Mass Weight And Density

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课程笔记

Mass & Weight

Mass is the quantity of matter in an object; it resists changes in motion (inertia).
Mass is a scalar quantity measured in kilograms (kg).
Weight is the gravitational force on an object; it is a vector measured in newtons (N).
Weight depends on the gravitational field strength (g): W = m × g.
On Earth, g ≈ 9.8 N/kg; on the Moon, g ≈ 1.6 N/kg – weight changes but mass stays the same.

Mass and Weight on Earth and the Moon

Gravitational Field Strength

Gravitational field strength (g) is the force per unit mass: g = W / m.
It is measured in N/kg and is equivalent to the acceleration of free fall (9.8 m/s² on Earth).
The weight of an object is given by W = m × g.

Gravitational Field Strength

Density

Density (ρ) is the mass per unit volume: ρ = m / V.
Units: kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³).
Low-density materials (e.g., gases) have particles spread out; high-density materials (e.g., solids) have particles closely packed.
Volume of regular solids: cube = l³, cuboid = l × w × h, cylinder = πr²h, sphere = (4/3)πr³.

Volume Formulas for Common Shapes

Measuring Density of Regular Solids

Measure mass using a digital balance.
Measure dimensions with a ruler, Vernier calipers, or micrometer.
Calculate volume from dimensions, then density = mass / volume.
Repeat measurements and take averages to reduce random error.

Equipment for Measuring Regular Solids

Measuring Density of Irregular Solids

Measure mass using a digital balance.
Use a displacement can (Eureka can) filled with water just below the spout.
Submerge the object; collect displaced water in a measuring cylinder.
Volume of displaced water = volume of object; then calculate density.

Eureka Can Setup

Measuring Density of Liquids

Measure mass of empty measuring cylinder, then add known volume of liquid.
Mass of liquid = (mass of cylinder + liquid) – mass of empty cylinder.
Density = mass of liquid / volume of liquid.
Zero the balance before each measurement to avoid systematic error.

Measuring the Density of a Liquid

Floating & Sinking

An object floats if its density is less than the fluid's density; sinks if greater.
Upthrust is an upward force on a submerged object, opposite to weight.
Floating occurs when upthrust = weight; sinking when upthrust < weight.
Upthrust depends on fluid density and volume of fluid displaced.

Upthrust and Weight on a Boat

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练习题

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1.Which of the following is a measure of the quantity of matter in an object?
Easy
- AWeight
- BMass
- CDensity
- DVolume
2.What is the unit of weight?
Easy
- Akilogram
- Bnewton
- Ckg/m³
- Dm/s²
3.Mass is a vector quantity.
Easy
True or false?
4.State the equation that links weight, mass and gravitational field strength.
Easy
5.An object has a mass of 4.5 kg. What is its mass in grams?
Easy
- A4950
- B5400
- C4050
- D4500
6.A paving slab has a mass of 73 kg and dimensions 0.04 m × 0.5 m × 0.85 m. Calculate its density in kg/m³ (round to two significant figures).
Hard
- A4730
- B4300
- C5160
- D3870
7.Which of the following correctly describes the relationship between density and floating?
Easy
- AAn object floats if its density is greater than the density of the fluid.
- BAn object floats if its density is less than the density of the fluid.
- CAn object floats if its density equals the density of the fluid.
- DAn object always floats regardless of density.
8.Name the force that pushes upwards on an object submerged in a fluid.
Easy

更多题目

9.Isabelle has a mass of 42 kg. Calculate her weight on the Moon where gravitational field strength is 1.6 N/kg.
Easy
- A73.9
- B67.2
- C60.5
- D80.6
10.Complete the sentence: The density of a substance is defined as its ___ per unit ___.
Easy
The density of a substance is defined as its ____ per unit ____.
11.A student measures the mass of an irregular object as 50 g. When placed in a eureka can, it displaces 20 cm³ of water. What is the density of the object in g/cm³?
Medium
- A0.4
- B2.5
- C30
- D1000
12.An object will sink in a fluid if its density is less than the density of the fluid.
Easy
True or false?
13.Which of the following is the correct definition of mass?
Easy
- AA measure of the quantity of matter in an object
- BThe gravitational force acting on an object
- CThe force per unit mass acting on an object
- DThe amount of space an object occupies
14.A student measures the mass of a regular solid as 120 g and its volume as 40 cm³. What is the density of the solid?
Medium
- A3.0 g/cm³
- B0.33 g/cm³
- C4800 g/cm³
- D160 g/cm³
15.An irregular object has a mass of 50 g. When placed in a eureka can, it displaces 20 cm³ of water. What is the density of the object?
Medium
- A2.5 g/cm³
- B0.4 g/cm³
- C1000 g/cm³
- D70 g/cm³
16.A block of wood has a density of 0.6 g/cm³ and a mass of 300 g. What volume of water (density 1.0 g/cm³) does it displace when floating?
Hard
- A300 cm³
- B180 cm³
- C500 cm³
- D100 cm³
17.Weight is a vector quantity.
Easy
True or false?
18.Which of the following statements about mass and weight are correct? (Select all that apply)
Medium
- AMass is the same everywhere in the universe.
- BWeight is the same everywhere in the universe.
- CWeight is a force measured in newtons.
- DMass is a vector quantity.
19.Match each quantity to its correct unit.
Easy
- Mass
- Weight
- Density
- kg
- N
- kg/m³
20.Arrange the following steps in the correct order to measure the density of an irregular solid using a eureka can.
Medium
- Measure the mass of the solid using a digital balance.
- Fill the eureka can with water up to just below the spout.
- Place an empty measuring cylinder below the spout.
- Carefully lower the solid into the can and collect displaced water.
- Record the volume of displaced water.
21.A student measures the mass of a regular solid as 120 g and its volume as 40 cm³. What is the density of the solid in g/cm³?
Medium
- A3.0 g/cm³
- B0.33 g/cm³
- C4800 g/cm³
- D160 g/cm³
22.Which of the following statements about density are correct? (Select all that apply)
Medium
- AA. Density is measured in kg/m³.
- BB. An object with a density less than water will float in water.
- CC. The density of a gas is usually greater than that of a liquid.
- DD. Density is a measure of the mass per unit volume of a substance.
- EE. The density of an object changes when it is taken to the Moon.
23.An object will sink in a fluid if its density is greater than the density of the fluid.
Easy
True or false?
24.A liquid has a mass of 120 g and a volume of 150 cm³. What is its density in g/cm³?
Medium
- A0.8 g/cm³
- B1.25 g/cm³
- C18000 g/cm³
- D0.008 g/cm³
25.A student measures the mass of a regular solid using a digital balance and its dimensions using a ruler. Which of the following is the correct order of steps to determine its density?
Medium
- AMeasure dimensions, calculate volume, measure mass, calculate density
- BMeasure mass, measure dimensions, calculate volume, calculate density
- CCalculate volume, measure mass, measure dimensions, calculate density
- DMeasure mass, calculate density, measure dimensions, calculate volume
26.The volume of an irregular object can be measured directly using a ruler.
Easy
True or false?
27.Which of the following is the most appropriate piece of equipment to measure the diameter of a small, regularly shaped object to the highest precision?
Easy
- A30 cm ruler
- BVernier calipers
- CMicrometer
- DMeasuring cylinder
28.A student determines the density of an irregular object using a eureka can. Which of the following could cause the calculated density to be too high? (Select all that apply)
Hard
- AThe object is not fully submerged in the water
- BSome of the displaced water splashes out and is not collected in the measuring cylinder
- CThe digital balance is zeroed correctly before taking the mass
- DThe measuring cylinder collects slightly more water than was actually displaced
29.Match each measurement to the most appropriate apparatus.
Easy
- Mass of a regular solid
- Volume of a liquid
- Length of a small object to 0.01 mm precision
- Digital balance
- Measuring cylinder
- Vernier calipers
30.Arrange the following steps in the correct order to measure the density of a liquid.
Medium
- Place an empty measuring cylinder on a digital balance and record its mass
- Pour a known volume of the liquid into the measuring cylinder
- Record the new mass of the measuring cylinder containing the liquid
- Calculate the mass of the liquid by subtracting the initial mass from the final mass
- Calculate the density using density = mass / volume
31.Which of the following is the correct definition of density?
Easy
- AThe volume per unit mass of a material
- BThe mass per unit volume of a material
- CThe weight per unit volume of a material
- DThe mass per unit area of a material
32.Mass is a scalar quantity.
Easy
True or false?
33.Which of the following is the correct unit for weight?
Easy
- Akilogram
- Bnewton
- Cgram
- Dmetre per second squared
34.The mass of an object changes when it is taken from Earth to the Moon.
Easy
True or false?
35.Which of the following statements about density is correct?
Easy
- ADensity is the volume per unit mass of a material.
- BDensity is the mass per unit volume of a material.
- CDensity is the weight per unit volume of a material.
- DDensity is the mass per unit area of a material.
36.A block of wood has a density of 0.6 g/cm³ and a mass of 300 g. When placed in water (density 1.0 g/cm³), what volume of water does it displace?
Medium
- A180 cm³
- B300 cm³
- C500 cm³
- D600 cm³
37.Which of the following is the correct definition of weight?
Easy
- AA measure of the quantity of matter in an object
- BA gravitational force on an object with mass
- CThe amount of space an object occupies
- DThe resistance of an object to a change in motion
38.An object's mass changes when it is moved from Earth to the Moon.
Easy
True or false?
39.Arrange the following steps in the correct order to measure the density of a regular solid using a ruler and a digital balance.
Medium
- Measure the dimensions of the solid using a ruler.
- Calculate the volume of the solid using the appropriate formula.
- Place the solid on a digital balance and record its mass.
- Calculate the density using ρ = m / V.
40.A student measures the mass of a liquid as 150 g and its volume as 120 cm³. What is the density of the liquid in g/cm³?
Medium
- A0.8
- B1.25
- C1.8
- D270
41.Which of the following are correct methods to measure the volume of an irregular solid? (Select all that apply)
Medium
- AUse a ruler to measure its dimensions and calculate volume
- BUse a displacement can and measure the volume of water displaced
- CPlace it in a measuring cylinder containing water and measure the rise in water level
- DWeigh it and divide by its density
- EUse a micrometer to measure its diameter
42.The weight of an object on the Moon is less than its weight on Earth because its mass is less on the Moon.
Medium
True or false?
43.In an experiment to measure the density of an irregular solid, a student uses a eureka can filled with water. After placing the object in the can, the volume of water collected in the measuring cylinder is 25 cm³. The mass of the object is 75 g. What is the density of the object?
Medium
- A3.0 g/cm³
- B0.33 g/cm³
- C1.5 g/cm³
- D2.0 g/cm³
44.Complete the sentence.
Easy
The weight of an object is the force acting on it due to ____.
45.An object has a mass of 250 g. What is its mass in kilograms?
Easy
46.Complete the sentence using the words provided.
Easy
Mass is measured in ____ and weight is measured in ____.
47.Calculate the weight of a 5.0 kg object on Earth where gravitational field strength is 9.8 N/kg.
Easy
48.A liquid has a mass of 120 g and a volume of 150 cm³. Calculate its density in g/cm³.
Easy
49.A block of aluminium has a mass of 135 g and a volume of 50 cm³. Calculate its density in g/cm³.
Easy
50.Complete the sentence with the correct words.
Easy
The weight of an object is the force of ____ on its mass. Weight is measured in ____.
51.State the difference between mass and weight.
Easy
52.An object has a weight of 196 N on Earth where g = 9.8 N/kg. Calculate its mass.
Easy
53.Explain why an object made of iron sinks in water while a wooden block of the same volume floats.
Medium
54.Describe an experiment to determine the density of a liquid. Include the measurements you would take and how you would use them to calculate density.
Medium
55.Describe an experiment to determine the density of an irregular solid. Include the measurements you would take and how you would use them to calculate density.
Hard
56.Describe an experiment to determine the density of a regular solid cuboid. Include the measurements you would take and how you would calculate the density.
Medium
57.An object has a mass of 250 g. What is its mass in kilograms?
Easy
- A1.25 kg
- B2.25 kg
- C0.25 kg
- D-0.75 kg
58.Calculate the weight of a 5.0 kg object on Earth where gravitational field strength is 9.8 N/kg.
Easy
- A49 N
- B54 N
- C44 N
- D59 N
59.A liquid has a mass of 120 g and a volume of 150 cm³. Calculate its density in g/cm³.
Medium
- A0.8 g/cm³
- B1.8 g/cm³
- C2.8 g/cm³
- D-0.2 g/cm³
60.A block of aluminium has a mass of 135 g and a volume of 50 cm³. Calculate its density in g/cm³.
Medium
- A2.7 g/cm³
- B1.7 g/cm³
- C3.7 g/cm³
- D4.7 g/cm³
61.An object has a weight of 196 N on Earth where g = 9.8 N/kg. Calculate its mass.
Easy
- A22 kg
- B18 kg
- C24 kg
- D20 kg

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