Mass, Weight & Density

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수업 노트

Mass & Weight

Mass is a measure of the quantity of matter in an object; it is a scalar quantity measured in kg (or g).
Weight is the gravitational force on an object with mass; it is a vector quantity measured in N.
Mass is constant everywhere; weight depends on gravitational field strength.
Equation: W = m × g, where g = gravitational field strength (N/kg).
On Earth, g ≈ 9.8 N/kg; on the Moon, g ≈ 1.6 N/kg.
A balance measures mass (kg); a force meter (newton meter) measures weight (N).

Comparing a person's mass and weight on Earth and on the Moon; mass stays the same but weight is much lower on the Moon.

Density

Density is the mass per unit volume of a material: ρ = m / V.
Units: kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³).
Low-density materials have low mass for a given volume; high-density materials have high mass.
Gases are less dense than solids/liquids because particles are more spread out.
Volume of regular shapes: cube (side³), sphere (4/3πr³), cylinder (πr²h).

Volume formulas for a sphere, a cube and a cylinder, used to find volume before calculating density.

Measuring Density of Regular Solids

Use a digital balance to measure mass.
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 errors.

Equipment for measuring density of regular solids

Measuring Density of Irregular Solids

Use a eureka can (displacement can) and measuring cylinder.
Fill can to just below spout; place empty cylinder under spout.
Lower object gently; collect displaced water; volume = volume of object.
Alternatively, submerge object in measuring cylinder with water; rise in level = volume.
Density = mass / displaced volume.

Setup for measuring density of irregular solids using a eureka can and measuring cylinder

Measuring Density of Liquids

Place empty measuring cylinder on digital balance; record mass.
Add known volume of liquid; record new mass.
Mass of liquid = (mass of cylinder + liquid) – (mass of empty cylinder).
Density = mass of liquid / volume.

Measuring the mass of a liquid using a measuring cylinder and digital balance

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.
Object floats when upthrust = weight; sinks when upthrust < weight.
Upthrust depends on fluid density and volume of fluid displaced.
Example: polystyrene (0.05 g/cm³) floats on water (1.0 g/cm³); iron (7.9 g/cm³) sinks.

Free-body diagram showing upthrust and weight on a boat and a fish

Floating Liquids (Extended)

A less dense liquid floats on a denser liquid if they do not mix.
For an object to sink in a liquid, object density must be greater than liquid density.
Example: potassium (0.862 g/cm³) sinks in liquid paraffin (0.825 g/cm³) but floats in denser oils.

A density column showing different liquids layered according to their densities.

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연습 문제

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1.Which of the following quantities is weight an example of?
Easy
- AForce
- BMass
- CAcceleration
- DField strength
2.Which of the following statements about mass or weight is true?
Easy
- AWeight is measured in Newtons
- BWeight is measured in kilograms
- CMass = weight × gravitational field strength
- DMass is a force
3.How is the weight of an object defined?
Easy
- AThe gravitational force acting on an object with mass
- BThe force of the ground pushing on an object
- CA measure of the quantity of matter of an object at rest to the observer
- DThe mass per unit volume of an object
4.Which row in the table gives the correct units for mass and for weight?
Easy
- AMass kg, Weight kg
- BMass N, Weight kg
- CMass N, Weight N
- DMass kg, Weight N
5.Which of the following quantities is measured in kilograms?
Easy
- Amass
- Bweight
- Cpressure
- Ddensity
6.Which statement about the mass and the weight of an object is correct?
Easy
- AThey have different units.
- BThey are both affected by changes in the acceleration of free fall.
- CThey are both forces.
- DWeight is calculated by dividing mass by the acceleration of free fall.
7.The gravitational field strength on the Moon is 1.6 N/kg. An astronaut has a mass of 75 kg. What is the weight of the astronaut on the Moon?
Easy
- A120 N
- B47 N
- C75 N
- D740 N
8.Which unit is a unit of weight?
Easy
- Akilonewton
- Bkilogram
- Ckilojoule
- Dkilometre

더 많은 문제

9.A shopkeeper pours rice into a dish that hangs from a spring balance. He records the reading. A customer buys some pasta. The shopkeeper notices that the reading on the spring balance, with just pasta in the dish, is the same as it was with just rice in the dish. Which quantity must be the same for the rice and for the pasta?
Medium
- Aweight
- Bdensity
- Ctemperature
- Dvolume
10.A student determines the density of an irregularly shaped stone. The stone is slowly lowered into a measuring cylinder partly filled with water. Which other apparatus does the student need to calculate the density of the irregularly shaped stone?
Easy
- Aa balance
- Ba thermometer
- Ca metre rule
- Da stop-watch
11.An object has a mass of 4.0 kg on Earth, where the acceleration of free fall is 9.8 m/s². The object is taken to the Moon, where the acceleration of free fall is 1.6 m/s². Which row gives the correct mass and weight of the object on the Moon?
Medium
- Amass 2.5 kg, weight 4.0 N
- Bmass 4.0 kg, weight 6.4 N
- Cmass 4.0 kg, weight 39 N
- Dmass 6.4 kg, weight 39 N
12.Which piece of equipment is used to measure the mass of an object?
Easy
- AA balance
- BA burette
- CA thermometer
- DA trundle wheel
13.A baker uses a balance to weigh out some ingredients to make bread. She weighs out some white flour, then she weighs out some wholemeal flour. She notices that the reading on the balance is the same for both types of flour. The baker can conclude that the two flours have the same:
Medium
- Aweight
- Bvolume
- Cdensity
- Dinternal energy
14.A measuring cylinder is weighed empty, then weighed again containing a liquid. The empty cylinder has a mass of 30 g. The cylinder with liquid has a mass of 93 g and the liquid volume is 20 cm³. What is the density of the liquid?
Medium
- A3.15 g/cm³
- B6.30 g/cm³
- C0.33 g/cm³
- D0.16 g/cm³
15.A geologist wants to determine the density of a cone-shaped rock sample. What needs to be known in order to calculate its density?
Medium
- AThe volume of the cone and the mass of the cone.
- BThe radius of the base of the cone and the weight of the cone.
- CThe surface area of the base of the cone and the height of the cone.
- DThe height of the cone and the mass of the cone.
16.Two beams have the same rectangular cross section, but one is longer than the other. Both beams are made from the same material. Which quantity is the same in both beams?
Easy
- AThe density
- BThe volume
- CThe weight
- DThe mass
17.A student wants to measure the density of a piece of rock. She starts by measuring its mass, and finds that it is 2500 g. Next she puts 500 cm³ of water into a large measuring cylinder, then adds the rock. The level in the measuring cylinder rises to 800 cm³. What is the density of the rock?
Medium
- A8.33 g/cm³
- B3.125 g/cm³
- C0.12 g/cm³
- D0.32 g/cm³
18.Some unknown liquid in a beaker has a mass of 200 g and a volume of 230 cm³. The density of water is 1.0 g/cm³. How does the density of the unknown liquid compare with the density of water?
Medium
- AIts density is less than the density of water
- BIts density is greater than the density of water
- CIts density is the same as the density of water
- DWith the information given, it is impossible to tell.
19.The two diagrams below show a measuring cylinder. In the diagram on the left, the measuring cylinder is empty. In the diagram on the right, the measuring cylinder contains a liquid. The empty cylinder has a mass of 40 g. The cylinder with liquid has a mass of 110 g and the liquid volume is 25 cm³. What is the density of the liquid?
Medium
- A2.80 g/cm³
- B5.00 g/cm³
- C0.28 g/cm³
- D3.57 g/cm³
20.A lump of butter has a volume of 350 cm³ and a mass of 319 g. What is the density of the butter?
Medium
- A0.911 g/cm³
- B1.10 g/cm³
- C1.00 g/cm³
- D31 g/cm³
21.A cube of side length 5 cm is placed on a mass balance. The balance reads 128 g. What is the density of the cube?
Medium
- A1.024 g/cm³
- B0.20 g/cm³
- C5.12 g/cm³
- D4.88 g/cm³
22.An astronaut has a mass of 80 kg on the Earth. The gravitational field strength on the Moon is 1.6 N/kg. What is the weight of the astronaut on the Moon?
Easy
- A128 N
- B50 kg
- C800 N
- D80 kg
23.The density of a block of wood is 2.7 g/cm³ and a mass of 583.8 g. What is its volume?
Medium
- A216.2 cm³
- B0.5 cm³
- C21.6 cm³
- D1574.9 cm³
24.Two objects P and Q are placed in a beaker containing a liquid. Object P floats in the liquid and object Q sinks. Which row for the densities of object P, object Q and the liquid is possible?
Hard
- AP = 1.2 g/cm³, Q = 0.6 g/cm³, liquid = 0.8 g/cm³
- BP = 1.2 g/cm³, Q = 1.4 g/cm³, liquid = 1.0 g/cm³
- CP = 11.3 g/cm³, Q = 8.9 g/cm³, liquid = 13.6 g/cm³
- DP = 11.3 g/cm³, Q = 19.3 g/cm³, liquid = 13.6 g/cm³
25.A measuring cylinder contains 30 cm³ of a liquid. Some more of the liquid is added until the liquid level reaches the 50 cm³ mark. The reading on the balance increases by 30 g. What is the density of the liquid?
Medium
- A1.5 g/cm³
- B0.60 g/cm³
- C0.67 g/cm³
- D1.7 g/cm³
26.A space rocket travels to the Moon. The acceleration of free fall is greater on the Earth than it is on the Moon. How do the mass and weight of the space rocket on the Moon compare with their values on the Earth?
Easy
- Amass same as on Earth, weight less than on Earth
- Bmass less, weight same
- Cmass less, weight more
- Dmass same, weight more
27.The table shows the mass and the volume of two objects, P and Q. The objects are placed in a tank of water, which has a density of 1.0 g/cm³. | Object | Mass (g) | Volume (cm³) | |---|---|---| | P | 15 | 5 | | Q | 15 | 20 | Which statement is correct?
Medium
- AObject Q floats because its density is less than the density of water.
- BObject P floats because its density is greater than the density of water.
- CObject P sinks because its mass is equal to the mass of object Q.
- DObject Q sinks because its volume is greater than the volume of object P.
28.A teacher has two blocks of the same material. Block A has a mass of 200 g and a volume of 100 cm³. Block B has a mass of 400 g. What is the volume of block B?
Easy
- A200 cm³
- B50 cm³
- C100 cm³
- D400 cm³
29.A student measures the mass of a liquid as 250 g and its volume as 200 cm³. She then pours out half the liquid. What is the density of the remaining liquid?
Medium
- A1.25 g/cm³
- B2.5 g/cm³
- C0.625 g/cm³
- D0.8 g/cm³
30.An object has a weight of 50 N on Earth where g = 10 N/kg. What is its mass?
Easy
- A5 kg
- B0.2 kg
- C50 kg
- D500 kg
31.A piece of metal has a density of 8.9 g/cm³ and a volume of 10 cm³. It is cut into two equal halves. What is the density of one half?
Easy
- A8.9 g/cm³
- B4.45 g/cm³
- C17.8 g/cm³
- D0.89 g/cm³
32.A liquid has a density of 0.8 g/cm³. A solid object has a mass of 120 g and a volume of 100 cm³. When placed in the liquid, the object will:
Medium
- Asink
- Bfloat
- Cremain suspended at any depth
- Dpartially float with half submerged
33.A force meter (newton meter) is used to measure the weight of an object on Earth. The reading is 20 N. The object is then taken to a planet where gravitational field strength is half that of Earth. What will be the reading on the force meter?
Easy
- A10 N
- B20 N
- C40 N
- D5 N
34.A student uses a measuring cylinder to measure the volume of a stone by water displacement. The initial water level is 40 cm³. After adding the stone, the level is 55 cm³. The stone's mass is 45 g. What is its density?
Medium
- A3.0 g/cm³
- B0.33 g/cm³
- C1.22 g/cm³
- D0.82 g/cm³
35.A bottle contains 500 cm³ of cooking oil of density 0.9 g/cm³. What is the mass of the oil?
Easy
- A450 g
- B555.6 g
- C500 g
- D0.0018 g
36.Which of the following correctly describes the relationship between mass and weight?
Easy
- AWeight is mass multiplied by gravitational field strength.
- BMass is weight multiplied by gravitational field strength.
- CWeight is mass divided by gravitational field strength.
- DMass and weight are the same quantity.
37.A block of wood floats in water with half its volume submerged. The density of water is 1.0 g/cm³. What is the density of the wood?
Medium
- A0.5 g/cm³
- B1.0 g/cm³
- C2.0 g/cm³
- D0.25 g/cm³
38.A student wants to determine the density of a liquid. She places an empty measuring cylinder on a digital balance and records the mass as 50 g. She then pours 100 cm³ of the liquid into the cylinder and records the new mass as 130 g. What is the density of the liquid?
Medium
- A0.80 g/cm³
- B1.30 g/cm³
- C0.50 g/cm³
- D1.80 g/cm³
39.A student uses a measuring cylinder to measure the volume of a stone by water displacement. The initial water level is 40 cm³. After adding the stone, the level rises to 65 cm³. The mass of the stone is 75 g. What is the density of the stone?
Medium
- A3.0 g/cm³
- B1.875 g/cm³
- C0.533 g/cm³
- D2.0 g/cm³
40.Mass is a vector quantity.
Easy
True or false?
41.Which of the following is the correct definition of weight?
Easy
- AThe quantity of matter in an object
- BThe force acting on an object with mass when placed in a gravitational field
- CThe resistance of an object to a change in motion
- DThe mass per unit volume of a material
42.The weight of an object on the Moon is the same as its weight on Earth.
Easy
True or false?
43.Which instrument is used to measure the weight of an object?
Easy
- ADigital balance
- BNewton meter (force meter)
- CMeasuring cylinder
- DRuler
44.Density is defined as the volume per unit mass of a material.
Easy
True or false?
45.The density of water is 1.0 g/cm³. Which of the following objects will float in water?
Easy
- AA block of iron with density 7.9 g/cm³
- BA block of wood with density 0.9 g/cm³
- CA stone with density 2.5 g/cm³
- DA piece of glass with density 2.6 g/cm³
46.Which of the following statements about mass are correct? (Select all that apply)
Medium
- AMass is measured in kilograms.
- BMass is a vector quantity.
- CMass is the quantity of matter in an object.
- DMass changes when an object is taken to the Moon.
- EMass is a scalar quantity.
47.Match each quantity to its correct unit.
Easy
- Mass
- Weight
- Density
- kg
- N
- kg/m³
48.Arrange the following steps in the correct order to measure the density of an irregularly shaped solid using a eureka can.
Medium
- Measure the mass of the object using a digital balance.
- Fill the eureka can with water up to just below the spout.
- Place an empty measuring cylinder under the spout.
- Carefully lower the object into the eureka can.
- Measure the volume of water collected in the measuring cylinder.
49.Weight is a vector quantity.
Easy
True or false?
50.Calculate the weight of a 5.0 kg object on Earth where gravitational field strength is 9.8 N/kg.
Easy
51.Complete the sentence: The gravitational field strength on Earth is approximately ___ N/kg.
Easy
The gravitational field strength on Earth is approximately ____ N/kg.
52.State the equation that links weight, mass, and gravitational field strength.
Easy
53.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

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