Transcript 1. scalars and vectors

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
Vector – magnitude
- direction
- reference point
eg distance, d = 34 km
eg. Displacement, s = 34 km
south of Edinburgh
Vectors always added
nose to tail.
Back of notes jotter
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
Metres per
second per sec
Acceleration
Time
F
newtons
Energy
J
m
kilogram
kg
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
In rough work jotter
Tutorial Questions Nat 5 Review and Vectors pages 2 and 3
Now some more challenging vectors question.
Directions
Left/right, up/down
30o above horizontal
North, south etc
3 figure bearings 315o north west
North
000° 010°
020°
030°
North West 315°
North East 045°
060°
070°
080°
East 090°
West 270°
100°
110°
120°
South West 225°
South East 135°
150°
200°
160°
190° South 170°
180°
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.
N
4 km at 045o
Scale 1cm: 1km
2 km due south
6 km at 60o south of east
resultant
Now do the extra
example sheet in
rough jotter.
Distance = 12 km
Displacement = 7.4 km at 128o
Distance = 12 km
Displacement = 7.4 km at 128o
(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?
(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.)
(a)
65 N
140 N
(b)
For forces the resultant vector is
called the unbalanced force.
The wind blows with a force of 3N to
the North. The current is 4N to the
East. What is the resultant force?
(c)
10 N
30o
30o
10 N
Now you try some examples resolving vectors (rough jotter)
500 N
a
b
40 N east
horizontal
5 N south
c
40 N east
20 N at 120o
100 N down
d
10 N
30o
20 N
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?
e
f
3000 N
Find the resultant force on
Santa’s sledge.
140o
1000 N