Mechanics

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Mechanics

K Warne

http://www.sciencecafe.org.za/





Position?

• Position of an object is always defined ………. to other objects.

• Compass points.

• Absolute bearings. (From …………..) always taken to the ……….

?

…..…..

S

N NE ……o

…….

……. ….

….o

……o……o

……..o

…..

…….o360o/0






Displacement & Distance

A B

Distance = Path traveledHome School

Straight Line distance = displacement

Displacement = distance

Displacement is a VECTOR – it has both MAGNITUDE and DIRECTION






Units of Distance & Displacement

K m Hm Dm m dm cm mm

1 m

0. 1 Dm

0. 0 1 Hm

0. 0 0 1 Km

1000 (103) 100 (102) 10 1/10 (10-1) 1/100 (10-2)1/1000 (10-3)

1 0 dm

1 0 0 cm

1 0 0 0 mm

1m = 0.1 Dm = 0.01Hm = 0.001Km

1m = 10dm = 100cm = 1000mm






Units of Distance & DisplacementConvert the following to m.

1. 5 cm

2. 20 mm

3. 40 km

4. 2 dm

5. 10 Hm

6. 0.1 cm

7. 0.11 dm

8. 0.506 Dm

9. Length of your foot (m)

10. Your height (Km)

11. Lab dimensions (mm)






Speed & Velocity

*

A

*

B

Average Speed = ….….

Average Velocity = ………….…………..

V = =

Path traveled

V = =

Position (distance & displacement) is changing by the _________________ every second.

|

Uniform velocity

s

….….

….….

….….

….….






Units of VelocityConvert between different units of speed and

velocity, e.g. m.s-1, km.h-1.

60 m.s-1 0.06Km.s-1 0.06x60x60 = 216 Km/h

10 m.s-1 = 36 Km/h






Example:

An athlete runs one lap of a 400m track A-A in 60s at constant (uniform) speed.

Find:-

1. distance A-B

2. displacement A-B

3. average speed A-B

4. average velocity A-B

5. Average velocity A-A

A

B






Example:

An athlete runs one lap A-A in 60s at constant (uniform) speed.

1. distance A-B = 200m

2. displacement A-B

Circum circle = 2r .: 200 = d .: d = 200/= 63.66 m

S(A-B) = (63.66)2 + (100)2 = 14 052.85 m = 118.5 m towards B

3. average speed A-B

v = s/t = 200/30 = 6.67 m.s-1

4. average velocity A-B

v = s/t = 118.5/30 = 3.95 m.s-1 towards B

5. Average velocity A-A

v = s/t = 0/60 = 0

A

B






.. . . . . . . . . . . . .0m/s 120Km/h

Changing Velocity - Acceleration

0 km/h

120 km/h

Average = 60 km/h

X = (vi + Vf)*t /2 = (0 + 120)*10/2 = 600 km






.. . . . . . . . . . . . .0m/s 2m/s 4m/s 6m/s 8m/s0 1s 2s 3s 4s


The AVERAGE VELOCITY at any point is HALF the INSTANTANEOUS VELOCITY. (Dotted lines - - - - >)

TIME t (s) 0 1 2 3 4 5 6 FInal Total Time

INSTANTANEOUS VELOCITY

Inst v (m/s) 0 2 4 6 8 10 12 12 INSTANTANEOU

S VELOCITY

AVERAGE VELOCITY /s

av v (m/s) 0 1 2 3 4 5 6 6 Average Velocity

DISPLACEMENT s (m) 0 1 4 9 16 25 36 36 Total displacement

EQUIVALENT UNIFORM VELOCITY

Unfm v 0 6 6 6 6 6 6 6 Average Velocity

Rate of change in velocity = 2m.s-1 per second = acceleration!

The AVERAGE VELOCITY over an interval is EQUAL to the INSTANTANEOUS VELOCITY at the midpoint (time) of the interval.







The AVERAGE VELOCITY at any point is HALF the INSTANTANEOUS VELOCITY.

The AVERAGE VELOCITY over an interval is EQUAL to the INSTANTANEOUS VELOCITY at the midpoint of the interval.

Av & Inst Velocity

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7

Time (s)

Velo

co

ty (

m/s

)

INSTANTANEOUS VELOCITY

AVERAGE VELOCITY

Instantaneous Velocity

Average Velocity

14

12

10

8

6

4

2

0





AccelerationAcceleration

• Velocity ……………… – you travel ……………… every second.

• Acceleration is the ……… of ……………. of velocity.

•

• In SI units, acceleration is measured in ………………….(………).

Positive acceleration

A > 0

Velocity increasing

| V1 = 1m.s-1

V2 = 4m.s-1

a =

2s

DecelerationDeceleration

• Velocity ………………. – you travel ……………….. distance every second.

• Acceleration is the rate of change of velocity.

……………. acceleration

a 0

Velocity …………….

|

a =4m.s-1

0m.s-1

2s


For. Acceleration = rate of change of velocityTime (s)

Disp. (m)

A 0 0

B 1 5m

C 2 20m

D 3 45m

E 4 80m

Time (s)

Displacement (m)

Average Velocity

Instantaneous Velocity (m.s-

1)

Acceleration (m.s-2)

0 0 0 0 10

5 5 10 10

20 10 20 10

45 15 30 10

4 80 20 40 10

5 125 25 50 10

6 180 30 60 10

1

2

3

Uniform acceleration

a = = = = 10m.s-2V v2 – v1 60 - 0

t t2 - t1 6


Hi -

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Keith Warne

Mechanics

Education

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