Chapter 4 Mass, Weight and Density - WordPress.com 4 Mass, Weight and Density (iv) Tomato sauce is shaken out from the bottle by moving the bottle downwards and stopping abruptly.

Chapter 4 Mass, Weight and Density

Chapter 4 Mass, Weight and Density

Learning Outcomes

After completing this chapter, students should be able to:

1. state that mass is a measure of the amount of substance in a body 2. state that mass of a body resists a change in the state of rest or motion of the body (inertia) 3. state that a gravitational field is a region in which a mass experiences a force due to gravitational

attraction 4. define gravitational field strength, g, as gravitational force per unit mass 5. recall and apply the relationship weight = mass x gravitational field strength to new situations or to

solve related problems 6. distinguish between mass and weight 7. recall and apply the relationship density = mass .;- volume to new situations or to solve related

problems

4.1 Mass and Weight page 71 1. Explain that in physics mass is different from weight. Students realise that even when an object is

moved around the Earth, it is the same object, made of the same molecules, in the same order and that something about it remains constant. This is the amount of matter it contains.

2. This unchanging quantity, mass, is the quantity one is usually interested in when buying, say, fruit or vegetables.

3. Both the beam balance and electronic balance shown in Fig. 4.2(a) and 4.2(b) respectively are used to measure the mass of an object.

4. A spring balance or a Newton-meter (Fig. 4.3) that works according to Hooke's Law can be used to measure the force or the weight of a body. It can be used to measure the mass only at its point of calibration, i.e. the place where it was made.

5. The mass of a body is constant everywhere, whereas the weight of a body changes from place to place according to the different value of acceleration due to gravity at different places (W = mg) . E.g. (i) the weight of a body at the poles is greater than that at the equator; (ii) the weight of a body on the moon is less than that on earth; (iii) the weight of a body up on a hill is less than that at sea level.

Answer to Think Time question page 71

It is easier to lift a 10 kg mass on the Moon because the weight of the 10 kg mass on the Moon is lower.

Inertia and Mass page 74 1. Explain that mass determines how difficult it is to change the motion of a body (e.g. to speed it up); it

determines the inertia of the body.

2. The concept of inertia is consistent with Newton's first law of motion.

3. The concept of inertia or ewton's first law of motion may be used to explain the following: (i) Dishes on a tabletop remain at rest if yo u pull the tablecloth from beneath them very quickly. (ii) Drops of water on an umbrella can be removed by shaking the umbrella. (iii) The loose handle of a hammer can be tightened by hitting the handle against the ground.

Chapter 4 Mass, Weight and Density

(iv) Tomato sauce is shaken out from the bottle by moving the bottle downwards and stopping abruptly.

(iv) The use of seat belt to restrain passengers from moving forward in a collision. (v) The use of head restraints to prevent whiplash injury in a car accident.

Answer to Think Time question page 74

The greater the mass the greater is the inertia

Answers to Section Review questions page 75

1. In physics, weight is a force and it is measured in newton. It should either be the mass of the chicken is 2 kilograms or the weight of the chicken is 20 newtons.

2. The weight of the boy is 500 N. His mass on the Moon is sti1l50 kg but his weight on the Moon will be less than that on Earth.

3. The can which is more massive has a greater inertia. So when the same force is exerted on the two cans, the more massive can will move with a smaller amount.

4.2 Gravitational Field and Field Strength page 75 1. Explain that a gravitational field is a region whereby an object experiences a gravitational force.

2. Students readily accept that as an objectjoumeys around the Solar System, the force of attraction to the nearest planet changes with the planet's mass.

3. On Earth this force is approximately 10 N for every kilogram of the object's mass. Emphasise that this force decreases as the height above sea-level increases.

4. Gravitational field strength is defined as the ratio of the gravitational force to the mass of an object (or ratio of the weight to the mass) . It happens to be equivalent to the acceleration due to gravity. It can be taken as 9.81 N kg-Ion the surface of the Earth.

5. Ask the students to calculate their weight on the Earth and on the Moon using the equation weight = mass x gravitational field strength

6. As in the case of weight, (i) the gravitational field strength at the poles are greater than that at the equator; (ii) the gravitational field strength on the Moon is less than that on Earth; (iii) the gravitational field strength up on a hill is less than that at sea level.

Answer to Think Time question Page 76

No. In this case the gravitational field strength acting on the coin and the feather is the same but the gravitational forces acting on the coin and the feather depend on their masses.

Answers to Section Review questions page 77

1. W

m =-g

55 N ---=-=--:..:~= 5.5 kg LO N kg- 1

2. W= mg = 70 kg x 26 N kg- 1

= 1820 N

Chapter 4 Mass, Weight and Density

4.3 Density page 78 1. Ask students this question: Is iron heavier than cotton?

Some might say iron, but the question actually has no answer, as it depends on how much iron and cotton we are comparing. For those who say that iron is heavier, their understanding is that the same amount, or volume, of each item is being compared. So, a better question ask is "Is iron denser than cotton?"

2. Emphasise that volume and mass are properties of an object. They vary from object to object even when they are of the same material.

3. Density, however, is the physical property of the material from which the substance is made. We determine density by finding the mass per unit volume of the substance. Density is used to determine whether samples of a substance are pure.

4. You may like to tell the story of how Archimedes was able to confIrm that the gold crown of King Hero of Syracuse was actually alloyed with silver, instead of pure gold. (Refer to Physics in Society: Archimedes' Discovery on page 84 of the Textbook.)

The king suspected that his goldsmith had not used all the gold he had been given to make the crown and that he had replaced some of it with silver. Archimedes found that the crown weighed the same as gold but he was not sure if it had the same volume. He was still thinking about the problem when one day, as he stepped into his bath, the water started to overflow suddenly. He realised that he could cause water to overflow by placing the crown in the water, thereby measuring the volume of the crown.

Archimedes was so thrilled by the thought of this discovery that, according to the story, he jumped out of his bath and ran naked through the streets, shouting "Eureka, Eureka!" meaning "I have found it!"

Answer to Think Time question page 78

Since the volume of ice is greater than the volume of the same mass of water, ice is less dense than water. So, ice floats on water.

Answer to Think Time question page 79

Since water is denser than ice, a litre of water weighs more.

Floating and Sinking page 81 1. Floating or sinking of an object in a liquid tells us whether the object is denser or less dense than the

liquid.

2. When an object is placed in different liquids, the denser the liquid, the higher the object will float in the liquid. This principle is used in the construction of a hydrometer.

3. Ask students why a solid iron ball will sink in water, whereas a hollow iron ball will not sink. This can be explained using the average density of the iron ball.

Answer to Think Time question Page 81

When the object floats more, it indicates that its density is much lower than the liquid.

Answers to Section Review questions page 82

1. Use equation: p = m -:- V 2. Use equation: V = m -:- p 3. Use equation: p = m -:- V

Chapter 4 Mass, Weight and Density

Physics in Society: Archimedes' Discoveries page 82 Answers to Q 1. I would measure the mass of the wreath and immerse it in a large displacement can to determine its

volume. I would calculate its density and compare the value obtained through measurement with that in the Table of constants (e.g. Table 4.2 on page 80).

2. Archimedes was famous for his many mathematical treatises, his ingenious inventions and the numerous accounts of his experiments.

Answers to Misconception Analysis page 83, 84

1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

True True False. True False.

False. False. False. True True

A beam balance determines the weight by comparing it with a standard weight.

A bigger object has a bigger volume but not necessarily has a bigger mass, so its inertia may not be greater.

Inertia acts when there is a change in motion Not necessary. Inertia is not a measure of the strength of a substance. This is true only if they have the same volume.

Answers to Multiple Choice Questions page 84, 85

1. 2. 3. 4.

5.

6.

7.

8.

9.

e e B Mass is constant and weight = mg

B

B WE = k; WE = lQ. ; WE = 400 N WM gM 64N 1.6

D

D m

p = -V

180 0 -3 = o = 9 g'cm

(80 -60)cm3

e m p = -

V

3.6g = 0.24 g cm -3 =

(45-30)cm3

m D p = ­

V

[(lO x 1.5) + 0.6] kg 0.20 m x 0.30 m x 0.25 m

-3 1040 kg m

10. e When the diameter is doubled, the volume is 8 times bigger, so the weight is also 8 times bigger.

Answers to Structured Questions page 85

1. (a) Weight = mass x gravitational field strength = 80 kg x 3.0 N kg-1

=240N (b) Resultant force = Upward force - weight

= 160 N upwards (c) F = ma

160 = 80a a = 2.0 m S-2

2. (a) Density is the mass per unit volume. (c) Mass = volume x density

3. (a) (i) Mass = Weight 7 g

= (70 - 5) = 6.5 kg 10

(ii) Density = mass 7 volume (b) Mass of tin = 0.5 kg

Volume = mass 7 density = 0.577800 = 6.4 x 10-5 m3

4. (a) Capacity of bottle = volume of water = mass of water = 1500 cm3

density of water

(b) Density of cooking oil = mass of cooking oil volume of bottle

= 1200 = 0.8 g cm-3

1500

5. (a) Volume of solid = volume of liquid overflowed mass of liquid

density of liquid

= 180 = 150 cm3

l.2

(b) Mass of solid = volume of solid x density of solid

6. Let the total volume of alloy be V. Volume of aluminium = 0.7V Mass of aluminium = volume x density = 0.7Vx 2700 Volume of magnesium = 0.3 V Mass of aluminium = volume x density = 0.3 V x 1700

Density of alloy = mass of alloy volume of alloy

_ (0.7V x 2700 +0.3V x 1700 )

v = 2400 kg m-3

Chapter 4 Mass, Weight and Density

Answers to Critical Thinking Questions page 85

1. As the handle of the hammer is moved down and stopped, the inertia of the hammerhead will cause

the head to move further down into the handle, causing it to fit tightly. If it is moved with the hammerhead down, then the best that can be done is the hammerhead being at level with the handle.

This will not tighten the hammerhead.

2. If the string below is pulled, the string above experiences greater tension. The ·tension experience by the string above equals the weight of metal baU and the force exerted on the string below. Weight is important here. If the string below is jerked downwards suddenly, then it will be more likely to break. Mass (inertia) is more important in this case.

3. Since the mass (inertia) of the elephant is large, it is difficult for the elephant to change its motion.

4 . An ocean liner is made up of both steel and a lot of air space in it. Its average density is lower than that of water, thus it floats.

Chapter 4 Mass, Weight and Density

5. The average density of our body is less than the density of water. To estimate the average density of our entire body:

(i) Find the mass of the person. (ii) Fill the bathtub to the brim. (iii) Get into the bathtub and immerse the whole body in water. Water will overflow.

(iv) Fill the bathtub again using a container with known volume (e.g. a 5-litre pail). (v) Density = mass -;- volume

Extension page 85

1. According to Einstein's special theory of relativity, as an object approaches the speed of light, its mass approaches infinity.

2.

The increase in effective mass with speed is given by the expression:

where rno = rest mass, v = speed of the object, c = speed of light.

• A lever arm balance is used to find the mass of the large plastic container shown in the drawing above.

• Air is pumped into the container using a foot pump and the tap is closed. • The mass of the container and extra air is found. • A box or large beaker with known volume is inverted full of water with its open end downwards.

Air is allowed to flow into the beaker from the container as shown in the diagram and tap is closed as soon as the box is filled .

• The process is repeated each time releasing a beaker of air until all the extra air has been released.

mass of extra air in the container • Density of air = ------- - - - - ­

volume of extra air released