CONCEPT OF TIME AND ITS MEASUREMENT

Time is defined as the duration of an event and its measured in seconds. Measurement of time works on the principle of constant oscillation. The standard unit of time is seconds (s).

Examples of measuring devices are

1. Ticker - Tape Timer

2. Stop watch / clock

3. Sand clock

4. Simple Pendulum

5. Heart - Beat

Ticker Tape Timer

The Ticker Tape Timer is a piece of apparatus that we use to measure time. 

It makes dots on a paper tape. The amount of dots depends on its frequency. 

Ticker Tape Timer

Note:

We have to count the number of SPACES and not the number of dots themselves to measure the time taken. 

The first dot at the direction of movement is the starting dot.

Example:

A ticker tape timer makes 40 dots in 1 second. The result of an experiment to find the average speed of a toy car is shown below.

What is the average speed of the toy car?

Answer:

time = 1/40 * 10 = 0.25 s

speed = 0.6 / 0.25 = 2.4 m/s

STOP WATCH / CLOCK

A stopwatch is used to measure the time interval of an event.

Types of stopwatch 

1.  Digital stopwatch 

2.  Mechanical stopwatch 

How to read Digital stop watch?

It is commonly used in laboratories,it can measure a time interval up to 0.01 second.It starts to indicate the time lapsed as the start/stop button is pressed.As soon as start/stop button is pressed again,it stops and indicates the time interval recorded by it between start and stop of an event.A reset button restores its initial zero setting.

How to read analog or Mechanical stopwatch

A mechanical stop watch can measure a time interval up to 0.1 second.It has a knob that is used to wind the spring that powers the watch.It can also be used as a start stop and reset button.The watch starts when the knob is is pressed once.When pressed second time,it stops the watch while the third press brings the needle back to zero.

SAND CLOCK OR HOUR GLASS

An hourglass (or sandglass, sand timer, or sand clock) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material from the upper bulb to the lower one. Factors affecting the time interval measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty. Depictions of hourglasses in art survive in large numbers from antiquity to the present day, as a symbol for the passage of time.

SIMPLE PENDULUM

A pendulum is an instrument which is mostly used in the laboratory to measure time. The pendulum swings right and left. The time taken or the time of oscillation is determined through this instrument.

Pendulum clock has seconds hand made in form of the pendulum.It oscillates in order to tick the minute hand and 60 oscillations of the seconds hand makes a minute.

HEART - BEAT

Heart beat is a natural way of counting. It is mostly used in medical line. The pumping of blood in the body. An increase in heart beat is an increase in blood pressure and vice versa.

MASS AND WEIGHT

What is Mass?
The quantity of matter present in a body is called Mass. It remains unchanged irrespective of the shape, volume or position of the body. Its numerical value remains constant. It is a fundamental property of a body and numerical measure of inertia. In physics, we can classify mass into two types namely gravitational mass and inertial mass.
If we compare the masses of the body by using a beam balance against standard masses then the gravitational mass of a body could be determined. This is done to eliminate the gravitational factor. The measure of a body’s resistance to its acceleration while responding to some external force is called inertial mass.
The symbol to represent mass is m and the SI unit of mass is kilogram
                                          

What is Weight?

The force exerted by the gravity on a body due to which it is pulled towards the Earth is called the weight of a body. It is measured by mass of a body times the acceleration due to gravity.

W = mg

where, W = Weight of a body

M = Mass of the body

g = Acceleration due to gravity. The value of it on Earth has a constant value of 9.8 m/s2 

The weight of a body varies at different places as it depends on acceleration due to gravity. The weight of a body on Earth would remain constant whereas the weight on moon would change as the acceleration due to gravity on moon is one-sixth to that of Earth.

                       

WEIGHT (W) = MASS(M) X ACCELERATION DUE TO GRAVITY(g)

Relation Between Mass & Weight

The relation between mass and weight of a body is defined by Newton’s Second Law of Motion. The law as stated by Newton goes by “Force is equal to the change in momentum (mv)per change in time. For a constant mass, force equals mass times acceleration”

F = m×a

F = Force
m = mass
a = acceleration

When this acceleration ‘a’ is due to gravity ‘g’ then the force applied on or exerted by the body becomes the weight of the body

Weight of the body = Mass of the body ×× Acceleration due to gravity

Example: Calculate the weight of a body given the mass of the body = 4kgs

Solution: Weight of the body = Mass ×$\times$ Acceleration = 4kgs×9.8m/s2= 39.2N

Unit of Mass & Weight:

The international system ff units (SI)of mass is kilogram and that of weight is Newton. The Centimeter-Gram-Second (CGS)unit of mass is gram and that of weight is Dyne

Kilogram and gram are the basic unit of mass. While kilogram is the unit of mass of larger body having a greater quantity of matter, a gram is the unit of mass of smaller body having less amount of matter. 

Relation between mass and weight:

1 kilogram = 1000 grams

Newton is the SI unit of force. It is the amount of force required by a body of mass one kilogram to produce an acceleration of one meter per Second Square
Dyne is the CGS unit of force. It is the amount of force required by a body of mass one gram to product an acceleration of one centimeter per square second

Relation between Newton and Dyne:

1 Newton = 1,00,000 Dyne= 105 Dyne

Effect of Gravity

Effect of gravity on mass – Mass of a body is constant irrespective of its place and position. There is no effect of gravity on mass. It remains the same be it on Earth or any other planet like Moon even though the acceleration due to gravity value keeps on changing at different planets

Effect of gravity on weight – Weight is how heavy an object is in a gravitational field. The weight of a body keeps on decreasing at higher altitude where it is furthest away from the center of gravity of Earth. They are directly proportional to each other. The acceleration due to gravity on Moon is one-sixth to that of Earth so the weight also becomes 16 ,16th to that on Earth.

Difference Between Mass & Weight

Definition: Mass is defined as the amount of matter with which it is made up of, regardless of its configuration or any force acting on the body. Weight is the computation of the force of gravity acting on a body and it depends on the value of acceleration due to the gravity of the place in which the body resides.

Gravitational effect: Mass of a body being constant at any place is unaffected by the gravity whereas weight of an object is directly proportional to the value of gravity of that place.

Unit of Measurement: The S.I and C.G.S unit of mass is kilogram and gram respectively whereas that of weight is Newton and dyne respectively.

Device used for measurement: For mass the device used for measurement could be lever balance, beam balance, pan balance or any electronic device whereas the device used for measuring weight is spring balance.

Type of quantity: Mass is a scalar quantity having the only magnitude of the body whereas weight is a vector quantity having both magnitude of the body and direction of the force.

Examples

i) Calculate the weight of a car with a mass of 1000 kg. Given, gravity on the Earth's surface is 10 newtons per kilogram

Solution: 
Weight = Mass ×$\times$ Gravity

           = 1000 ×$\times$ 10

   = 10,000 Newtons

ii) An astronaut has a mass of 50 kg on Earth, what is the astronaut's mass on the Moon? Given, gravity on the Moon is 1.6 newtons per kilogram.

Solution:

Mass is independent of place or position, so the astronaut's mass on the Moon and that on Earth is the same

Therefore, Astronaut's mass on the Moon = Astronaut's mass on the Earth

 
                                                             = 50 kgs

Position , Distance and Displacement

Content

Position, displacement and distance

In this module, we are only talking about motion in a straight line. For a horizontal line, there are only two directions to consider: right and left. For a vertical line, the two directions are up and down. We choose a point O on the line, which we call the reference point or origin. For convenience, we will measure distance in metres and time in seconds.

Position

The line is coordinatised and referenced from a point O, the origin. For a horizontal line, the convention is that positions to the right of O are positive, and positions to the left are negative.

For example:

• The position of the particle at B is 3 m.
• The position of the particle at A is −4m.

The position of a particle is often thought of as a function of time, and we write x(t) for the position of the particle at time t#.

Displacement

The displacement of a particle moving in a straight line is the change in its position. If the particle moves from the position x(t1) to the position x(t2), then its displacement is x(t2)−x(t1)over the time interval [t1,t2]. In particular, the position of a particle is its displacement from the origin.

For example:

• If a particle moves from O to B, its displacement is 3 m.
• If a particle moves from O to A, its displacement is −4m.
• If a particle moves from A to B, its displacement is 7 m.
• If a particle moves from B to A, its displacement is −7m.

Position and displacement are vector quantities, that is, they have both magnitude and direction. In this module, we are dealing with vectors in one dimension. The sign of the quantity (positive or negative) indicates its direction. The absolute value of the quantity is its magnitude.

Distance

The distance is the 'actual distance' travelled. Distances are always positive or zero.

For example, given the following diagram, if a particle moves from A to B and then to O, the displacement of the particle is 4 m, but the distance travelled is 10 m.

Example

A particle moves along a straight line so that its position at time t$t$ seconds is x(t) metres, relative to the origin. Assume that x(0)=0, x(3)=2and x(6)=−5, and that the particle only changes direction when t=3. Find the distance travelled by the particle from time t=0 to time t=6.

Solution

The distance travelled is 2+7=9metres.

Summary

• The position of a particle moving in a straight line is a vector which represents a point P on the line in relation to the origin O. The position of a particle is often thought of as a function of time, and we write x(t) for the position of the particle at time t.
• The displacement of a particle moving in a straight line is a vector defined as the change in its position. If the particle moves from the position x(t1) to the position x(t2), its displacement is x(t2)−x(t1) for the time interval [t1,t2].
• The distance travelled by a particle is the 'actual distance' travelled.

What is the difference between distance and displacement?

1. Distance is a scalar measure while displacement is a vector.
2. Displacement is indicated with an arrow while distance is never indicated with an arrow.
3. Distance only considers magnitude while displacement takes into account both magnitude and direction.
4. Displacement can have both positive and negative values while distance can only have positive values.
5. The symbol delta Δ is used for displacement while this is not the case for distance.
6. Distance can be used to calculate speed given time, while displacement can be used to calculate velocity given change of distance (displacement), over time.
7. Displacement is always measured along a straight line path, while distance can be measured along a non-straight path.

MEASUREMENT OD LENGTH (DISTANCE BETWEEN TWO POINTS)

SI unit for length is metre (m). It is a scalar quantity.

Things you need to know:
Accuracy refers to the maximum error encountered when a particular observation is made.
Error in measurement is normally one-half the magnitude of the smallest scale reading.
Because one has to align one end of the rule or device to the starting point of the measurement, the appropriate error is thus twice that of the smallest scale reading.
Error is usually expressed in at most 1 or 2 significant figures.


Tape

Equipment: It is made up of a long flexible tape and can measure objects or places up to 10 – 50 m in length. It has markings similar to that of the rigid rule. The smallest marking could be as small as 0.1 cm or could be as large as 0.5 cm or even 1 cm.

How to use: The zero-mark of the measuring tape is first aligned flat to one end of the object and the tape is stretched taut to the other end, the reading is taken where the other end of the object meets the tape.

Accuracy: ± 1 cm


Rule

Equipment: It is made up of a long rigid piece of wood or steel and can measure objects up to 100 cm in length. The smallest marking is usually 0.1 cm.

How to use: The zero-end of the rule is first aligned flat with one end of the object and the reading is taken where the other end of the object meets the rule.

Accuracy: ± 0.1 cm

Vernier Caliper

Equipment: It is made up of a main scale and a vernier scale and can usually measure objects up to 15 cm in length. The smallest marking is usually 0.1 cm on the main scale.

It has:
a pair of external jaws to measure external diameters
a pair of internal jaws to measure internal diameters
a long rod to measure depths

How to use: The jaws are first closed to find any zero errors. The jaws are then opened to fit the object firmly and the reading is then taken.

Accuracy: ± 0.01 cm

Micrometer Screw Gauge

Equipment: It is made up of a main scale and a thimble scale and can measure objects up to 5 cm in length. The smallest marking is usually 1 mm on the main scale (sleeve) and 0.01 mm on the thimble scale (thimble). The thimble has a total of 50 markings representing 0.50 mm.

It has:
an anvil and a spindle to hold the object
a ratchet on the thimble for accurate tightening (prevent over-tightening)

How to use: The spindle is first closed on the anvil to find any zero errors ( use the ratchet for careful tightening). The spindle is then opened to fit the object firmly (use the ratchet for careful tightening) and the reading is then taken.

Accuracy: ± 0.01 mm

Parallax Error

For accurate measurement, the eye must always be placed vertically above the mark being read. This is to avoid parallax errors which will give rise to inaccurate measurement.





Parallax errors affects the accuracy of the measurement. If you consistently used the incorrect angle to view the markings, your measurements will be displaced from the true values by the same amount. This is called systematic error.

However, if you used different angles to view the markings, your measurements will be displaced from the true values by different amounts. This is called random error.
Parallax error for micrometer screw gauge:




Zero Error
Zero Errors of Vernier Caliper

When the jaws are closed, the vernier zero mark coincides with the zero mark on its fixed main scale.

Before taking any reading it is good practice to close the jaws or faces of the instrument to make sure that the reading is zero. If it is not, then note the reading. This reading is called “zero error”.

The zero error is of two types:
Positive zero error; and
Negative zero error.



Positive Zero Error

If the zero on the vernier scale is to the right of the main scale, then the error is said to be positive zero error and so the zero correction should be subtracted from the reading which is measured.

Negative Zero Error

If the zero on the vernier scale is to the left of the main scale, then the error is said to be negative zero error and so the zero correction should be added from the reading which is measured.

Zero Error for micrometer screw gauge

Positive Zero Error

If the zero marking on the thimble is below the datum line, the micrometer has a positive zero error. Whatever reading we take on this micrometer we would have to subtract the zero correction from the readings.

Negative Zero Error

If the zero marking on the thimble is above the datum line, the micrometer has a negative zero error. Whatever readings we take on this micrometer we would have to add the zero correction from the readings.

Note: You do not have to memorise

positive error = subtract, negative error = add, just think this through for a while. It is rather straightforward and intuitive.