Category: Physic Tutorials

A simple pendulum consists of a bob attached to a string the other end of which is suspended from a firm support. If a simple pendulum is undisturbed, it is in equilibrium. To start it swinging, it must be pulled to one side of its equilibrium position. The forces on the mass are unbalanced and so it moves back towards its equilibrium position. The mass swings past this point and continues until it comes to rest momentarily at the other side; the process is then repeated in the opposite direction. Note that a complete oscillation is from right to left and back again. This is why a simple pendulum is an example of a simple harmonic motion.

Time Period Formula of a Simple Pendulum

Before I give the expression for the time period formula for a simple pendulum, there is need to list the assumptions made.

• In a simple pendulum, the string is inextensible
• The initial angle of oscillation is small

Note that period is defined as the time taken to complete one oscillation.

ω₀ = 2πf

F = 1/T (f is frequency, T is the period)

ω₀ = 2π/T

So , make T the subject of the equation

T = 2π/ω₀ = 2π × √(L/g)

The period of a simple pendulum is affected by the following

• Length of the pendulum
• Acceleration due to gravity

Energy transformation

When the pendulum swings from end to end, the energy of the system changes from potential to kinetic and vice-versa, but at each stage of the swing, the total energy remains constant.

The pendulum swings from the highest point A through the centre of the swing C, to the other highest point B. At C, the bob is at the lowest position. Note this is a mechanical arrangement that demonstrate periodic motion. Therefore the potential energy of the system is zero. Also at C, the speed of the pendulum is maximum and so the kinetic energy is maximum at this point.

As the bob moves from C to B, the K.E at C is gradually transformed to P.E, with potential energy becoming maximum at B which is at a height h above C. At the point B, the total energy is potential energy and is equal to mgh. This is also P.E at A which is at the height above C as B.

We can find the maximum velocity of the swinging bob, which occurs as the bob passes through C. let this velocity be v_max. Since total energy is always conserved, we have

1/2mv²_max = mgh

Hence v²_max = 2gh

V_max = square root of (2gh)

At A and B, the energy is all P.E. At C, energy is all K.E. At any intermediate point e.g P, the energy is partly potential and partly kinetic. At each point , however, the total energy (P.E + K.E) is constant and is equal to mgh.

Energy is the ability to do work, and mechanical energy is one of the forms of energy. This form of energy is all around us. For example, a child on a swing is one of the familiar examples of the conservation of mechanical energy. So, in this article, I will discuss the types and uses of this form of energy.

There is a need to understand the meaning of mechanical energy before diving into the full details. Mechanical energy is either kinetic or potential energy; it can even mean the sum of potential and kinetic energy. So, to put it in simple terms, it is either energy in motion or energy stored in an object.

Is Mechanical Energy Potential or Kinetic?

The answer is Yes. Mechanical energy can either be potential or kinetic energy. This is well spelt out when I defined mechanical energy.

Applying the law of conservation of energy to mechanical energy – it shows that the sum of potential energy and kinetic energy is always constant for a given body. Still, the energy may change from kinetic to potential or viz a viz. For example, when the pendulum swings from end to end, the system’s energy changes from potential to kinetic and vice-versa, but at each stage of the swing, the total energy remains constant.

Types

Mechanical energy is classified into two types – potential energy and kinetic energy.

Potential Energy

It is stored energy or the energy a body possesses by its position or state. Such stored energy is used to do work when the body is free to move. A heavy stone on top of a table has potential energy. when allowed to fall on a glass plate on the floor, it will shatter the plate. The stone’s potential energy due to its position above the floor, is expended in shattering the plate.

A body may have potential energy due to its position in a force field. If the force field is the gravitational field, the body is said to possess gravitational potential energy. the stone resting on top of a table has gravitational potential energy due to its height above the ground level. If the body is of mass m and the height of the table is h, then the gravitational potential energy is given by

E_p = mgh

Kinetic Energy

It is the energy possessed by a body by its position. While gravitational potential energy depends on the body’s mass, its height above a reference level, and the acceleration due to gravity, kinetic energy depends only on the body’s mass and velocity. The kinetic energy of a body in motion is given by

K.E = ½ mv²

Examples

The examples of kinetic and potential energy are also the same as mechanical energy.

Potential energy

• A magnet at rest in a magnetic field
• An electric charge at rest in an electric field
• A coiled spring when stretched or compressed
• Chemical potential energy is released when petrol, wood, and other fuel sources burn

Kinetic energy

• A student running a race
• An object falling freely under gravity
• Wind or air in motion
• Electrical charges in motion
• A moving hammerhead

The mass of a body is usually measured by comparing it with the standard masses. So in this article, I will discuss the instrument for measuring mass and the one for measuring weight.

mass

Mass is defined as the quantity of matter in a body. The mass of a body is measured with a balance of which there are various types – a beam or chemical balance or a lever balance.

To measure with a beam balance, the object is placed on the left-hand scale pan and standard masses are placed on the right-hand scale pan. The working of the beam balance is based on the principle of moments’ and its reading accuracy could be up to 0.001 grams.

Read: Temperature measurement

weight

The weight of an object is measured using a spring balance. The balance is calibrated using Hooke’s law. The balance, therefore, has a uniform scale and measures the weight directly.

The object whose weight is required is suspended from the hook of the spring balance. The weight causes the spring to stretch moving the pointer which directly indicates the weight on the graduated scale.

Energy is the ability and capacity to do work. Also, energy can be transformed from one form to another. It is a conserved quantity.

There are two main sources of energy: Renewable and Non-renewable source of energy.

Renewable sources of energy are the ones that are available abundantly in nature and are sustainable. They are referred to as Green energy. These energy resources can be naturally replenished and are safe for the environment.

The major types of renewable energy are:

• Biomass from plants
• Hydropower from flowing water
• Solar energy from the sun
• Wind energy
• Geothermal energy
• Tidal energy

Non-renewable sources: this type of energy is found underneath the earth. These energy resources replenish at different speeds, and it can take up to millions of years to replenish.

The main examples of non-renewable energy are:

• Coal
• Crude oil
• Natural gas
• hydrocarbon gas liquids
• Nuclear energy

Uses

1. Heat energy is used for cooking, pressing clothes, and drying things. Heat energy is also used for welding, purification, and expansion of metals
2. Nuclear energy is used in power generators, transportation, agriculture, and medicine.
3. Solar energy is used for electrification
4. Mechanical energy is used to drive vehicles and automobile machines
5. Animals and human beings see things around clearly due to light energy.
6. Chemical energy in foods enhances all living organisms to carry out their daily activities
7. Green plants utilize radiant energy for photosynthesis.
8. Sound energy is used in communication
9. Electrical energy is used to power our appliances, television sets, computer sets, radio sets, e.t.c
10. It is use for cooling

Progressive wave is the propagation of energy as a result of vibrating waves that move energy from place to place. Longitudinal and Transverse waves are the two types of progressive waves.

The distinction between the two types of waves depends on the direction of the vibrating particles with respect to the direction of travel of the wave.

Longitudinal

In this type of wave, the particles of the medium vibrate parallel to the direction of the wave velocity. Longitudinal waves are readily formed on a stretched spring or ‘slinky’ by alternatively compressing and expanding one end or by moving the slinky to and fro in the direction of its length.

A series of compressions and expansions or rarefactions propagate along the slinky or spring. The compressions are areas where the coil is momentarily close together, rarefactions or expansions are areas where the coils are momentarily far apart. Compressions and rarefactions in longitudinal waves correspond to the crests and troughs, respectively, of a transverse wave.

Examples: Sound Waves, Tsunami waves, seismic-P waves, and vibration in spring.

Transverse

In this type of wave, the particles of the medium vibrate at the right angle to the direction of the wave velocity.

Examples: Light waves, radio waves, and waves produced in a rope or string.

Differences

Transverse	Longitudinal
It can be plane polarized	It can’t be plane polarized
Wave particles move perpendicularly to the direction of the wave velocity	Wave particles move in the same direction to the direction of the wave velocity

Note the condition for a wave to be plane polarized is for the vibrations to be in just one direction normal to the direction in which the wave is traveling.

Thermos Flask is one of the applications of the three modes of heat transfer in physics. The principal features of the flask will be shown in the diagram below. Because of all the features in a thermos flask, heat loss or gained by the flask from the surroundings is very small. Hence the flask keeps cold liquid and hot liquids for a long time.

Diagram and Working Principles

The flask has a double-walled glass vessel with a vacuum between the walls. The vacuum is to reduce the loss or gain of heat by conduction or convection. The double walls of the glass vessel are silvered on the vacuum side. This minimizes the loss or gain of radiant heat to the outside.

The bottom of the flask rests on cork supports, and the mouth of the flask is also closed by a cork stopper or hollow plastic stopper with air inside. Cork, plastic, and air materials are all poor conductors; hence, no heat is lost or gained by conduction.

The cork stopper prevents heat loss by evaporation and convection if the flask contains hot liquid. The glass vessel is placed in an outer container made of plastic.

The above has explained the function of the key features of the thermos flask to reduce heat loss or gain.

Read: Thermal conductivity explained

This is one of the questions that students want to know, and I will answer in this article. The question is always in this form “ hot water in an ideal thermos flask is an example of ?”

From what I have explained above, hot water inside a thermos flask cannot change energy and matter with the environment. So, this made the flask an example of an isolated system. You know that in an isolated system, energy is conserved.

Also, in the flask, the heat energy remains constant. This makes it an adiabatic system.

Therefore, hot water in a thermos flask is an example of an isolated and adiabatic system.

This article will look at the dimensions of impulse and momentum and check whether the two dimensions are the same.

For instance, a question was asked in this line in a particular exam. The question says the dimensional formula for impulse is the same as (a) Momentum (b) force (c) rate of change of momentum (d) torque

Dimensional analysis is the study of the relation between physical quantities based on their units and dimensions. It is used to convert a unit from one form to another. Also, it will be easy to know the S.I. base unit of any quantity in physics.

To find the dimension of any quantity, we make use of length, mass, and time. The symbols that are used to specify length, mass, and time are [L], [M], [T], respectively. They are usually enclosed in brackets.

Impulse

The first thing to do is to write the formula for impulse. Impulse is expressed as force x time

Mathematically,

Impulse = force (F) x time (T)

The next thing is to find the dimension of force and that of time

Force = mass x acceleration = MLT^-2

Time = T

So, impulse = MLT^-2 x T = MLT^-1

Therefore, the dimension of impulse is MLT^-1

Momentum

Like I did for impulse, I will first write the formula for momentum. Momentum is mass x change in velocity

Momentum = mass x velocity

Mass = M

Velocity = LT^-1

Momentum = M x LT^-1 = MLT^-1

Therefore, the dimension of momentum is MLT^-1

Read: Dimension of pressure, power, force, energy

Impulse and momentum have the same dimension from what I have explained above. To also validate our result, let’s check Newton’s second law of motion

It states that the rate of change in the momentum of an object is proportional to the force applied and takes place in the direction of the force.

Mathematically, Force = m(v-u) /t

If cross multiply,

F *t = M(V-U)

So, this shows that impulse is equal to momentum.

In this article, I will list some instruments and what they are used to measure. Several instruments are used for different purposes. And it is in their purpose lies their design.

Fathometer: It is used to measure the depth of the ocean. It also produces an echo. It is used on ships to determine the depth of the ocean. Also, fathom is the unit used to measure the depth of the ocean.

Galvanometer: It is an electromechanical measuring instrument that is used for detecting the presence of small current and voltage. It works by deflecting a pointer in response to an electric current flowing through a coil in a constant magnetic field.

Udometer: It is also known as a rain gauge used by a meteorologist or hydrologist to measure the amount of liquid precipitation of a predefined area over a period of time.

Dynamometer: It is a measuring device used to determine the torque, force, speed, and power required to operate the drive on a machine or motor. There are two categories of dynamometers and they are power absorption and power transmission.

Anemometer: It is used to measure wind speed and wind pressure.

Pyrometer: It is an instrument that measures temperature, and this is done by measuring radiation from the object without having to be in contact.

Altimeter: It is a device that measures altitude i.e. the distance of a point above sea level.

Read: Laboratory apparatus in schools and their uses

Other instruments include,

A hydrometer is used to measure density or specific gravity

A manometer is used to measure the pressure of a particular gaseous or liquid matter, while a barometer is used for measuring atmospheric pressure

A fluxmeter is used to measure Magnetic Flux.

An ammeter is used for measuring the current in a circuit.

A voltmeter is used to measure the voltage or potential difference between two points in an electrical or electronic circuit.

Instruments	Uses
Fathometer	Measures depth of ocean
Galvanometer	Measures electric current
Udometer	Measures amount of rainfall
Dynamometer	Used to determine the torque, force, speed, and power required to operate the drive on a machine or motor
Anemometer	For measuring wind speed
Pyrometer	For measuring temperature
Altimeter	To measure altitude
Hydrometer	To measure specific gravity
Manometer	For measuring pressure
Fluxmeter	To measure magnetic flux
Ammeter	To measure electric current in a circuit
Voltmeter	To measure voltage in a circuit

Read: ICT gadgets and their uses

Thermal conductivity is the ability of a metal to conduct heat. Though most metals are good conductors, their thermal conductivities differ from metal to metal. It is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’.

The thermal conductivity of a material is described by the following formula:

K = (QL)/(AΔT)

Where,

    K is the thermal conductivity in Wm^-1k^-1

    Q is the amount of heat transferred through the material in Joules/second or Watts

    L is the distance between the two isothermal planes

    A is the area of the surface in square meters

    ΔT is the difference in temperature in Kelvin

Derivation

From K = (QL)/(AΔT)

The unit of Q is Joules/second or Watts i.e. the unit of power

The unit of L is meter (m)

A which is the area has unit of m²

ΔT has S.I unit of Kelvin

Then substituting all these into the above expression

K = Watt * m/m²K

K = Wm^-1k^-1

Therefore, the S.I unit of thermal conductivity is watt per meter per kelvin (Wm^-1k^-1). This can also mean Joule per second per meter per kelvin (Js^-1m^-1k^-1)

Read: Differences between heat and specific heat capacity

In other to convert degree Celsius to Fahrenheit, you will have to make use of an equation. The equation can also be used vice-versa.

There are three types of scales for measuring temperature, and they are

• The Celsius scale
• The Fahrenheit scale
• The absolute scale (Kelvin)

The lower and upper fixed point for a Celsius scale is 0^oc to 100^oc while for a Fahrenheit scale, it is 32^of and 212^of.

In order to covert, you will use c/5 = f-32/9. The c represent the value for the Celsius while the f represents the value for the Fahrenheit.

Read: Temperature measurement

50C

c/5 = f-32/9

c = 50

substitute, 50/5 = f-32/9

10/1 = f-32/9

Cross multiply

10*9 = 1(f-32)

90 = f -32

Make f the subject of the equation

F = 90 +32 = 122

Therefore, 50c to Fahrenheit is 122^oF

30C

c/5 = f-32/9

c = 30

substitute, 30/5 = f-32/9

6/1 = f-32/9

Cross multiply

6*9 = 1(f-32)

54 = f -32

Make f the subject of the equation

F = 54 +32 = 86

Therefore, 30c to Fahrenheit is 86^oF

60C

c/5 = f-32/9

c = 60

substitute, 60/5 = f-32/9

12/1 = f-32/9

Cross multiply

12*9 = 1(f-32)

108 = f -32

Make f the subject of the equation

F = 108 +32 = 140

Therefore, 60c to Fahrenheit is 140^oF

40C

c/5 = f-32/9

c = 40

substitute, 40/5 = f-32/9

8/1 = f-32/9

Cross multiply

8*9 = 1(f-32)

72 = f -32

Make f the subject of the equation

F = 72 +32 = 104

Therefore, 40c to Fahrenheit is 104^oF

45C

c/5 = f-32/9

c = 45

substitute, 45/5 = f-32/9

9/1 = f-32/9

Cross multiply

9*9 = 1(f-32)

81 = f -32

Make f the subject of the equation

F = 81 +32 = 113

Therefore, 45c to Fahrenheit is 113^oF

100C

c/5 = f-32/9

c = 100

substitute, 100/5 = f-32/9

20/1 = f-32/9

Cross multiply

20*9 = 1(f-32)

180 = f -32

Make f the subject of the equation

F = 180 +32 = 212

Therefore, 100c to Fahrenheit is 212^oF