Physical Quantities & Measurement Techniques (Cambridge International IGCSE Physics): Exam Questions

Extract:

Accept "velocity is speed in a given direction", "velocity has direction" or "velocity is the rate of change of displacement" for the velocity mark; the exact phrase "both magnitude and direction" is not required.

Accept "speed is a scalar and velocity is a vector" as a valid distinction: this earns both marks.

Do not accept "velocity can be positive, negative or zero" alone for the velocity mark.

Extended tier only

Explain the difference between speed and velocity

Extended tier only

Identify the scalar quantities.

Tick all the boxes that apply.

square time

square weight

square acceleration

square distance

Extract:

The scalar quantities from the list are:

• Time; [1 mark]
• Distance; [1 mark]

Extended tier only

State:

(i) one example of a vector quantity.

(ii) one other example of a scalar quantity, apart from time and distance.

Extended Only

Fig. 1.1 shows a vector diagram for the effects of two forces.

Fig. 1.1

Calculate the resultant force.

resultant force = ....................................

Extract:

Time for 50 drops is 20 s. Expected answer 0.4 s (accept 0.40 s). Award both marks for the correct answer alone.

Some students observe drops of water falling from a tap that leaks, as shown in Fig. 1.1.

The students measure the time for 50 drops to fall from the tap. The time for 50 drops to fall is 20 s.

Calculate the average time between two drops falling.

average time = ..................................................... s

Extract:

(i) Expected answer: measuring cylinder. (ii) Gravitational field strength g = 9.8 N/kg. Expected answer 2.058 N, rounded to 2.1 N; accept any answer from 2.0 N to 2.1 N, including 2.1 N obtained with g = 10 N/kg. Award all three marks for the correct answer alone.

The students collect some drops of water.

(i) The students measure the volume of the water they collect.

State the term for the equipment that is suitable for measuring the volume accurately.

(ii) In a similar experiment, another student collects 0.21 kg of water.

Calculate the weight of this water.

weight of water = .................................................... N [3]

Four students P, Q, R and S each attempt to measure the time period (the time for one complete oscillation) of a pendulum. The arrows in Fig. 2.1 show the movements of the pendulum that each student times.

State the student who has chosen the correct movement for one period of a pendulum.

Another student uses a stopwatch to measure the time taken for 50 periods of a pendulum.

Fig. 2.2 shows the time taken on the stopwatch.

Calculate the time for one period of the pendulum. Give your answer to 3 significant figures.

time for one period = ...................................................... s

The student measures the displacement of the pendulum bob from its rest position. The displacement is 16.5 cm, as shown in Fig. 2.3.

State the displacement in millimetres.

displacement = ...................................................... mm

Extract:

Expected: side A = 7.5 cm (accept 7.4 cm to 7.6 cm, 74 mm to 76 mm, or 0.074 m to 0.076 m); side B = 4.0 cm (accept 3.9 cm to 4.1 cm); side C = 2.0 cm (accept 1.9 cm to 2.1 cm). Trailing zeros are required to show precision to the nearest millimetre: do not accept 4 cm or 2 cm. A unit is required for each mark.

A student measures the length of the sides of a metal cuboid using a 30 cm ruler.

State the measured lengths of the following sides to an appropriate level of precision.

Include the appropriate units in your answer.

(i) Side A in Fig. 1.1

length of side A = .................................... [1]

(ii) Side B in Fig 1.2

length of side B = .................................... [1]

(iii) Side C in Fig 1.3

length of side C = .................................... [1]

Extract:

Side lengths from part (a): A = 7.5 cm, B = 4.0 cm, C = 2.0 cm. Expected answer 0.075 times 0.040 times 0.020 = 6.0 × 10^{-5 m³ (accept 0.00006 m³ or 0.000060 m³). Also accept 60 cm³ divided by 10}6. Award the final mark by error carried forward for a volume correctly calculated from the candidate's own accepted side lengths, e.g. 5.6 × 10^-5 m³ from 7.4 / 4.0 / 1.9 cm.

Calculate the volume of the metal cuboid. Give your answer in cubic metres.

volume = .................................... m³

Extract:

Scale reading 164 g. Expected answer 0.164 kg.

The student measures the mass of the metal cuboid on a scale. The measurement is shown in Fig. 1.4.

Fig. 1.4

State the reading for mass. Give your answer in kg.

mass = ................................... kg

Extract:

Table of densities in kg/m³: iron 7870, magnesium 1740, titanium 4510, aluminium 2700. Volume V = 6.0 × 10^-5 m³ (from part (b)); mass m = 0.164 kg (from part (c)). Density = m divided by V = 2733 kg/m³ (accept 2700 or 2730 kg/m³), closest to aluminium. Error carried forward: award the identification mark for the metal whose density is closest to the candidate's own calculated value.

The densities of different metals are listed in the following table:

Use the information in the table to identify the type of metal which the cuboid is made of.

Extended tier only

Identify the unit of velocity.

Tick one box.

square m

square m/s

square m/s²

Extended tier only

Explain how a scalar quantity is different to a vector quantity.

Extract:

Determine the scale of the vector v1:

• v1 is 3 large squares
• v1 = 6 m/s ÷ 3 squares = 2 m/s per square

Determine the velocity of vector v2:

• v2 is 5 large squares
• v2 = 5 × (2 m/s) = 10 m/s

Extended tier only

Fig. 1.1 shows a vector diagram for two component velocities.

Fig. 1.1

Determine the velocity of the vector labelled $v_{2}$.

Extract:

Fig. 1.1 shows a vector diagram for two component velocities.

v1 = 6 m/s v2 = 10 m/s

Extended tier only

Calculate the magnitude of the resultant velocity of the components shown in Fig. 1.1.

Give your answer to 2 significant figures.

Extract:

Expected method: measure the thickness of a large number of sheets (e.g. 100) with the ruler, then divide by the number of sheets. Both steps are needed for two marks.

A stack of paper is used for a design project.

Describe how to determine accurately the thickness of one sheet from this stack, using only a ruler.

Extract:

Expected method: measure length, width and height with the ruler, then multiply the three measurements. Do not credit a water displacement method because the stem specifies a ruler.

A small rectangular block is required for the design project.

Describe how to accurately measure the volume of the block using a ruler.

Extract:

Expected method: record the water volume in the measuring cylinder, fully submerge the object and record the new volume, then subtract to find the volume of the object. Only a measuring cylinder and water may be used.

Describe how to measure the volume of a small, irregularly shaped object using only a measuring cylinder and some water.

A student has a pile of A4 paper for his computer printer.

Fig. 1.1 shows the dimensions of the pile of paper.

The pile contains 500 sheets of paper.

Calculate the average thickness of one sheet of paper.

average thickness = .................................................... cm

Extract:

Height of paper = 5.0 cm Length of paper = 30.0 cm Width of paper = 20.0 cm

Show that the pile of paper has a volume of 3000 cm³. Use the information shown in Fig.1.1.

The student measures the total mass of the paper in the pile.

State the name of a device used to measure mass.

Extract:

Volume of paper = 3000 cm^3 (from part (b))

The mass of the paper in the pile is 2400 g.

Calculate the density of the paper.

density = .............................................. g/cm³

A teacher investigates the reaction time of five students. A 0.50 m ruler is held above the hand of a student before being allowed to fall. The arrangement is shown in Fig. 3.1.

As soon as the ruler falls the student closes their hand, catching the ruler. The further the ruler falls, the greater the reaction time of the student. The results obtained are shown in Fig. 3.2.

Using the results shown in Fig. 3.2, calculate the average distance that the ruler drops.

average distance = ................................................... cm

Extract:

A teacher investigates the reaction time of five students. A 0.50 m ruler is held above the hand of a student before being allowed to fall. The arrangement is shown in Fig. 3.1.

As soon as the ruler falls the student closes their hand, catching the ruler. The further the ruler falls, the greater the reaction time of the student. The results obtained are shown in Fig. 3.2.

Sum of distances = A + B + C + D + E = 9 + 12 + 8 + 16 + 22

List the students in order of their reaction times, with the shortest reaction time at the top of the table. One has been done for you.

Extract:

A teacher investigates the reaction time of five students. A 0.50 m ruler is held above the hand of a student before being allowed to fall. The arrangement is shown in Fig. 3.1.

As soon as the ruler falls the student closes their hand, catching the ruler. The further the ruler falls, the greater the reaction time of the student. The results obtained are shown in Fig. 3.2.

In a similar investigation, a ruler drops a distance of 11.0 cm and has an average speed of 16 cm / s.

Calculate the reaction time.

reaction time = ...................................................... s

Fig. 1.1 shows a large tank containing water. The tank leaks. Drops of water fall from the tank.

The drops hit the ground at a regular rate.

A student measures the time interval between two drops of water hitting the ground.

They use a stopwatch and repeat the procedure three times. Fig. 1.2 shows each stopwatch reading.

(i) On the line below each stopwatch, state the time readings shown, in seconds.

(ii) Calculate the average time interval between two drops of water hitting the ground.

average time = ....................................................... s [2]

Extract:

Distance, s = 12 m (from part (a))

Another student measures the average time taken for a drop of water to fall from the tank to the ground. The time taken is 1.6 s.

Calculate the average speed of this drop of water.

average speed = ................................................... m/s

A student has a piece of metal that has an irregular shape. The weight of the metal is 3.0 N.

Calculate the mass of the metal.

mass = ..................................................... kg

Fig. 2.1 shows the piece of metal, a measuring cylinder and a beaker containing water.

(i) Describe how to determine the volume of the metal, using the equipment in Fig. 2.1.

(ii) Explain why the procedure in (b)(i) is not suitable for finding the volume of a piece of low-density wood that is of similar shape and size to the piece of metal in (a).

(iii) The mass of another piece of metal is 405 g and its volume is 150 cm³.

Calculate the density of the metal. State the unit.

density = .......................................................... [3]

Extended tier only

Two students are discussing mass and weight.

Student 1 claims that a person's weight will be different on Mars than it is on Earth.

State whether you agree with Student 1, and explain your reasoning.

Extended tier only

Identify the vector quantities.

Tick all the boxes that apply.

square displacement

square distance

square speed

square velocity

Extended tier only

Two forces act at right angles to one another: a 35 N force acts to the right and a 42 N force acts downward.

Construct a scale diagram showing the effect of these two forces, and label the resultant force as X.

Use the scale 10 N = 1 cm

Extract:

Two forces act at right angles to one another: a 35 N force acts to the right and a 42 N force acts downward.

Extended tier only

Calculate the magnitude and direction of the resultant force of the forces acting from part (c)

magnitude of resultant force = ....................................

direction of resultant force = .................................... to the horizontal

Fig. 1.1 shows a dripping tap and a measuring cylinder. The water drops all have the same volume. The drops fall from the tap at equal time intervals.

(i) The student collects 200 of the drops in a measuring cylinder. The total volume collected is 60 cm³.

Calculate the average volume of one drop of water.

volume = .................................................. cm³ [3]

(ii) Another student uses a stop-watch to measure the time taken for the tap to produce 200 drops. Fig. 1.2 shows the time reading on the stop-watch.

Determine the time, in seconds, for the tap to produce 200 drops.

time = ...................................................... s [2]

(iii) Determine the average time interval between one drop starting to fall and the next drop starting to fall.

time interval = ...................................................... s [2]

Fig. 1.3 shows the volume of water collected in the measuring cylinder by another student.

Determine the volume of water in the measuring cylinder in Fig. 1.3.

volume = .................................................. cm³

A student uses a stopwatch in a timing experiment.

Fig. 1.1 shows the stopwatch readings.

Calculate the time interval between the two readings.

time interval = ...................................................... s

A device has a light-emitting diode (LED) that flashes briefly at regular intervals.

Describe how to determine accurately the average time for each interval, using a stopwatch.

A student places 8 similar coins in a pile, as shown in Fig. 1.1.

The height of the pile of coins is 2.4 cm.

Calculate the average thickness of one coin.

average thickness = .................................................. cm

Fig. 1.2 shows the pile of coins, a measuring cylinder and a beaker containing some water.

Describe how the student can measure the volume of one of the coins using the set-up shown in Fig. 1.2.

Extended tier only

An object of weight W is suspended by two ropes from a beam, as shown in Fig. 1.1.

Fig. 1.1

The tensions in the ropes are 45.6 N and 81.1 N, as shown.

Using a scale of 1 cm = 10 N, construct a scale drawing to show the resultant force of the two tensions.

Clearly label the resultant force.

Extract:

An object of weight W is suspended by two ropes from a beam, as shown in Fig. 1.1. The tensions in the ropes are 45.6 N and 81.1 N, as shown. Using a scale of 1 cm = 10 N, construct a scale drawing to show the resultant force of the two tensions. 45.6 N force is drawn of length 4.5 - 4.6 cm AND 81.1 N force is drawn of length 8.1 - 8.2 cm; Forces are drawn at a right angle to one another (by eye); Parallelogram is completed; Resultant force is drawn and clearly labelled.

Extended tier only

Using your scale diagram from part (a), determine the magnitude and direction of the resultant force.

magnitude of resultant force = ....................................

direction of resultant force = ....................................

Extract:

magnitude of resultant force = 93.0 N

Extended tier only

State the value of W.

W = ....................................

Extended tier only

State another vector quantity other than a type of force.

Extended tier only

State the definition of a vector quantity.

Extended tier only

A list of vector quantities and their SI units are given in the following table.

Complete the information missing from the table.

Extended tier only

A horizontal force of 136 N to the right, and a vertical downward force of 54 N act on an object perpendicularly to one another.

By use of a scale diagram (not by calculation) determine the magnitude of the resultant force.

magnitude of resultant force = ....................................

Extract:

A horizontal force of 136 N to the right, and a vertical downward force of 54 N act on an object perpendicularly to one another. Magnitude of resultant force = 146 N (from scale diagram in part c).

Extended tier only

Using the information from part (c), determine the direction of the resultant force.

direction of resultant force = .................................... from the horizontal

Extended Tier Only

A bucket of water hangs from a rope attached to a pole as shown in Fig. 1.1.

Fig. 1.1

The tension force, $T$ = 31 N and the ropes are perpendicular to one another.

Calculate the magnitude of the downward force acting on the bucket of water.

magnitude of downward force = ....................................

Extract:

A bucket of water hangs from a rope attached to a pole as shown in Fig. 1.1.

The tension force, T = 31 N and the ropes are perpendicular to one another.

State the name of the downward force acting on the bucket.

Extended tier only

Weight is a vector quantity. Name one other vector quantity.

Extract:

The downward force on bucket = 44 N

The bucket has a mass of 0.65 kg.

Calculate the mass of the water in the bucket.