Ph sical Quantities and Units

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n Facts to Know

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Q: State what is meant by scalar and vector quantities and give common examples of each.

. A scalar is a quantity having magnitude only. E.g.: length, distance, volume, density, mass, time,

speed.

. A vector is a quantity having both magnitude and direction. E.g.: weight, displacement, force,

velocity, acceleration.

Problems to SolveFigure I shows the reading of a pair of vernier calipers when its jaws are totally closed. Figure 2 shows

the reading of the same pair of vernier calipers when it measures the outer diameter of a steel pipe.

0cm lcm

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Figure I

a. What is the zero error of the vernier calipers?

10 cm 11 cm

00 5

Figure 2

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( 2 marks )

b. What is the outer diameter of the steel pipe? ( 2 marks )

c. Given that the pipe is 2.00 cm thick, what is the inner diameter of the steel pipe? ( 1 mark )

10.04 cm

2.00 cm

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2. Figure 1 shows the reading of a micrometer screw gauge when the spindle is totally closed. Figure 2shows the reading of the same micrometer screw gauge when it measures the diameter of a wire.

l0

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45

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Figure I

a. What is the zero error of the micrometer screw gauge?

Figure 2

( 2 marks )

b. What is the diameter of the wire? ( 2 marks )

c. Given that the wire is 2.0 cm long, calculate the volume of the diameter. ( 2 marks )

3. A steel rod is shown below.

a. What is the suitable equipment to measure the diameter of the rod to an accuracy of 0.01 cm?( l mark)

b. Describe a way to measure the diameter of the rod as accurately as possible using the equipmentmentioned in (a). ( 2 marks )

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c. The diagram below shows the reading of the vernier calipers when it measures the diameter of the

cylinder.

l0 cm 1l cm

0 5 l0

What is the diameter of the cylinder? ( 2 marks )

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4. A cuboid has dimensions 1.0 cm x 4.5 mm x 10.20 mm.

a. What is/are used to measure the cuboid? Explain your answer. ( 4 marks )

b. What is the volume of the cuboid in cm3? Give your answer to the correct number of signilicant

figures. (3marks)

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5. A type of microorganism has a length of 20 trrm.

a. What is the minimum number of such microorganism to fill up a 2.0 cm gap? ( 2 marks )

b. Given that every I m3 of water contains 2 x l0l0 of such microorganisms, how many of suchorganism can be found in I mm3 of water? ( 3 marks )

6. Steel wire meshes are used to reinforce concrete. A typical 4,6 type wire mesh of dimensions6.0 m x 2.4 mis shown below.

'A' means that the square gap is 20 cm x 20 cm and '6' means that the diameter of the wire is 6 mm

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2.4m I

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20 cm'.

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l0cm X

l0 cm 20 cm 20 cm

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a. Given that the density of such steel is 7500 kg/m3, calculate the mass of the A6 type wireshown on the previous page. (Thke x = 3.14) ( 5 marks )

b. Given that a piece of the 46 mesh of dimensions 2.4 m x 6.0 m costs $27, what is the cost ofA12 wire mesh of dimensions 2.4 m x 6.0 m assuming that the price of mesh is solely based on

the amount of material used? ( 3 marks )

Dickson wants to set up a sea water aquarium of dimensions2feetwide,2 feet high and 5 feet long. Itis stated that 1.4 pounds of sea salt is needed for every 5 gallons of fresh water.

Conversion table

I feet = 30.5 cml pound =0.454k9I gallon = 3.75 litres1 litre = 1000 cm31 USD (US dollar) = 1.5 SGD (Singapore dollar)

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a. Calculate the mass of sea salt (in kg) he needs to buy if he wants the tank to be 50 cm deep.( 5 marks )

b. A manufacturer of another brand of sea salt claims that their sea salt is more concentrated. Only1.0 pound of their sea salt is needed for 4 gallons of fresh water. Given that the new sea salt costsUSD2.00 per kg, calculate the amount of SGD needed to pay for the sea salt to make the samevolume of sea water as in part (a). ( 5 marks )

8. Kinston attempts to calculate the gravitational acceleration using the formula

r =zn lJ-Iswhere 7 is the period of oscillation, L is the length of the pendulum and g is the Earth's gravitationalacceleration.

At home, he sets a 1 m long pendulum into small amplitude oscillation and measures 40.0 seconds for20 complete oscillations.

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a. What is meant by period of oscillation? (lmark)

b. What is the period of the oscillation of the pendulum? (1mark)

c. Calculate the gravitational acceleration of that location. (1mark)

d. Ali did the same experiment in his hometown and obtained 41.0 s for 20 oscillations. Explain thedifference in time taken for 20 oscillations. ( 2 marks )

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9. The distance from the Earth to the Sun is 150 x 106 km and the distance from Jupiter to the Sun is

778 x 106 km. Assuming that Sun, Earth and Jupiter are in a straight line,

a. what is the nearest possible distance between the Earth and Jupiter? ( 2 marks )

b. what is the furthest possible distance between the Earth and Jupiter? ( 2 marks )

c. what is the time taken for a spacecraft in (b) to travel from the Earth to Jupiter at a speed of17 500 miles per hour? (1 mile = 1.61 km) ( 2 marks )

d. how many light years away is the Earth from Jupiter in (b)? (One light year is the distance travelledby light in one year. The speed of light in vacuum is 3 x 108 m/s.) ( 2 marks )

10. An ant is walking at a speed of 4 cm/s across a conveyer belt which is traveling at a speed of 3 cm/s as

shown below.

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4 cm/s i

3 cm,/s------>

x

a. What is the magnitude of the resultant speed of the ant? ( 2 marks )

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b. How far is the ant away from its original position when it reaches the other end of theconveyer belt? ( 3 marks )

I l. A small cube with side 2 cm and a big cube with side 6 cm are shown below

a. What is the minimum number of small cubes that can be placed on top of the big cube to completelycover the top of the big cube? ( 2 marks )

b. How many small cubes are required to make up the volume of the big cube? ( 2 marks )

c. The two cubes are melted together and made into a bigger cube. What is the length of each side of thebigger cube? ( 2 marks )

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d. 1 cm3 of paint can paint 8 cm2 of the cube's surface. How thick is the paint when applied onthe cube? (Give your answer in mm.) ( 2 marks )

e. How much paint is required to paint the bigger cube completely? ( 2 marks )

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12. It is very common to see water droplets dripping from taps, cistems, pipes and various types ofcontainers in the households. Assume that every household has a dripping tap and water drips at a rateof two drops per second. From the information given in the table below,

Length of Olympic-size swimming pool 50m

Breadth of Olympic-size swimming pool 25m

Depth of Olympic-size swimming pool 2m

Volume of each drop of water 5 x 10-2cm3

Number of households in Singapore 950 000

Number of taps in Singapore 10 000 000

Population in Singapore 4 550 000

Density of water 1.0 g/cm3

Cost of water per cubic metre $1.s0

a. calculate how many days it takes for water from dripping taps to fill up a volume equivalent toan Olympic-size swimming pool. ( 4 marks )

b. calculate the cost of water wastage due to dripping taps in one full day. ( 2 marks )

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Misconceptions to Clarifr

The diagram below shows part of the scale ona pair of vernier calipers.

2. The diagram below shows part of the scale ona micrometer screw gauge when its spindle istotally closed.

Which of the following is the correct readingfor the zero error shown?

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A -0.03 mmB -0.47 mmC 0.03 mmD 0.47 mm ()

4cm 5cm

J The diagram below shows part of the scaleon a pair of vernier calipers when its jaws areclosed.

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Which of the following is the correct readingfor the zero error shown?

A -0.06 cmB -0.04 cmC 0.04 cmD 0.06 cm

A pendulum released from point X achievesan instantaneous stop at point Y. Given thatthe time for the bob to move from point X topoint Y is 0.4 s, calculate the time taken forthe same pendulum to make 10 oscillations.

x Y

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A 0.4sB 2.0sC 4.0sD 8.0s ()

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Which of the following is the correct reading?

A 3.85 cmB 3.95 cmC 4.30 cmD 4.50cm ( )

()

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