Monday, July 8, 2019

Chapter 2.5 - Measurement of Mass and Time

In the previous sectionwe completed a discussion on length. In this section, we will see mass. Later in this section, we will see time also.


Measurement of mass

■ Mass is a basic property of matter. It does not depend on temperature, pressure or location in space. This can be explained as follows:
1. Mass does not depend on temperature.
• Consider an object having a definite mass.
    ♦ Even if we heat it, it’s mass will remain the same.
    ♦ Even if we cool it, it’s mass will remain the same.
• Note that this is true only if the following conditions are satisfied:
    ♦ No matter is lost from or added to the object when it is heated.
    ♦ No matter is lost from or added to the object when it is cooled.
2. Mass does not depend on pressure.
• Consider an object having a definite mass.
    ♦ Even if we apply pressure on it, it’s mass will remain the same.
    ♦ Even if we place it in a container of low pressure, it’s mass will remain the same.
• Note that this is true only if the following conditions are satisfied:
    ♦ No matter is lost from or added to the object when pressure is applied.
    ♦ No matter is lost from or added to the object when it is placed in a container of lower pressure.
3. Mass does not depend on location.
• Consider an object having a definite mass.
    ♦ We know that: weight = mass × acceleration due to gravity (g).
    ♦ The ‘g’ may vary depending on the location.
    ♦ That means, weight may vary depending on the location.
• But mass will remain the same.

Unit of mass

• The SI unit for measuring mass is the kilogram.
• It's symbol is kg.

There is an interesting question that one might ask:
■ How much is one kilogram?
• The answer can be written in steps:
1. One kg is the mass of the cylinder kept at the International bureau of weights and measures near Paris. 
2. Prototypes of this cylinder are supplied to various countries so that, the kg will be same all over the world.
3. The cylinder is made up of platinum-iridium alloy. This special alloy is used so as to avoid corrosion.
4. If corrosion occurs, the mass of the cylinder will change. The mass will increase if particles accumulate on the surface.
5. Let us see the effect in such a situation:
• The mass of the cylinder in a lab has increased from 1 kg to 1.002 kg.
• So all the  standard 1 kg weights based on this cylinder will be faulty.
• A merchant uses one of those faulty weights while selling sugar.
    ♦ On one side of his balance he places that faulty weight.
    ♦ On the other side of the balance he will be placing more than 1 kg of sugar
• So the merchant would lose and the buyers would gain.
6. In 2019, scientists agreed upon a new method for defining 1 kg. In this method, physical objects like cylinders or rods are not required. So the question of corrosion or deformation does not arise. We will learn about this new definition in higher classes.

• Once the kg is fixed, we can use it for measurements of mass.
• In our day to day life, we can measure the mass of various objects using the common balance or an electronic balance.
• For weighing precious metals like gold, we use balances which have more precision. Such balances give mass in grams or milligrams.
• For very large masses also we use the kg.
• Some examples:
    ♦ Mass of the sun = 1.989 ×1030 kg.
    ♦ Mass of the Milky way galaxy = 6.0 ×1042 kg.
• But for very small masses, the kg is inconvenient.
• In such cases, we use the unified atomic mass unit.
• It’s symbol is u.
• We have learned about it in our earlier classes (Details here).
• Some examples:
    ♦ Mass of a proton = 1 u.
    ♦ Mass of a neutron = 1 u.
    ♦ Mass of a sodium atom = 22.989 u.

• There are special methods for measuring the following:
    ♦ Very large masses like those of planets and stars.
    ♦ Very small masses like those of protons and neutrons.
• We will see those special methods in later chapters.

Range of Masses

We will write about the range in steps:
1. In our day to day life, we come across ordinary masses such as:
    ♦ Mass of sugar bought from grocery store = 2 kg.
    ♦ Mass of a fully loaded book shelf = 350 kg.
    ♦ Mass of a car = 950 kg.
2. But when we do problems in science, we will have to deal with a wide range of masses.
• On the left end of that range, we have very small masses.
Some examples:.
    ♦ Mass of an electron = 9.1 × 10-31 kg.
    ♦ Mass of a proton = 1.67 × 10-27 kg.
• On the right end of that range, we have very large masses.
Some examples: 
    ♦ Mass of the earth = 5.972 × 1024 kg.
    ♦ Mass of the sun = 1.989 × 1030 kg.
3. In addition to the above two extremes, we must be able to deal with any masses which fall in between them.


Measurement of time

• We use a watch or a clock to measure time.
• A stop watch is convenient to measure the 'time duration' in which an event takes place.
• For example, the time duration required by a car to travel from point A to point B.
■ The SI unit for time is the second. It's symbol is s.
• Let us see how the second is defined. We will write it in steps:
1. An ordinary pendulum clock uses the ‘oscillation of a pendulum’ to measure time.
• A pendulum usually completes one back and forth movement (that is one oscillation) in one second.
• The oscillations are recorded by springs and gears, which transmit the information to the clock needles.
2. In modern times, we have a quartz crystal in the place of a pendulum.
• The crystal vibrates when an electric current passes through it.
• These vibrations are recorded by digital counters.
(One vibration is one complete to and fro motion).
• But the crystals are prone to manufacturing defects. Faulty crystals will vibrate at different rates at different times. This will lead to wrong measurements.
(Rate of  vibration is the number of vibrations in one second).
3. So scientists developed a new method in which the rate of vibration does not vary.
• In this method, the vibration of the cesium atom is used.
• This vibration is consistent under all conditions.
■ The clock based on this method is called the cesium atomic clock.

To appreciate the merits of a cesium clock, we must first see the demerits of ordinary clocks. We will write it in steps:

1. Consider a watch which uses quartz crystal.
• When electricity is passed through the crystal, it must vibrate 32768 times in each second.
• These vibrations are recorded by digital counters.
2. But if there is appreciable changes in surrounding temperature or pressure, the crystal will not be vibrating at the required rate of 32768 times per second.
• The rate may increase of decrease.
3. Because of this, the watch will gain or lose time.
An example:
• Let us say, in reality 30 s have passed. But the watch shows 35 seconds.
    ♦ The watch has gained 5 s in 30 s.
Another example:
• Let us say, in reality 37 s have passed. But the watch shows only 35 seconds.
    ♦ The watch has lost 2 s in 37 s.
4. The above given examples are for the purpose of illustration only .
• Modern quartz watches lose or gain by only about 1 s a year.
• 1 year = 365 × 24 × 60 × 60  = 31536000 s.
An example:
• In reality 31536000 s have passed. But the watch shows 31536001 seconds.
    ♦ This is a gain of 1 s in a year.
Another example:
• In reality 31536000 s have passed. But the watch shows 31535999 seconds.
    ♦ This is a loss of 1 s in a year.
5. This much error is negligible in our day to day life. Besides, 1 s lost in a year may be compensated by 1 s gained in the next year.
• But for scientific purposes, this is not acceptable. So scientists devised the cesium atomic clock.
6. The rate of vibration in cesium atom is very consistent.
The gain or loss will be as follows:
• Let us say, in reality 31536000 s have passed. The cesium clock shows (31536000 s + 3 𝝁 s).
    ♦ This is a gain of 3 microseconds in a year.
(1 microsecond is 11000000 th of a second)
• Let us say, in reality 31536000 s have passed. The cesium clock shows (31536000 s - 3 𝝁 s)
    ♦ This is a loss of 3 microseconds in a year.
■ So we can say that cesium clock have great accuracy.
7. Since we are able to measure time with such a high degree of accuracy, time has found a place in the definition of metre:
■ 1 m is the distance traveled by light in vacuum during a time interval of 1299,792,458 of a second.


Range of time

We will write about the range in steps:
1. In our day to day life, we come across ordinary duration of time such as:
    ♦ Time required to walk to school.
    ♦ Time duration of a football match.
    ♦ Time required by the car to travel from town A to town B.
2. But when we do problems in science, we will have to deal with a wide range of time duration.
• On the left end of that range, we have very small duration.
Some examples:
    ♦ Life span of the most unstable particle (10-24 s).
    ♦ Time required by light to travel from one side of a nucleus to the other (10-22 s).
• On the right end of that range, we have very large duration.
Some examples: 
    ♦ Time since the dinosaurs became extinct (1015 s).
    ♦ Age of the universe (1017 s).
3. In addition to the above two extremes, we must be able to deal with any duration which fall in between them.


Measurement of temperature
A detailed description about the units for measuring temperature can be seen here.

In the next section, we will see accuracy and precision of measuring instruments.

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