Density

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課程筆記

What is Density?

Density is a measure of how much mass is contained in a given volume.
If particles have the same mass, more particles in the same volume means higher density.
Density determines whether an object floats or sinks in a fluid.

The Density Equation

Density = Mass ÷ Volume
Mass is the amount of matter in an object, measured in kilograms (kg).
Volume is the space an object occupies, measured in cubic metres (m³).
Density has units of kg/m³.

Calculating Density

Example: Wood with mass 210 kg and volume 0.3 m³ has density = 210 ÷ 0.3 = 700 kg/m³.
Always write the equation, substitute values, then calculate with units.

Rearranging the Equation

To find volume: Volume = Mass ÷ Density.
To find mass: Mass = Density × Volume.
Example: Granite density 2700 kg/m³, mass 5400 kg → volume = 5400 ÷ 2700 = 2 m³.

Floating and Sinking

Water density = 1000 kg/m³.
Objects with density less than water float; objects with density greater than water sink.
Wood (700 kg/m³) floats on water.
Oil (800 kg/m³) floats on water because it is less dense.

Example Calculations

Book: mass 1 kg, volume 0.002 m³ → density = 1 ÷ 0.002 = 500 kg/m³.
Gold bar: mass 3.8 kg, volume 0.0002 m³ → density = 3.8 ÷ 0.0002 = 19,000 kg/m³.
Rock: mass 300 kg, volume 0.1 m³ → density = 300 ÷ 0.1 = 3000 kg/m³.

Finding Volume from Density and Mass

Steel density 7800 kg/m³, mass 3900 kg → volume = 3900 ÷ 7800 = 0.5 m³.
Human body density 995 kg/m³, mass 70 kg → volume = 70 ÷ 995 ≈ 0.0704 m³.
Crate: mass 250 kg, density 50 kg/m³ → volume = 250 ÷ 50 = 5 m³.

Finding Mass from Density and Volume

Car: density 280 kg/m³, volume 4.2 m³ → mass = 280 × 4.2 = 1176 kg.

Particle arrangement in solids, liquids, and gases. Density is higher when particles are more closely packed.

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練習題

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1.Which equation correctly relates density, mass and volume?
Easy
- ADensity = Mass × Volume
- BDensity = Mass ÷ Volume
- CDensity = Volume ÷ Mass
- DDensity = Mass + Volume
2.What are the standard SI units for density, mass and volume respectively?
Easy
- Akg/m³, kg, m³
- Bkg, m³, kg/m³
- Cm³, kg, kg/m³
- Dkg/m³, m³, kg
3.Water has a density of 1000 kg/m³ and oil has a density of 800 kg/m³. What will happen when oil is poured into water?
Easy
- AThe oil will sink because it is denser.
- BThe oil will float because it is less dense.
- CThe oil will mix completely.
- DThe oil will float because it has a higher density.
4.A book has a mass of 1 kg and a volume of 0.002 m³. What is its density?
Medium
- A500 kg/m³
- B2000 kg/m³
- C0.002 kg/m³
- D5000 kg/m³
5.A gold bar has a mass of 3.8 kg and a volume of 0.0002 m³. Calculate its density.
Medium
- A19000 kg/m³
- B1900 kg/m³
- C190 kg/m³
- D0.0000526 kg/m³
6.A rock has a mass of 300 kg and a volume of 0.1 m³. What is its density?
Medium
- A30 kg/m³
- B3000 kg/m³
- C300 kg/m³
- D0.000333 kg/m³
7.Steel has a density of 7800 kg/m³. What is the volume of a steel object with a mass of 3900 kg?
Medium
- A0.5 m³
- B2 m³
- C30,420,000 m³
- D0.5 kg/m³
8.The average human body density is 995 kg/m³. Why can humans float in water (density 1000 kg/m³)?
Medium
- ABecause the human body is less dense than water.
- BBecause the human body is more dense than water.
- CBecause humans have air in their lungs.
- DBecause humans can swim.

更多題目

9.A human body has a mass of 70 kg and density 995 kg/m³. What is its volume?
Medium
- A0.0704 m³
- B69,650 m³
- C0.0704 kg/m³
- D70.4 m³
10.A crate has a mass of 250 kg and a density of 50 kg/m³. What is its volume?
Medium
- A5 m³
- B0.2 m³
- C12,500 m³
- D50 m³
11.A car has an average density of 280 kg/m³ and a volume of 4.2 m³. What is its mass?
Medium
- A1176 kg
- B66.7 kg
- C1176 kg/m³
- D0.015 kg
12.Which of the following statements about density is correct?
Easy
- ADensity is a measure of how much mass is in a given volume.
- BDensity is a measure of how much volume is in a given mass.
- CDensity is the same as weight.
- DDensity is measured in kilograms.
13.A student measures the mass of a stone as 150 g and its volume by displacement as 50 cm³. What is the density of the stone in g/cm³?
Medium
- A3.0 g/cm³
- B0.33 g/cm³
- C7500 g/cm³
- D100 g/cm³
14.A rectangular block has dimensions 2 m × 0.5 m × 0.2 m and a mass of 400 kg. What is its density?
Medium
- A2000 kg/m³
- B800 kg/m³
- C4000 kg/m³
- D200 kg/m³
15.A liquid has a density of 1200 kg/m³. What is the mass of 0.5 m³ of this liquid?
Medium
- A600 kg
- B2400 kg
- C0.000417 kg
- D6000 kg
16.Which of the following substances will float on water (density 1000 kg/m³)?
Easy
- AIce (density 920 kg/m³)
- BAluminium (density 2700 kg/m³)
- CCopper (density 8900 kg/m³)
- DConcrete (density 2400 kg/m³)
17.A student has a measuring cylinder containing 50 cm³ of water. She adds a small rock and the water level rises to 65 cm³. The rock has a mass of 39 g. What is the density of the rock?
Medium
- A2.6 g/cm³
- B0.6 g/cm³
- C2.8 g/cm³
- D3.0 g/cm³
18.A gas has a density of 1.2 kg/m³. What is the volume of 6 kg of this gas?
Medium
- A5 m³
- B0.2 m³
- C7.2 m³
- D4.8 m³
19.A cylindrical can has a volume of 0.002 m³ and is filled with a liquid of density 800 kg/m³. What is the mass of the liquid?
Medium
- A1.6 kg
- B0.0000025 kg
- C2.5 kg
- D1600 kg
20.The density of a substance is 500 kg/m³. Which of the following is the same density in g/cm³?
Medium
- A0.5 g/cm³
- B500 g/cm³
- C500000 g/cm³
- D5 g/cm³
21.A piece of wood floats in water with half of its volume above the surface. What can you conclude about the density of the wood?
Hard
- AIt is half the density of water (500 kg/m³)
- BIt is equal to the density of water (1000 kg/m³)
- CIt is greater than the density of water
- DIt is less than the density of water but not necessarily half
22.An object of mass 2 kg and volume 0.001 m³ is placed in a liquid of density 1500 kg/m³. Will it float or sink?
Medium
- AFloat, because its density (2000 kg/m³) is greater than the liquid
- BSink, because its density (2000 kg/m³) is greater than the liquid
- CFloat, because its mass is small
- DSink, because its volume is small
23.A student wants to find the density of an irregularly shaped object. Which two measurements must they take?
Easy
- AMass and volume
- BMass and weight
- CVolume and weight
- DLength and width
24.The density of air is about 1.2 kg/m³. A balloon is filled with helium of density 0.18 kg/m³. The balloon has a volume of 0.5 m³. What is the mass of helium in the balloon?
Medium
- A0.09 kg
- B0.6 kg
- C0.36 kg
- D0.09 g
25.A student wants to find the density of an irregularly shaped stone. Which two measurements must they take?
Easy
- AMass and volume
- BMass and length
- CVolume and weight
- DWeight and length
26.In an experiment to find the density of a liquid, a student measures the mass of an empty measuring cylinder as 150 g. She then pours 50 cm³ of the liquid into the cylinder and measures the total mass as 190 g. What is the density of the liquid?
Medium
- A0.8 g/cm³
- B1.25 g/cm³
- C3.8 g/cm³
- D0.25 g/cm³
27.A student uses a displacement can to find the volume of a metal object. The initial water level in the measuring cylinder is 20 cm³. After immersing the object, the water level rises to 35 cm³. The object has a mass of 120 g. What is the density of the metal in kg/m³?
Hard
- A8000 kg/m³
- B800 kg/m³
- C0.008 kg/m³
- D8 kg/m³
28.A student is asked to determine the density of a regular-shaped block of wood. Which apparatus would be most suitable?
Easy
- ARuler and balance
- BMeasuring cylinder and balance
- CDisplacement can and ruler
- DRuler and displacement can
29.A student measures the mass of a rock as 250 g. She places it in a measuring cylinder containing 100 cm³ of water, and the water level rises to 150 cm³. She then removes the rock and finds its volume by displacement again, getting 55 cm³. Which volume should she use to calculate density?
Medium
- A50 cm³
- B55 cm³
- C100 cm³
- D150 cm³
30.What is the name of the method used to find the volume of an irregularly shaped object?
Easy
- AWater displacement
- BWeighing
- CMeasuring length
- DUsing a balance
31.A student finds the density of a liquid twice. First, she uses a 50 cm³ measuring cylinder and gets a density of 0.79 g/cm³. Second, she uses a 100 cm³ measuring cylinder and gets 0.81 g/cm³. Which result is likely to be more accurate?
Medium
- AThe result using the 50 cm³ cylinder
- BThe result using the 100 cm³ cylinder
- CBoth are equally accurate
- DNeither is accurate
32.A student has a block of material of mass 500 g and volume 200 cm³. She cuts the block in half. What is the density of one of the halves?
Medium
- A2.5 g/cm³
- B1.25 g/cm³
- C5 g/cm³
- D0.4 g/cm³
33.The diagram shows a measuring cylinder with water before and after adding a metal bolt. The initial volume is 30 cm³ and the final volume is 42 cm³. The bolt has a mass of 96 g. What is the density of the metal?
Medium
- A8 g/cm³
- B0.125 g/cm³
- C3.2 g/cm³
- D2.3 g/cm³
34.A student wants to find the density of a piece of cork that floats on water. Which method should she use to measure its volume?
Medium
- AUse a displacement can with a thin wire to push the cork underwater
- BMeasure its dimensions with a ruler
- CUse a displacement can without submerging it
- DWeigh the cork and calculate volume from mass
35.A student measures the mass of an empty beaker as 50 g. She adds 20 cm³ of a liquid and records the total mass as 66 g. She then adds another 30 cm³ of the same liquid and the total mass becomes 90 g. What is the density of the liquid?
Medium
- A0.8 g/cm³
- B0.9 g/cm³
- C1.0 g/cm³
- D1.2 g/cm³
36.A student is given a sample of an unknown liquid. She measures its mass and volume and calculates its density as 1.2 g/cm³. She then heats the liquid, causing some to evaporate, and measures the density of the remaining liquid. What would you expect the density to be?
Medium
- ARemain the same
- BIncrease
- CDecrease
- DCannot be determined
37.Which of the following is the correct definition of density?
Easy
- AThe amount of matter in an object
- BThe mass per unit volume of a substance
- CThe volume per unit mass of a substance
- DThe weight of an object divided by its volume
38.What are the standard SI units for density?
Easy
- Akg/m³
- Bg/cm³
- Ckg/m²
- DN/m³
39.An object has a density of 500 kg/m³. Which of the following is the same density in g/cm³?
Medium
- A0.5 g/cm³
- B5 g/cm³
- C0.05 g/cm³
- D5000 g/cm³
40.The density of water is 1000 kg/m³. A liquid has a density of 0.92 g/cm³. Which of the following is correct?
Medium
- AThe liquid will float on water because its density is less than that of water.
- BThe liquid will sink in water because its density is greater than that of water.
- CThe liquid will float on water because its density is greater than that of water.
- DThe liquid will sink in water because its density is less than that of water.
41.Density is defined as the amount of mass per unit volume.
Easy
True or false?
42.Which of the following is the correct equation for density?
Easy
- ADensity = Mass × Volume
- BDensity = Mass ÷ Volume
- CDensity = Volume ÷ Mass
- DDensity = Mass + Volume
43.An object with a density of 1200 kg/m³ will float on water (density 1000 kg/m³).
Easy
True or false?
44.A block of wood has a density of 600 kg/m³. Which of the following is true?
Medium
- AIt will float on water because its density is less than water's.
- BIt will sink in water because its density is less than water's.
- CIt will float on water because its density is greater than water's.
- DIt will sink in water because its density is greater than water's.
45.Match each term to its correct definition.
Easy
- Density
- Mass
- Volume
- The amount of matter in an object
- The amount of space an object takes up
- The amount of mass per unit volume
46.Arrange the following substances in order of increasing density (lowest to highest): ice (917 kg/m³), water (1000 kg/m³), iron (7800 kg/m³), air (1.2 kg/m³).
Medium
- air
- ice
- water
- iron
47.Which of the following are correct units for density? (Select all that apply)
Medium
- Akg/m³
- Bg/cm³
- Ckg/m²
- Dg/mL
48.A liquid has a density of 0.8 g/cm³. What is its density in kg/m³?
Medium
- A0.8 kg/m³
- B80 kg/m³
- C800 kg/m³
- D8000 kg/m³
49.The diagram shows three gases in the same volume. Assuming each particle has the same mass, which gas has the highest density?
Medium
- ATop gas
- BMiddle gas
- CBottom gas
- DAll have the same density
50.Complete the sentence.
Easy
The SI unit of mass is the ____.
51.What is the density of a substance with mass 50 kg and volume 0.02 m³? Give your answer in kg/m³.
Medium
52.The density of aluminium is 2700 kg/m³. What is the mass of a piece of aluminium with volume 0.5 m³? Give your answer in kg.
Medium
53.The density of a liquid is 800 kg/m³. What volume of the liquid has a mass of 200 kg? Give your answer in m³.
Medium
54.State the equation that links density, mass and volume.
Easy
55.A piece of wood has a mass of 420 g and a volume of 600 cm³. Calculate its density in g/cm³.
Medium
56.Complete the sentence using the correct words.
Easy
If an object has a density ____ than water, it will sink. If it has a density ____ than water, it will float.
57.Explain why a piece of wood with density 700 kg/m³ floats on water, while a piece of iron with density 7800 kg/m³ sinks.
Medium
58.What is the density of a substance with mass 50 kg and volume 0.02 m³? Give your answer in kg/m³.
Medium
- A2500 kg/m³
- B2250 kg/m³
- C3000 kg/m³
- D2750 kg/m³
59.The density of aluminium is 2700 kg/m³. What is the mass of a piece of aluminium with volume 0.5 m³? Give your answer in kg.
Medium
- A1215 kg
- B1620 kg
- C1350 kg
- D1485 kg
60.The density of a liquid is 800 kg/m³. What volume of the liquid has a mass of 200 kg? Give your answer in m³.
Medium
- A2.25 m³
- B0.25 m³
- C-0.75 m³
- D1.25 m³
61.A piece of wood has a mass of 420 g and a volume of 600 cm³. Calculate its density in g/cm³.
Medium
- A2.7 g/cm³
- B-0.3 g/cm³
- C1.7 g/cm³
- D0.7 g/cm³

複習筆記

## Density Revision Notes ### Key Definition - **Density** is a measure of how much mass is in a given volume. ### Formula - **Density = Mass ÷ Volume** - Mass in kilograms (kg) - Volume in metres cubed (m³) - Density in kilograms per metre cubed (kg/m³) ### How to Calculate 1. Write down the equation: Density = Mass ÷ Volume 2. Insert the numbers with units. 3. Calculate and include units. **Example:** Wood with mass 210 kg and volume 0.3 m³ → Density = 210 ÷ 0.3 = 700 kg/m³ ### Rearranging the Formula - To find **Volume**: Volume = Mass ÷ Density - To find **Mass**: Mass = Density × Volume **Example:** Granite density 2700 kg/m³, mass 5400 kg → Volume = 5400 ÷ 2700 = 2 m³ ### Floating and Sinking - Water density = 1000 kg/m³ - Objects with density **less than 1000 kg/m³** float on water. - Objects with density **greater than 1000 kg/m³** sink. - Example: Wood (700 kg/m³) floats; granite (2700 kg/m³) sinks. ### Quick Tips - Always include units in your answer. - Check if you need to rearrange the formula. - Remember: lower density = floats (if less than water).

Density: A measure of how much mass is in a given volume.
Mass: The amount of matter an object contains, measured in kilograms (kg).
Volume: The amount of space an object takes up, measured in metres cubed (m³).
Density formula: Density = Mass ÷ Volume
Units of density: Kilograms per metre cubed (kg/m³).
Density of water: 1000 kg/m³. Objects with density less than this float; greater sink.

字卡

What is density?

Density is a measure of how much mass is in a given volume.

What is the equation linking density, mass and volume?

Density = Mass ÷ Volume

What are the units of density?

Kilograms per metre cubed (kg/m³).

What are the units of mass?

Kilograms (kg).

What are the units of volume?

Metres cubed (m³).

If each particle has the same mass, which gas in a diagram of three gases in the same volume has the least density?

The top gas has the least density because it has the fewest particles in the same volume.

What is the density of water?

1000 kg/m³.

Will an object with density less than 1000 kg/m³ float or sink in water?

It will float because its density is lower than that of water.

A wood has mass 210 kg and volume 0.3 m³. Calculate its density.

Density = 210 kg ÷ 0.3 m³ = 700 kg/m³.

Granite has density 2700 kg/m³ and mass 5400 kg. Calculate its volume.

Volume = Mass ÷ Density = 5400 kg ÷ 2700 kg/m³ = 2 m³.

Oil has density 800 kg/m³ and water has density 1000 kg/m³. Will oil float or sink in water?

Oil will float because its density (800 kg/m³) is less than that of water (1000 kg/m³).

A book has mass 1 kg and volume 0.002 m³. Calculate its density.

Density = 1 kg ÷ 0.002 m³ = 500 kg/m³.

A gold bar has mass 3.8 kg and volume 0.0002 m³. Calculate its density.

Density = 3.8 kg ÷ 0.0002 m³ = 19000 kg/m³.

A rock has mass 300 kg and volume 0.1 m³. Calculate its density.

Density = 300 kg ÷ 0.1 m³ = 3000 kg/m³.

Steel has density 7800 kg/m³ and mass 3900 kg. Calculate its volume.

Volume = Mass ÷ Density = 3900 kg ÷ 7800 kg/m³ = 0.5 m³.

The average human body density is 995 kg/m³. Explain why humans can float on water.

Humans can float because their average density (995 kg/m³) is less than that of water (1000 kg/m³).

A human body has mass 70 kg and density 995 kg/m³. Calculate its volume.

Volume = Mass ÷ Density = 70 kg ÷ 995 kg/m³ ≈ 0.07035 m³.

A crate has mass 250 kg and density 50 kg/m³. Calculate its volume.

Volume = Mass ÷ Density = 250 kg ÷ 50 kg/m³ = 5 m³.

A car has average density 280 kg/m³ and volume 4.2 m³. Calculate its mass.

Mass = Density × Volume = 280 kg/m³ × 4.2 m³ = 1176 kg.

What is the formula to calculate mass given density and volume?

Mass = Density × Volume.

What is the formula to calculate volume given density and mass?

Volume = Mass ÷ Density.

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