Kinematics – studying how objects move.

What do we know from Nat 5?

In your group write down as many different things as you can to do with movement.Note we are not looking at forces yet.Your group has 5mins.

Scalars and Vectors

With forces direction is important so force is a vector quantity.

Time has no direction so it is a scalar quantity.

Scalar – magnitude (size) only

eg distance, d = 34 km

Vector – magnitude- direction- reference point

eg. Displacement, s = 34 km

south of Edinburgh

Vectors always added nose to tail.

quantity symbol unit symbol Scalar

vector

d metre s

Displacement s metre m v

Speed v Metres per second ms-1 s

Velocity v Metres per second ms-1 v

Acceleration Metres per second per sec

Time

F newtons

Energy J

m kilogram kg

Back of notes jotter

quantity symbol unit symbol Scalar

vector

Distance d metre m s

Displacement s metre m v

Speed v Metres per second ms-1 s

Velocity v Metres per second ms-1 v

Acceleration a Metres per second per sec ms-2 v

Time t second s s

Force F newtons N v

Energy E joules J s

Mass m kilogram kg s

Tutorial Questions Nat 5 Review and Vectors pages 2 and 3

In rough work jotter

Now some more challenging vectors question.

North000°

020° 010°

North East 045°

060°

030°

070°

080°

East 090°

110°

South East 135°

100°

120°

150° 160°

South 180°

170° 190° 200°

South West 225°

West 270°

North West 315°

Directions

Left/right, up/down 30o above horizontal North, south etc

3 figure bearings 315o north west

Example 1 (You might want to copy this example in your notes jotter)

(a) Draw a scale diagram to find the distance travelled and the final displacement of someone following this route.

4 km at 045o

2 km due south

6 km at 60o south of east

N

resultant

Distance = 12 km

Displacement = 7.4 km at 128o

Scale 1cm: 1km

Now do the extra example sheet in rough jotter.

(b) If a boy took 4 hours to complete this course, what was his average speed in km/hour?(c) What was his average velocity in kmh-1?(d) What was his velocity in ms-1?

Distance = 12 kmDisplacement = 7.4 km at 128o

(b) Average speed = d ÷ t = 12 ÷ 4 = 3 kmh-1

( c) average velocity = s ÷ t = 7.4 ÷ 4 = 1.85 kmh-1 At 128o

(d) 1.85 km/h = 1850 m/h = 30.83 m/min = 0.51 ms-1 at 128o

2010 Higher paper Qu 21

A helicopter is flying at a constant height above the ground.

(a) The helicopter flies 20km on a bearing of 180o (due south). It then turns on to a bearing of 140o and travels a further 30km.

The helicopter takes 15 minutes to travel the 50km.

(i) By scale diagram or otherwise find the resultant displacement of the helicopter. (3)

(ii) Calculate the average velocity of the helicopter during the 15 minutes. (3)47km ± 1 at 156o ± 2 or 24o east of south or 66o south of east

V= 52.3 ms-1 at 156o ( or 52.2ms-1 or 188 kmh-1)

Example 2 Find the resultant vector (add vectors nose to tail.)

65 N 140 N(a)

For forces the resultant vector is called the unbalanced force.

(b) The wind blows with a force of 3N to the North. The current is 4N to the East. What is the resultant force?

30o

30o

10 N

10 N

(c)

40 N east

5 N south

a 500 N horizontal

100 N down

b

c 40 N east

20 N at 120o

d 30o

10 N

20 N

Now you try some examples resolving vectors (rough jotter)

Now do Purple book Ex 1.1 Qu 3 to 10

Past paper Questions 2007 Qu 21 2005 Qu 1 Homework number 3

Some more examples resolving vectors (rough jotter)

The plane’s engines are pushing the plane due north with a force of 250 kN. The wind is pushing it west with a force of 30 kN. What is the resultant force on the plane?

3000 N

1000 N

140o

e

f

Find the resultant force on Santa’s sledge.