Section 4.1 Position, Distance And Displacement

Section 4.1 Position, distance and displacement

• Position and distance • Position and displacement • Time • Scalar and vector quantities © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p. 4)

Position and distance Mechanics

Why? study motions of bodies How? 1. position 2. direction 3. time taken 4. other related physical quantities Go to © Manhattan Press (H.K.) Ltd.

Quiz

Go to

Activity 1

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4.1 Position, distance and displacement (SB p. 4)

Position and distance • position — denotes both the direction & distance from a given reference point • unit of distance: metre (m) / kilometre (km)

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4.1 Position, distance and displacement (SB p. 4)

Position of shopping centre X N

1 km east Tracy 1 km

X

1 km north

Shopping centre X from Chris: direction: north distance: 1 km position of Tracy

Shopping centre X from Tracy: direction: east position 1 of km Chris distance:

Chris

1 km

Y 1 km © Manhattan Press (H.K.) Ltd.

1 km 4

4.1 Position, distance and displacement (SB p. 4)

Position of church Y N

Tracy

X

The position of church Y from Chris:

1 km

direction = south-east distance = 2 km 　　 = 1.41 km

Chris

1 km

Y 1 km © Manhattan Press (H.K.) Ltd.

1 km 5

4.1 Position, distance and displacement (SB p. 4)

Position of church Y N

Tracy X

The position of church Y from Tracy:

1 km

direction = south-east distance = 8 km 　　 = 2.83 km

Chris

1 km

Y 1 km © Manhattan Press (H.K.) Ltd.

1 km 6

4.1 Position, distance and displacement (SB p. 4)

The reference point Different reference point

Position changes destination

200 m

starting point

200 m

• Distance from destination = 200 m • Distance from starting point (complete 1 loop) = 400 m © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p. 5)

Position and displacement • Distance alone is not enough

5m

5m

Distance = 5 m, represents A or B? © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p. 5)

Position and displacement

How can we solve it Displacement • represents change in position • a physical quantity which has both magnitude & direction

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4.1 Position, distance and displacement (SB p. 5)

Position and displacement Displacement of A and B from O: Magnitude =5m direction

Direction:

negative (–)

• Left (−) • Right(+) © Manhattan Press (H.K.) Ltd.

5m

−5 m

direction positive (+) 5m

+5 m 10

4.1 Position, distance and displacement (SB p. 5)

Position and displacement magnitude of displacement = shortest distance between starting point & end point • independent of the travelled path

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4.1 Position, distance and displacement (SB p. 5)

Position and displacement

distance displacement distance

Thinking 1

displacement

length length depend on the travelled path © Manhattan Press (H.K.) Ltd.

independent of the travelled path 12

4.1 Position, distance and displacement (SB p. 6)

Example 1: Chris and Edmond start from S and reach P and Q respectively. Their paths are in the shape of two semicircular arcs as shown in the figure. Find the distance and displacement. Take the direction to the right as positive and π to be 3.14. Solut ion

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4.1 Position, distance and displacement (SB p. 6)

Example 1: (Cont) Distance travelled by Chris = Distance travelled by Edmond

2πr 6 = = πr = 3.14 ×   = 9.42 m 2 2 Displacement of Edmond from S is +6 m, while displacement of Chris from S is −6 m.

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4.1 Position, distance and displacement (SB p. 6)

Class Practice 1: Jessis starts from A and walks around a square loop as shown below. She returns to A finally.

Ans wer

4 ×10 = 40 m Total distance travelled = _____________________ 0m Total displacement = ________________________

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4.1 Position, distance and displacement (SB p. 7)

Time Measure the duration of an event Unit: second (s), minute (min), hour (h) a sundial

a stopwatch an atomic clock

Thinking 2 © Manhattan Press (H.K.) Ltd.

a quartz clock

a watch 16

4.1 Position, distance and displacement (SB p. 7)

Scalar and vector quantities scalar quantity

vector quantity

magnitude only

magnitude & direction

time, distance & temperature

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displacement

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To section 4.2

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4.1 Position, distance and displacement (SB p.2)

Quiz

1. Displacement represents the change in position of an object. It is a quantity Ans with wer B. both magnitude and direction. © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p.2)

Quiz (Cont)

2. Are the displacement and distance for the coin the same for the whole journey? B. No © Manhattan Press (H.K.) Ltd.

Ans wer

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4.1 Position, distance and displacement (SB p.2)

Quiz (Cont)

3. Does the coin move at a uniform acceleration for the whole journey? A. Yes © Manhattan Press (H.K.) Ltd.

Return to

Text

Ans wer 21

4.1 Position, distance and displacement (SB p.3)

Activity 1 Location of school

Let’s start: 1. On the map, locate the position of your school. 2. Choose another point on the map (e.g., a nearby building or a post office).

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4.1 Position, distance and displacement (SB p.3)

Activity 1 (Cont) Location of school

3. With respect to the school, describe the position of the point to your classmate. Ask him to guess where it is. What physical quantities do you need to Ans mention? wer Distance and direction 4. Let your classmate choose a point and it is your turn to guess where it is. Return to

Text © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p. 5)

Thinking 1:

1. State one similarity and one difference between distance and displacement. Similarity: Both quantities have the same unit, metre.

Ans wer

Difference: Displacement includes the direction of a body with respect to a reference point, while distance does not include the direction. © Manhattan Press (H.K.) Ltd.

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4.1 Position, distance and displacement (SB p. 5)

Thinking 1 (Cont):

2.Give an example of motion of a body in each of the following cases (if any). The distance travelled by the body is Ans (a) greater than, wer (b) the same as, and (c) smaller than the magnitude of the displacement. (a) A runner completes the whole loop in a circular running track. Return to (b) A man walks along a straight line. Text (c) The case is impossible.

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4.1 Position, distance and displacement (SB p. 7)

Thinking 2

The sundial was first made by the Egyptians in the year 800 B.C. How does a sundial Ans work? wer

The sun casts a shadow on the face of the sundial and the position of the shadow on a scale gives the time. Return to

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Text

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