG SEATWORK OCTOBER 14, 2015

1. Find the x- and y- components of a 25.0m displacement at an angle of 210.0°

2. The five coplanar forces shown in the figure act on the object. Find their resultant. Find the x and y components of each force

3. A plane is travelling eastward at an airspeed of 500km/h. But a 90km/h wind is blowing south ward. What are the direction and speed of the plane relative to the ground?