1.1 Physical Quantities and Measurement Techniques CoreExtended
Covers: measuring length, volume and time; finding an average value for a small distance or short time by measuring multiples; scalars and vectors; and the resultant of two perpendicular vectors. Every question below is tagged Core or Extended. Work through the tiers in order — Basic, Intermediate, Difficult — then the Practical section, then attempt the Mastery Test as a timed check before looking at the solutions.
Basic (Recall)
Name the piece of apparatus most commonly used to measure the volume of a liquid.
State why the period of a pendulum is usually found by timing many oscillations rather than a single one.
Define a scalar quantity.
Define a vector quantity.
State two examples of a vector quantity, other than force.
Intermediate (Direct Application)
A student measures a pencil with a ruler. The left end aligns with the 2.3 cm mark and the right end aligns with the 15.8 cm mark. Calculate the length of the pencil.
A stack of 60 identical sheets of cardboard is 45 mm thick. Calculate the thickness of one sheet.
Classify each of the following as a scalar or a vector: energy, velocity, temperature, momentum, mass, gravitational field strength.
A student records the time for 25 oscillations of a pendulum as 40.0 s. Calculate the period of one oscillation.
Explain why a length measurement should be read to the nearest half of the smallest division on the scale, using a millimetre-graduated ruler as your example.
Difficult (Multi-Step / Unfamiliar Context)
Two forces act on a point object: 9 N acting due east and 12 N acting due north. Calculate the magnitude and direction of the resultant force.
A student wants to determine the diameter of a ball bearing more precisely than a millimetre ruler alone would allow. Describe how the “measuring multiples” technique could be adapted for this purpose.
An aircraft flies due north at 150 km/h through air that is itself moving due east at 30 km/h (a crosswind). Calculate the aircraft’s resultant speed and direction relative to the ground.
Explain why two forces of equal magnitude, acting at right angles to each other, produce a resultant force that is less than the arithmetic sum of the two magnitudes.
A student times 20 oscillations of a pendulum on three separate attempts, obtaining 36.4 s, 36.0 s, and 36.2 s. Calculate the best estimate for the period of the pendulum, and explain your method.
Practical / Experimental Design
Describe an experiment to determine the average diameter of a marble, using a ruler and a number of identical marbles placed in a row. Identify one source of error in this method and suggest an improvement.
Describe an experiment to determine the period of a simple pendulum. In your answer, identify the independent variable, the dependent variable, and one variable that should be controlled, and explain why timing multiple oscillations improves the accuracy of the result.
Mastery Test
- A ruler measurement gives a start reading of 1.5 cm and an end reading of 18.7 cm. Find the length of the object. Core
- A pile of 40 identical washers has a total mass of 62 g. Find the mass of one washer. Core
- State whether each of the following is a scalar or a vector: distance, weight, speed, acceleration. Extended
- A student times 15 oscillations of a pendulum as 27.0 s. Find the period. Core
- Two forces act on an object: 5 N north and 12 N east. Find the magnitude of the resultant force. Extended
- Explain why the “measuring multiples” method reduces the effect of reaction-time error on a timing measurement. Core
- A swimmer swims at 1.5 m/s directly across a river that flows at 0.8 m/s at right angles to her direction. Find her resultant speed. Extended
- State one advantage of using a digital timer over a stopwatch operated by hand. Core
- Explain the difference between a scalar and a vector quantity, using speed and velocity as your example. Extended
- A measuring cylinder reads 42 cm³ before an irregular object is lowered into it, and 58 cm³ afterward. Explain why this method was needed rather than measuring the object directly with a ruler, and state the volume of the object. Core
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