Mass, Weight & Density (Cambridge International IGCSE Physics): Exam Questions

Fig. 1.1 shows laboratory equipment used to find the density of an irregularly shaped solid.

Fig. 1.1

For each piece of equipment add a label stating the name and the quantity measured.

Extract:

The equipment needed to find density is:

• Measuring cylinder (containing water); [1 mark]

• Volume; [1 mark]

• (Digital) balance / scales; [1 mark]

• Mass; [1 mark]

Explain how a student can find the volume of a piece of modelling clay of irregular shape using only the equipment in part (a)

Extract:

Fig. 1.1 shows laboratory equipment used to find the density of an irregularly shaped solid.

The volume of the modelling clay is found to be 64 cm³.

State the volume in m³.

Extract:

The volume of the modelling clay is found to be 64 cm^3. To convert cm^3 to m^3: ... Calculate the answer:

• 64 cm^3 = 64 × 10^-6 m^3
• Volume = 64 × 10^-6 m^3 OR 0.000064 m^3

The mass of the modelling clay is 60 g.

(i) Determine the mass in kg.

(ii) Calculate the density of the modelling clay, stating your answer in terms of S.I. units.

Extract:

Expected answer: density (only one box should be ticked).

Fig. 1.1 shows a set of masses made from the same material.

Fig. 1.1

Identify the quantity that is the same for all the masses.

Tick one box.

square density

square volume

square weight

Extract:

Expected answer: 2500 g.

The largest mass is 2.5 kg.

State the number of grams in 2.5 kg.

2.5 kg = ...................................................... g

Extract:

g = 9.8 N/kg is given in the stem. Combined mass 4.0 kg. Expected value 39.2 (accept 39). Accept 40 only if g = 10 N/kg has been used. The unit N (newtons) earns its own independent mark; a bare number scores the value mark but not the unit mark. Error carried forward from an incorrect combined mass.

The three largest masses are 2.5 kg, 1.0 kg and 0.5 kg.

The gravitational field strength g is 9.8 N/kg.

Calculate the combined weight of these three masses. Include the unit.

weight = .........................................................

Extract:

Question stem:

• Eight logs, average mass of each log 65.0 kg
• The stem gives g = 9.8 N/kg

When marking this answer:

• A correct final answer of 5100 N or 5096 N with no working scores all three marks
• Accept any correct substitution for the second mark, for example 8 × 65.0 × 9.8, 637 × 8 or 520 × 9.8
• Only 5100 N (or 5.1 × 10³ N) or 5096 N earns the final mark; 5090 N is not a correct rounding and does not earn it
• An answer of 5200 N (g = 10 N/kg used) earns the W = mg mark only, never the substitution or final mark
• The weight of one log only (637 N) earns the W = mg mark only

Fig. 2.1 shows a wooden raft. The raft is made from eight logs.

The logs are all of the same type of wood.

The average mass of each log is $65 . 0 \text{kg}$.

The gravitational field strength g is $9 . 8 \text{N/kg}$.

Calculate the total weight of the raft.

total weight of the raft = ....................................................... N

Extract:

Question stem:

• One log: mass 66.0 kg, length 3.0 m, cross-sectional area 0.040 m²

When marking this answer:

• In part (i), a correct final answer of 550 kg/m³ with no working scores all three marks
• In part (i), award the final mark for a density correctly calculated from the candidate's own volume (ecf)

(i) The mass of one of the logs is $66 . 0 \text{kg}$. It is $3 . 0 \text{m}$ long and has a cross-sectional area of $0 . 040 \text{m}^{2}$.

Calculate the density of the wood in the log.

density = ............................................... kg/m³

(ii) Explain why the log in (b)(i) floats on water.

Identify the unit that is used for mass.

Tick one box.

square kg

square N

square m³

A student is asked to write definitions for mass and weight.

For each of their answers insert the missing word, selected from the list below.

force gravity kilogram mass matter newton rest

(i) Mass is a measure of the quantity of .................... in an object at .................. relative to an observer.

(ii) Weight is a gravitational ........................ on an object that has ...........................

A student needs to determine the density of a sample of oil.

They measure 0.001 m³ of oil and find it has a mass of 0.75 kg.

(i) State the equipment the student uses to find the mass of oil.

(ii) Calculate the density of the oil.

Extract:

They measure 0.001 m^3 of oil and find it has a mass of 0.75 kg.

Calculate the density of the oil.

• Mass, m = 0.75 kg
• Volume, V = 0.001 m^3
• Use the equation for density
• ρ = m / V
• ρ = 0.75 / 0.001 = 750 kg/m^3

Extended tier only

The oil in part (c) is poured into a beaker of water.

Assuming that the liquids do not mix, explain which liquid floats.

An astronaut travels from Earth to the Moon.

Gravitational field strength on Earth = 9.8 N/kg

Gravitational field strength on the Moon = 1.6 N/kg

Identify the quantity that is the different for the astronaut on the Moon compared to the Earth.

Tick one box.

square mass

square weight

square density

Extract:

Gravitational field strength on Earth = 9.8 N/kg Gravitational field strength on the Moon = 1.6 N/kg

The mass of the astronaut is 65 kg on Earth.

(i) Calculate the astronaut’s weight on Earth.

(ii) Calculate the astronaut’s weight on the Moon

Extract:

Gravitational field strength on Earth = 9.8 N/kg Gravitational field strength on the Moon = 1.6 N/kg The mass of the astronaut is 65 kg on Earth. Weight on Earth: W = m × g_E = 65 × 9.8 = 640 N Weight on the Moon: W = m × g_M = 65 × 1.6 = 100 N

Complete the following sentence.

The astronaut's weight on Earth is more than their weight on the Moon because, although their ..................... is the same, the .......................... force on Earth is ............................

State the piece of equipment that can be used to compare the mass and weight of the astronaut while they are still on Earth.

A student wishes to determine the density of a regular-shaped solid block, such as a cube.

State the two quantities the student must measure to find the density of the block.

The student then determines the density of an irregularly shaped stone.

To find the volume, the student lowers the stone into a measuring cylinder containing water.

Fig. 1.1 shows the water level in the measuring cylinder before the stone is added.

Fig. 1.1

(i) State the volume of water in the measuring cylinder shown in Fig. 1.1.

(ii) State the name of the curve formed by the water surface in Fig. 1.1.

(iii) The stone is lowered carefully into the water until it is fully covered.

The new volume reading is 46 cm³.

Calculate the volume of the stone.

Extract:

(iii) The stone is lowered carefully into the water until it is fully covered.

The new volume reading is 46 cm³.

Calculate the volume of the stone.

V = Vf - Vi V = 46 - 22 V = 24 cm³

The mass of the stone is 6.5 g.

Calculate the density of the stone.

Fig. 1.1 shows a coil of wire.

A student measures the length of the coil using a ruler. His measurement is 3.8 cm.

There are 20 turns of wire in the coil. The student uses his measurement to calculate the average thickness of the wire.

(i) Show that the average thickness of the wire is about 0.2 cm.

average thickness of wire = .................................................. cm [2]

(ii) The student’s measurement of 3.8 cm is inaccurate. Suggest one reason why the measurement is inaccurate.

The volume of the wire in the coil is 16.6 cm³ and its mass is 148 g.

Calculate the density of the metal used for the wire in the coil.

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

The student has a measuring cylinder and a beaker of water, as shown in Fig. 1.2.

Describe how the student can determine the volume of the coil by using the equipment shown in Fig. 1.2.

A 250 cm³ beaker containing some liquid is shown in Fig. 2.1.

(i) A student has a measuring cylinder and a balance.

Describe an experiment to determine the density of the liquid.

(ii) Suggest the unit of density used by the student.

Fig. 2.2 shows a block of polythene.

(i) Polythene floats in water. Explain why polythene floats.

(ii)

The weight of the polythene block is 0.84 N.

Calculate the mass of the block.

mass = ..................................................... kg [3]

A student has an irregularly shaped piece of metal, a beaker of water and a measuring cylinder, as shown in Fig. 2.1.

Describe how the student can accurately determine the volume of the piece of metal using the equipment provided.

The student measures the mass of the piece of metal. Its mass is 146 g.

(i) State the name of the instrument used to measure the mass.

(ii) The volume of the piece of metal is 20 cm³.

Calculate the density of the metal. State the unit.

density = ...................................................... [4]

Fig. 2.1 shows a raft floating on water.

A force of 20 000 N acts on the raft in the direction of the arrow shown in Fig. 2.1.

(i) State the name given to the force shown in Fig. 2.1.

(ii) Calculate the mass of the raft.

mass = ......................................................kg [3]

A sail is added to the raft, as shown in Fig. 2.2.

Fig. 2.2 shows the horizontal forces acting on the raft at one moment.

Calculate the resultant horizontal force acting on the raft and state the direction of this force.

force = ............................................................ N

direction = ...........................................................

Explain, in terms of their molecules, why the density of water is greater than that of oil.

State the difference between mass and weight.

The mass of a bucket is 1.2 kg.

When the bucket is filled with oil the total mass is found to be 14.1 kg.

Calculate the weight of the oil.

weight of oil =....................................................

Extract:

Mass of oil = total mass - mass of bucket = 14.1 − 1.2 kg = 12.9 kg

The volume of the oil in the bucket is 0.0163 m³.

Calculate the density of the oil.

density = ....................................................

A piece of metal 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 piece of 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 a similar shape and size to the piece of metal.

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

density = ..............................................  g/cm³ [3]

Extract:

(i) The face in contact with the ground is 12.0 cm by 2.0 cm; expected answer 24 cm². (ii) g = 9.8 N/kg; expected answer 8.232 N rounded to 8.2 N; accept 8.23 N; accept 8.4 N if g = 10 N/kg has been used. Award both marks in each sub-part for the correct answer alone.

Fig. 3.1 shows a metal block and its dimensions.

(i) Calculate the area of the metal block in contact with the ground.

area = .................................................. cm² [2]

(ii) The mass of the metal block is 0.84kg.

Calculate the weight of the metal block.

weight = ..................................................... N [2]

Fig. 1.1 shows a plastic water barrel. The barrel is full of water.

The water barrel contains 0.050 m³ of pure water. The density of pure water is 1000 kg/m³.

Calculate the mass of pure water in the barrel.

mass of water = ...................................................... kg

Extract:

The water barrel contains 0.050 m^3 of pure water. The density of pure water is 1000 kg/m^3. Calculate the mass of pure water in the barrel. mass of water = ...................................................... kg

The density of sea water is 1030kg/m³. The density of the plastic is 1000kg/m³. Use this information and the information in (a) to state and explain whether the full barrel will float in sea water.

A student has a metal object.

(i) The student measures the mass of the object.

State the name of the equipment used to measure the mass.

(ii) The mass of the metal object is 1260 g. The volume of the metal is 150 cm³.

Calculate the density of the metal. Include the unit.

density = .............................................. [4]

(iii) The mass of the metal object is given in grams. State the mass in kg.

mass = .................................................... kg [1]

A vase is placed on a table. Forces X and Y act on the vase, as shown in Fig. 1.1. The mass of the vase is 0.25 kg. The vase is not moving.

Calculate the value of force X and the value of force Y.

A group of students are asked to find the volume of their Physics Laboratory.

Fig. 1.1 is a top view of the room and shows the measurements of each wall.

Fig 1.1

The lab has a ceiling which is at constant height, found to be 3.5 m.

(i) State an instrument that would be suitable to make these measurements.

(ii) Describe a method the students could use to reduce errors in their measurements.

(iii) Explain how they should ensure the results are reliable.

Extract:

The lab has a ceiling which is at constant height, found to be 3.5 m.

Divide the shape into rectangles and calculate the two areas: (Area 1) = 38.5 / 38.48 AND (Area 2) = 12.6 Total area = 51.1(2) m^2^ Recall the height of the ceiling is 3.5 m (part (a)) and calculate the volume: Volume = area × height = 51.12 × 3.5 = 178.92 Volume = 179 m^3^

Calculate the volume of air in the room.

Extract:

Volume of air = 179 m^3

The density of the air is 1.2 kg / m³. Calculate the mass of air in the room.

Describe a method the students could use to find the density of air. You do not need to include details of the calculation.

The students have been provided with the following equipment:

Balloon Large measuring cylinder Bucket Water Digital scales

In a car boot sale a student sees what the seller says is a model soldier made from copper. The student buys the model, hoping that it is really made from gold.

At Science Club the student is allowed to investigate their theory.

Describe how the volume of the model could be measured.

You may use a diagram if you wish.

Extract:

In a car boot sale a student sees what the seller says is a model soldier made from copper. The student buys the model, hoping that it is really made from gold.

At Science Club the student is allowed to investigate their theory.

The student used a force meter for the next stage of their investigation.

(i) Describe how the force meter is used to find mass.

(ii) Explain how the student reduces errors in their reading.

Extract:

In a car boot sale a student sees what the seller says is a model soldier made from copper. The student buys the model, hoping that it is really made from gold.

At Science Club the student is allowed to investigate their theory.

The mass of the model is 625 g and the volume is 72 cm³.

The densities of various metals commonly used in model-making are:

By comparison with values in the data table, discuss the student's findings and whether the model is made from either copper or gold.

Extract:

To find the volume of the model:

• Use a measuring cylinder (half-filled) with water AND record the (initial) volume of water; [1 mark]
• Add the model AND record the new volume; [1 mark]
• Subtract the initial volume of water from the final volume; [1 mark]

Another student decides to find the density of a table-tennis ball using the same apparatus.

Discuss a change the student have to make before making their measurements.

Compare the arrangement and motion of the particles in ice and in liquid water.

Extended Tier Only

A lake has a layer of ice on its surface. The area of the lake is 1800 m² . The ice has a thickness of 0.025 m. The density of ice is 920 kg/m³ .

(i) Calculate the mass of ice on the lake.

mass = .......................................................... [2]

(ii) At night, the temperature of the ice on the lake falls by 3.5 °C.

The specific heat capacity of ice is 2.1 $\times$ 10³  J/kg °C.

Calculate the change in energy as the temperature falls.

energy = .......................................................  J [2]