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Cambridge IGCSE0625

Physical quantities and measurement techniques

Physics 0625 Chapter Notes

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Physical quantities and measurement techniques
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Physical quantities and measurement techniques notes

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In this chapter

  1. 1Measuring length and volume
  2. 2Measuring time
  3. 3Averages from multiples
  4. 4Scalars and vectors
  5. 5Resultant of two vectors at right angles

1. Measuring length and volume

Use a ruler to find a length. Measure from 0 on the ruler, keep it close and parallel to the object, and view the scale perpendicularly.

Use a measuring cylinder to find a volume. Read from the bottom of the meniscus with your eye level with the water surface. Lowering an object into a part-filled measuring cylinder gives its volume.

Examiner insight

“Few identified parallax errors as the cause of the difficulty.” “Measuring cylinders do not have a resolution of a tenth of the ml making answers of this nature incorrect.”

Worked example 11 mark

Which piece of apparatus is used to measure the length of a copper rod of length approximately 2 cm?

A digital timer · B measuring cylinder · C ruler · D balance

  1. 1

    C, a ruler. [1]

2. Measuring time

Use a stopwatch or digital timer to measure a time interval. Read the whole display, minutes included, and do not round it: 1 minute, 14 seconds and 83 hundredths is 74.83 s.

Examiner insight

“Some candidates did not include the one minute on the display and gave answers of 14.83 s” “Weaker candidates simply copied the digits on the stopwatch to give an answer of 0:00:83 s.”

Worked example 11 mark

A ball rolls down a slope. Which equipment is used to measure the time this takes?

A a thermometer · B a diverging lens · C a protractor · D a stopwatch

  1. 1

    D, a stopwatch. [1]

3. Averages from multiples

Find a small distance or a short time by measuring a multiple and dividing. For the thickness of one disc, measure the height of the stack and divide by the number of discs. For the period of a pendulum, time at least 10 complete oscillations and divide by the number of oscillations.

period = (time for n oscillations)/n

Examiner insight

“Others did not read the question fully and described the motion until the bob stopped swinging (i.e. many oscillations).”

Worked example 14 marks

A student pulls a pendulum bob to the side and releases it. A stopwatch and a vertical marker are available. Describe how the student uses the equipment to determine the time period for the pendulum bob.

  1. 1

    Start the stopwatch when the bob is at a certain point on its swing. [1]

  2. 2

    Use the vertical marker to count the oscillations. [1]

  3. 3

    Time at least 10 swings. [1]

  4. 4

    Divide the time for n complete oscillations by n. [1]

  5. 5

    Any four score. Also credited: stop the timer when the bob returns to its original position, describe one complete oscillation, repeat and take an average.

4. Scalars and vectors

A scalar has magnitude (size) only. A vector has magnitude and direction.

Scalars: distance, speed, time, mass, energy and temperature.

Vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength.

Examiner insight

“Weaker candidates sometimes wrote a contradictory statement following a correct answer, for example, stating that a vector has direction and magnitude, but a scalar only has direction.”

Worked example 13 marks

(i) Complete the sentence. A vector quantity has magnitude (size) and ........ .

(ii) Draw a line under each of the quantities in the list that is a vector quantity.

acceleration · electric field strength · energy · mass · time · weight

  1. 1

    direction [1]

  2. 2

    acceleration, electric field strength and weight. Three correct scores 2, two correct scores 1. [2]

5. Resultant of two vectors at right angles

Two forces, or two velocities, at right angles combine into one resultant. Find it by calculation or graphically.

By calculation, use Pythagoras' theorem for the magnitude.

Graphically, draw a scale diagram. The second vector starts where the first one ends, and the resultant runs from the tail of one vector to the tip of the other.

R = √(a² + b²)

Examiner insight

“Many weaker candidates did not recognise that the direction of the aircraft was at right angles to the direction of the wind, and therefore just subtracted one speed from the other.” “Candidates drawing scale diagrams should be taught that the resultant of two vectors at right angles to each other will be drawn from the tail of one vector to the tip of the other vector.”

Recap

  • Ruler for length, measuring cylinder for volume, stopwatch or digital timer for time.
  • View scales perpendicularly. Read a measuring cylinder from the bottom of the meniscus.
  • Small distance or short time: measure a multiple, then divide.
  • Scalar: magnitude only. Vector: magnitude and direction.
  • Resultant of two vectors at right angles: Pythagoras or a scale diagram.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. A student reads a measuring cylinder with their eye above the level of the water surface. State two things the student must do to read the volume correctly.2 marks
  2. A stopwatch display reads 2:05.40, showing minutes, seconds and hundredths of a second. State the time in seconds.1 mark
  3. A stack of 12 identical coins is 21.6 mm high. Calculate the average thickness of one coin.2 marks
  4. A stopwatch reads 3.20 s when a student starts counting the swings of a pendulum and 31.20 s after 20 complete oscillations. Calculate the period of the pendulum.2 marks
  5. A student times 25 oscillations of a pendulum as 15.0 s and states that the period is 1.67 s. Explain the mistake and give the correct period.2 marks
  6. Describe how to find the average thickness of one sheet of paper using a ruler and a pack of 500 identical sheets.3 marks
  7. From this list, state the three scalar quantities: speed, weight, energy, momentum, temperature, acceleration.2 marks
  8. A car travels around a bend at a steady 20 m / s. State and explain whether its velocity stays the same.2 marks
  9. A force of 6.0 N acts east and a force of 8.0 N acts north on the same object. Calculate the magnitude of the resultant force.2 marks
  10. A boat is steered straight across a river at 4.0 m / s. The current flows at 3.0 m / s parallel to the bank. (a) Calculate the magnitude of the resultant velocity of the boat. (b) A student subtracts the two speeds and gets 1.0 m / s. Explain why this is wrong. (c) Calculate the angle between the resultant velocity and the bank.5 marks

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