1.3 scalar & vector quantities

1.3 1.3 Understanding Scalar & Understanding Scalar &

Vector QuantitiesVector Quantities

www.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

1.3 1.3 Understanding Scalar & Vector Understanding Scalar & Vector

QuantitiesQuantities

Chapter 1 Chapter 1 Introduction To PhysicsIntroduction To Physics

Learning OutcomesLearning Outcomes

DefineDefine scalar and vector scalar and vector quantitiesquantities

Give examplesGive examples of scalar and of scalar and vector quantitiesvector quantities

Physical QuantitiesPhysical Quantities

MagnitudeMagnitudenono directiondirection

MagnitudeMagnitudedirectiondirection

vector vector ScalarScalar

Displacement, Displacement, velocity, force, velocity, force, Acceleration, Acceleration, Momentum, weight, Momentum, weight, impulse, pressureimpulse, pressure

Length, mass, time Length, mass, time electric current, electric current, temperature, area, temperature, area, distance, speed, distance, speed, energy,density,powerenergy,density,power

Conduct simple activity (pg 10)Conduct simple activity (pg 10)

Physics Lab PlanPhysics Lab Plan

Idea : Idea : distance & displacement ; distance & displacement ; speed & velocityspeed & velocity

Distance = total length of the Distance = total length of the path travelledpath travelled

Displacement = distance Displacement = distance travelled from its initial position travelled from its initial position to its final positionto its final position

Total Total distancdistance, s/me, s/m

Displacement, Displacement, d/md/m

time, time, t/st/s

speed/ speed/ m sm s-1-1

velocity/ velocity/ m sm s-1-1

AA 88 8 from O to A8 from O to A 2.402.40 3.333.33 3.33 3.33 from O from O to Ato A

BB 2222 16 from O to B16 from O to B 5.285.28 4.174.17 3.033.03

CC 3030 14 from O to 14 from O to CC

7.657.65 3.923.92 1.831.83

OO 4444 0 from O to O0 from O to O 10.3210.32 4.264.26 0.000.00

Displacement = Displacement = distance travelled from its initial position to its final position

Total Total distancdistance, s/me, s/m

Displacement, Displacement, d/md/m

time, time, t/st/s

AA 88 ___ from O to ___ from O to AA

7.517.51 1.071.07 1.07 1.07 from O from O to Ato A

BB 2222 ___ from O to ___ from O to BB

15.5115.51 1.421.42 1.031.03

CC 3030 ___ from O to ___ from O to CC

22.0522.05 1.361.36 0.630.63

OO 4444 ___ from O to ___ from O to OO

25.5025.50 1.731.73 0.000.00

Displacement = Displacement = distance travelled from its initial position to its final position

Total Total distancedistance, s/m, s/m

DisplacementDisplacement, d/m, d/m

time, time, t/st/s

AA 9.09.0 9 from O to 9 from O to AA

3.133.13 2.872.87 2.87 2.87 from O from O to Ato A

BB 15.515.5 11.1 from O 11.1 from O to Bto B

5.345.34 2.902.90 2.08 2.08 from O from O to Bto B

CC 24.524.5 6.5 from O to 6.5 from O to CC

8.248.24 2.972.97 0.79 0.79 from O from O to Cto C

OO 31.031.0 0 from O to O0 from O to O 10.6710.67 2.902.90 0.00 0.00 from O from O to Oto Owww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Scalar Scalar QuantitiesQuantities

Vector Vector QuantitiesQuantities

e.g: distance, e.g: distance, speedspeed

Displacement Displacement , velocity, velocity

Has Has magnitude but magnitude but no direction no direction

Has Has magnitude magnitude and direction and direction

Addition Scalar & Addition Scalar & Vector Quantities Vector Quantities

Adding Scalar QuantityAdding Scalar Quantity

Can be added, subtracted, multiplied and divided like ordinary numbers. e.g: (a) 3 kg of sand is added to 1 kg cement, resulting mixture has a mass of 4 kg(b) 5 liters of water are poured from a pail that has 8 liters of water in it.

The resulting volume is 3 litersNo direction is involved!

Scalar QuantitiesScalar Quantities

5 kg5 kg 10 kg 10 kg

Total mass Total mass = 5 + 10= 5 + 10 = 15 kg= 15 kg

Adding Vector QuantityAdding Vector Quantity

An arrow is used to represent the magnitude and direction of a vector quantity.

Same direction = sumOpposite direction = minus

eg. 1eg. 1

50 N50 N 30 N 30 N

Total ForceTotal Force* * = 50 + 30= 50 + 30= 80 N = 80 N (80 N due west//to the left)(80 N due west//to the left)

*=*=resultant forceresultant force////net forcenet forcewww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

50 N50 N 10 N 10 N

Total Force Total Force = 50 - 10= 50 - 10

= 40 N = 40 N

(40 N due west//to the left)(40 N due west//to the left)

eg. 2eg. 2

50 N50 N 50 N 50 N

Total Force Total Force = = 50 - 5050 - 50

= = 0 N 0 N

(object is (object is not movingnot moving////at restat rest////stationarystationary))

eg. 3eg. 3

How much is the resultant How much is the resultant force?force?

Adding Vector QuantityAdding Vector QuantityAn arrow is used to represent the magnitude and direction of a vector quantity.

velocity of airplane = 100 km/h

wind velocity = 20 km/h

(a) If same direction,

Resulting velocity of airplane= 100 + 20 = 120 km/h

(a) If opposite direction,

resulting velocity of airplane = 100 -20 = 80 km/h

Special Case: Special Case: Non-parallel vectorsNon-parallel vectors

Two vectors acting at a point can be replaced Two vectors acting at a point can be replaced by a single vector with the same effect.by a single vector with the same effect.

Case 1Case 1

Case 2Case 2

Two vectors acting at a point can be replaced Two vectors acting at a point can be replaced by a single vector with the same effect.by a single vector with the same effect.

Resultant Vector

Homework Homework

1. Jeremy walked 3 m due east, and then 1. Jeremy walked 3 m due east, and then 4 m due north.4 m due north.

(a) What is his total distance?(a) What is his total distance?

3 m + 4 m = 7 m3 m + 4 m = 7 m

(b) What is his displacement?(b) What is his displacement?

5 m5 m

5 m4 m

2. Every morning Amirul walks to Badrul’s 2. Every morning Amirul walks to Badrul’s house which is situated 80m to the east house which is situated 80m to the east of Amirul’s house. of Amirul’s house.

They then walks towards their school They then walks towards their school which is 60m to the south of Badrul’s which is 60m to the south of Badrul’s house.house.

What is the distance traveled by Amirul What is the distance traveled by Amirul and his displacement from his house?and his displacement from his house?

1.3 scalar & vector quantities

bfrom o

afrom o

distance displacement

total distance

single vector

addition scalar vector

total displacement

opposite direction

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