Resultant force definition

What is the resultant force?

A resultant force is defined as a total force acting on the body along with their directions. 

On the other words, it is the single force obtained by combining a system of forces acting on a rigid body and it has the same effect on the rigid body as the original system of forces.

The resultant force may be determined by the following laws :

Parallelogram law of forces :

By this law, two forces acting simultaneously on a particle and it can be represented in magnitude and direction by two adjacent sides of a parallelogram, then their results may be represented in magnitude and direction by the diagonal of a parallelogram which passes through their point of intersection. 

Similar kind of application applicable for triangle, polygon and for similar types of another shape. 

Resultant of two or more intersecting forces found :

Where two or more intersecting forces are found then for solving resultant of that forces steps given below :

Step -1: First of all resolving all the horizontal forces 
Step -2: Then resolving vertical forces 
Step - 3: Then put all data in the below equation and equate. 
Step - 4: Answer will be the resultant force that what we find. 

R = √ ( ∑horizontal force ) ² + ( ∑vertical force )²

A number of force acting on a particle will be called in equilibrium when :

∑ horizontal force = 0

∑ vertical force = 0

Resultant force for the two forces that are not parallel or any kind of forces :

Step - 1: Draw a free-body diagram of the object.
Step - 2: Draw coordinate axes on the free-body diagram.
Step -3: Decompose the forces acting on the object into x and y components.
Step - 4: Calculate the x and y component of the resultant force by adding the x and y components of all forces.
Step - 5: Find the magnitude and direction of the resultant force by using x and y component. 

Notes :

If the resultant force acting on a stationary object is zero, the object will remain stationary. 

If the resultant force acting on a moving object is zero, the object will carry on moving at the same speed in the same direction.

Force basic definition

Force is a push or a pull that tends to change the state of uniform motion of an object. 

A force can cause an object to accelerate, slow down, remain in original shape or change shape. 

A force while acing on a body may :

• Change the motion of a body 
• Retard the motion of a body 
• Balance the forces already acting on a body 
• Give rise to the internal stresses in a body

In order to determine the effects of a force acting on a body, one must know the following characteristics of the forces. 

• The magnitude of the force
• The line of action of the force  
• The nature of the force 
• The point at which force is acting 

The magnitude of the force is given by in MKS system - kilogram-force ( kgf ) and in SI system - Newton ( N ). 

1 kgf = 9.81 N

There are different types of force. You can check it out below :

• Applied force
• Gravitational force
• Normal force 
• Frictional force 
• Air resistance force 
• Tension force 
• Spring force 

Ericsson cycle

The Ericsson cycle is a thermodynamic cycle that can be invented by John Ericsson in 1840.

What is the Ericsson cycle?

In the Ericsson cycle, two isothermal processes and two constant pressure process are done in a heat engine. 

This cycle is mostly used in a closed cycle gas turbine. 

Process of Ericsson cycle :

The Ericsson cycle consist of four processes following below :

• A reversible isothermal gas expansion process is air as a working fluid which is heated from the heat addition process so work is done during this process.
• A constant pressure heat transfer or isobaric process is the air passed through the re-generator is released as exhaust gas. The heat absorbed by the re-generator is used during the next part of the cycle. 
• A reversible isothermal gas compression process is air is drawn into the engine is compressed and pressurized air drawn into the air storage sink.
• A constant pressure heat transfer is the compressed air at high pressure passe through the regenerator and absorbs the previously stored heat then flows to the piston and cylinder where it gets expands and produces the work.  

Efficiency of Ericsson cycle :

The efficiency of Ericsson cycle is given by :

                                         Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁ 

Although the thermodynamic process of the Ericsson cycle differ from those of the Carnot cycle both cycles have the same value of the thermal efficiency when both are operating between its T₁ and T₂.

The Ericsson cycle doesn't have any practical application but is mainly used in a gas turbine employing a large number of stages with insulators, reheaters and heat exchangers.

Stirling cycle

The Stirling cycle is a thermodynamic cycle that can be invented by Robert Stirling in 1845.

What is the Stirling cycle?

In the Stirling cycle, two isothermal processes and two constant volume process are done in a heat engine. Constant volume process is performed with the help of a re-generator to make this cycle reversible.

Process of Stirling cycle :

The Stirling cycle consist of four processes following below :

• A reversible isothermal gas expansion process is heat addition process from the external source so work is done during this process.
• A constant volume heat transfer process is internal hear transfer takes place from the gas to the re-generator.  
• A reversible isothermal gas compression process is heat rejection to the external sink.
• A constant volume heat transfer is internal heat is transfer from the re-generator to a gas. 

The efficiency of the Stirling cycle :

The efficiency of the Stirling cycle is the same as that of the Carnot cycle. This is due to the fact that this cycle is also reversible as Carnot cycle. So remember that all reversible cycle have the same efficiency.

                                         Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁ 

Also, the COP of the Stirling cycle and Carnot cycle are the same.

Linishing machine

Linishing is a process of using grinding or belt sanding technique to improve the flatness of a surface. The machine that does this is called the linisher or a Linishing Machine.

Linishing process is one types of the metal finishing process.

There are three types of linishing machine are used. List are following below :

• Drum linishing machine 
• Orbital linishing machine 
• Centerless linishing machine 

Linishing machine use in relation to work piece :

• Bent tubes
• Round or Oval tubes 
• Bars 
• Cylindrical rode 
• Metal profiles with square and rectangular section
• Flat surfaces 
• Extremities 

Mainly it used for the preparation of the ends of rubber extrusions that will be fused together to make a closed-loop. 

Now you can check it out some product where the linishing machine used : 

• Shop fittings
• Urban furniture 
• Taps components
• Bathroom fittings 
• Curtain poles 
• Lighting equipment 
• Motorbike handles 
• Car and motorbike exhaust system 
• Bicycle parts 
• Handrails 

What is carnot cycle

The Carnot cycle is a thermodynamic cycle that can be invented by French Physicist Sadi Carnot in 1824.

What is the Carnot cycle?

In the Carnot cycle, two reversible isothermal processes and two reversible adiabatic processes are done in a heat engine.

Process of Carnot cycle :

The Carnot cycle consist of four processes following below :

• A reversible isothermal gas expansion process. From the diagram shown below the ideal gas in the system absorbs some amount of heat from the heat source at a high temperature and then expands thus the work was done on surroundings. 
• A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas expands continuously and does work on surrounding, which causes the system to cool to a lower temperature. 
• A reversible isothermal gas compression process. In this process, work has done surrounding gas and cause a loss of heat.
• A reversible adiabatic gas compression process. In this process, surrounding continue to do work to a gas, which causes the temperature to rise back to high temperature attain in the first process. 

The efficiency of the Carnot cycle :

It can be defined as the ratio of the energy output to the energy input. Here energy output is work done and energy input is heat addition.  

From the calculation,

Q₁ = Heat addition = R T₁ ln v₂ / v₁

W_net = R ln v₂ / v₁ (T₁ – T₂ )

Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁

The large back work is a big drawback of this cycle. 

Assumption of the Carnot cycle :

• No friction at all between the piston and cylinder and also other moving parts of the engine, thus there is no heat generated and lost due to friction.
• There is no transfer of heat with the external atmosphere because the engine is completely insulated.
• There is also no exchange of heat between various parts of the engine.

Rankine cycle vs Carnot cycle

Carnot cycle is two reversible isothermal and two reversible adiabatic process are done in a heat engine. Rankine cycle is a thermodynamic cycle of heat engine that converts heat into mechanical work undergoing the phase change. Let us have a deep insight into the difference between the Rankine cycle and the Carnot cycle. 

Main difference :

The pressure of working fluid is raised from the pressure of condenser to the boiler pressure in Carnot cycle, whereas in the Rankine cycle, the saturated liquid is pumped to the boiler with a pump. 

Difference between Carnot and Rankine cycle :

• The heat addition process is isothermal in case of Carnot cycle, whereas isobaric in Rankine cycle. 
• Heat addition and heat rejection are done by keeping the temperature constant in the Carnot cycle while both are done by keeping the pressure constant in the Rankine cycle. 
• Carnot cycle is a theoretical cycle while the Rankine cycle is a practical cycle. 
• Rankine cycle like other cycles leads to entropy generation due to the heat transfer process, but Carnot cycle doesn’t.
• The efficiency of the Rankine cycle is less than a Carnot cycle.
• Carnot cycle uses air as the working substance while the Rankine cycle uses water as a working substance. 
• Carnot cycle is an ideal cycle for heat engine while the Rankine cycle is ideal for the vapour power cycle. 

What is rankine cycle

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed. 

What is the Rankine cycle?

For each process in the vapour power cycle, it is possible to assume a hypothetical or ideal process which represents the basic intended operation and involves no extraneous effects. 

For the steam boiler, this would be a reversible constant pressure heating process of water to form steam.
For the turbine, the ideal process would be a reversible adiabatic expansion of steam. 
For the condenser, it would be a reversible constant pressure heat rejection as the steam condenses until it becomes saturated liquid. 
For the pump, the ideal process would be the reversible adiabatic compression of this liquid ending at the initial pressure. 

When all these four processes are ideal, the cycle is an ideal cycle, called the Rankine cycle.

The efficiency of the Rankine cycle :

Efficiency is the ratio between energy output to energy input. Here work done is energy output and energy input is heat addition. 

Net work is done = Work done in turbine + Work done in pump 

Net heat transfer = Heat produced in boiler + Heat rejected in the condenser 

ŋ = W_T - W_P / Q_S 

Difference between brayton and rankine cycle

What is the Brayton cycle?

Brayton cycle is a jet engine, the air is sucked, compressed and then released into the atmosphere, thus making an open cycle.

What is the Rankine cycle?

Rankine cycle is a steam engine, the water is boiled, evaporated, used for work and then condensed for re-use, thus making it a closed cycle. 

Main difference :

The working fluid undergoes a phase change in the Rankine cycle whereas in Brayton cycle there is no phase change the working fluid always remains in the gaseous phase.

Let us have a deep insight into the Brayton cycle vs Rankine cycle. 

Difference :

• Brayton cycle consists of two reversible isobaric processes and Rankine cycle consist of two reversible adiabatic processes.
• Both the pump and the steam turbine in the case of the Rankine cycle, and the compressor and the gas turbine in the case of the Brayton cycle operate through the same pressure difference. 
• The average specific weight of air handled by the compressor is less than the same of gas in the gas turbine in Brayton cycle so the work done by the gas turbine is more than the work input to the compressor while in the case of Rankine cycle, the specific weight of water in the pump is much less than the steam expanding in the steam turbine, therefore, steam power plants are more popular than gas turbine plants for electricity generation.
• Brayton cycle operates between a higher pressure ratio than the Rankine cycle for the same capacity.

What is thermocouple

A thermocouple circuit made up from joining two wires of two dissimilar metals so due to the different effect net e.m.f is generated in the circuit which depends on the difference in temperature between the hot and the cold junctions.

This e.m.f can be measured by a microvoltmeter to a high degree of accuracy. The choice of selecting metal depends on the temperature range to be investigated, and copper constantan, chrome-alumni and platinum-rhodium are mostly used combinations. 

Advantages of a thermocouple are that it comes to thermal equilibrium with the system, whose temperature is to be measured, quite rapidly, because its mass is small.

Different effect to generate net e.m.f is :

• Seebeck effect 
• Peltier effect
• Thomson effect 

Electrical resistance thermometer

In the resistance thermometer, the change in resistance of a metal wire due to its change in temperature is the thermometric property. The wire, frequently platinum, may be incorporated in a Wheatstone bridge circuit. The platinum resistance thermometer measures temperature to a high degree of accuracy and sensitivity, which makes it suitable as a standard for the calibration of other thermometers.

In a restricted range, the following quadratic equation is often used :

R = R₀ ( 1 + At + Bt² )

Where,

R₀ = Resistance of platinum wire when it is surrounded by melting ice and A and B are constants.

Gas thermometer

To measure temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. 

The change in the selected characteristics is an indication of the change in temperature and selected characteristics are the thermometric property and reference body which is used is called thermometer.

All thermometers are working examples of the zeroth law of thermodynamics. 

Significance :

They used to calibrate other thermometers. 

Working principle and construction :

Constant pressure gas thermometer :

A small amount of gas is enclosed in bulb B which is in communication via the capillary tube C with one limb of the mercury manometer M. The other limb of the mercury manometer is open to the atmosphere and can be moved vertically to adjust the mercury levels so that the mercury just touches lip L of the capillary. The pressure in the bulb is used as a thermometric property and it is given by :

p = p₀ + ρ_M Z_g

Where,
p₀ = atmospheric pressure 
ρ_M = density of mercury

When the bulb is brought in contact with the system whose temperature is to be measured, the bulb, in course of time, comes in thermal equilibrium with the system.

The gas in the bulb expands, on being heated, pushing the mercury downward. The flexible limb of the manometer is then adjusted so that the mercury again touches the lip L. The difference in mercury level Z is recorded and the pressure p of the gas in the bulb is estimated. Since the volume of the trapped gas is constant, from the ideal gas equation, 

ΔT = V / R * Δp

The temperature increase is proportional to the pressure increase. 

Constant volume gas thermometer :

In a constant-pressure gas thermometer, the mercury levels have to be adjusted to keep Z constant, and the volume of gas V, which could vary with the temperature of the system, becomes the thermometric property. 

ΔT = V / R * ΔV

The temperature increase is proportional to the observed volume increase.

Constant volume gas thermometer is mostly use, since it is simpler in construction and easier to operate. 

Ideal gas

From the experimental observations p-v-T behaviour of the gases given by,

pṽ = ṜT

Where Ṝ is the universal gas constant value of  Ṝ is 8.3141 J / mol K

ṽ is the molar specific volume m³/gmol

Dividing upper equation by the molecular weight µ.

pv = RT

Where v is specific weight m³/gmol

R is the characteristic gas constant

We also get this the equation in terms of total volume V of gas, 

PV = nṜT

PV = mRT

Where n is the number of moles and m is the mass of the gas. An equation can be written for two states of the gas is 

P₁V₁ / T₁ = P₂V₂ / T₂

All equation is called the ideal gas equation of state. At very low pressure or density, all gases and vapours approach ideal gas behaviour.

Celsius temperature scale

The Celsius temperature scale employs a degree of the same magnitude as that of the ideal gas scale, but its zero points are shifted, so that the Celsius temperature of the triple point of water 0.01 degree Celsius or 0.01⁰C. 

If t denotes the Celsius temperature, then 

t = T - 273.15⁰ 

Thus the Celsius temperature ts at which steam condenses at 1-atmosphere pressure 

t_s = T_s - 273.15⁰ 

    = 373.15 - 273.15 = 100.00 ⁰C

Similar measurements for ice points show this temperature on the Celsius scale to be 

0.00 ⁰C.

Measurement of temperature

The temperature of a system determines that the system is in thermal equilibrium with other system or not? 

If a body is at 85⁰ C, it will be 85⁰ C, whether measured by mercury in glass thermometer, resistance thermometer or constant volume gas thermometer. 

If X is the thermometric property, let us arbitrarily choose for the temperature common to the thermometer and to all systems in thermal equilibrium with it the following linear function of X :

Θ(X)  = aX

Where, 

a = arbitrary constant 

Two temperatures on the linear X scale are to each other as the ratio of the corresponding X.

Zeroth law of thermodynamics

Zeroth law of thermodynamics is the basis of temperature measurement. The property which distinguishes thermodynamics from other sciences is temperature. 

One might say that temperature bears as important relation to thermodynamics as the force does to statics or velocity does to dynamics. 

When two bodies maintain at different temperatures are brought into contact, after some time they attain a common temperature and are then said to exist in thermal equilibrium.

Zeroth law of thermodynamics :

When a body A is in thermal equilibrium with a body B, and also separately with a body C, then B and C will be in thermal equilibrium with each other. 

Notes :

In order to obtain a quantitative measure of temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. 
The change in the selected characteristics may be taken as an indication of the change in temperature. The selected characteristics are called thermometric property, and the reference body which is used in the determination of temperature is called thermometer. 

There are five different kinds of thermometer used are following below :

1. Constant volume gas thermometer
2. Constant pressure gas thermometer 
3. Electrical resistance thermometer
4. Thermocouple 
5. Mercury in glass thermometer 

Specific heat and latent heat

What is the specific heat?

Specific heat is the amount of heat required to raise a unit mass of the substance through a unit rises in temperature. 

The symbol c will be used for specific heat. 

C = Q / m * Δt J / kg k 

Where, 

Q = The amount of heat transfer ( J )

m = Mass of the substance ( kg )

Δt = The rise in temperature ( K ) 

Since heat is not a property, so the specific heat is qualified with the process through which exchange of heat is made. 

The product of mass and specific heat ( mc ) is called the heat capacity of the substance. 

For gases, 

If the process is at constant pressure ( c_p ).

If the process is at constant volume ( c_v ).

For solids and liquids, 

The specific heat does not depend on the process. 

What is latent heat?

The amount of heat required to cause a phase change in a unit mass of a substance at constant pressure and temperature.

There are three phases in which matter can exist: solid, liquid, and vapour or gas.

The latent heat of fusion is the amount of heat transferred to melt a unit mass of solid into a liquid. 

OR

to freeze unit mass of liquid to solid. 

The latent heat of vaporization is the quantity of heat required to vaporize unit mass of liquid into vapour. 

OR

to condense unit mass of vapour into liquid. 

The latent heat of sublimation is the amount of heat transferred to convert unit mass of solid to vapour. 

Welding distortion

One of the major problems found with weldments is called distortion. Distortion is caused mainly because of the shrinkage that takes place in weldments. The shrinkage taking place is a weldment depends upon the geometry and type of the weld. 

There are three types of distortions possible in welding :

• Transverse shrinkage occurring perpendicular to the weld line.
• Longitudinal shrinkage occurring parallel to the weld line, which is very small of the order of about 0.1 % of the weld length and hence can be neglected.
• Angular change as a rotation about the weld line.

Now we can check the methods for reducing all three types of shrinkage :

The methods for reducing the transverse shrinkage are :

• Decrease the total weight of the weld metal. 
• Increase the metal deposited in the first pass.

Some other factors which influence the transverse shrinkage are :

• Root opening.
• Joint design.
• Electrode diameter.
• Degree of constraint.

The methods for reducing the angular shrinkage are :

• Fillet welds in a structure are affected by the way the structure is designed and the type of restraint provided.

Control of distortion :

As we saw above, distortions are inevitable in a welding operation. It is, therefore, necessary to find ways by which these can be minimized to prepare to satisfactory weldment.

• One of the important ways to control the distortions is a good design of the product with a minimum number of joints.
• Proper design of the joint helps in reducing the magnitude of the problem.

In spite of this, there still will be distortion and therefore during the assembly process care should be taken to see that the distortions are controlled. 

There are two possibilities one is to present the members to compensate for this distortion another one is to assemble parts correctly and then apply a proper restraint to minimize the distortion during the welding process. 

The most generally preferred method in the industry is using restraint. There are many ways used for restraining such as clamps, fixtures and even tack welds. Through this method reduces the distortion, it causes high residual stresses, which may lead to cracking. Hence it is necessary to carefully apply restraint without causing too high a magnitude of harmful residual stresses. 

Another method available for reducing the distortions is the preheating of the members of the weldment such that the heat of welding would be properly balanced. 

Applications of friction welding

The quality of weld obtained is very high so that the friction welding has been widely accepted in the aerospace industry as well as the automobile industry for the welding of critical parts. 

It is frequently being used instead of upset welding applications where one of the components to be joined has axial symmetry.

Applications of friction welding :

• The main applications of this process are welding of studs to plates of any thickness. 
• For welding of tubes and shafts. 
• Gears, axle tube, valves, driveline all these components of automobile industries are made by this process. 
• It is used to replace forging or casting assembly.
• Hydraulic piston rod, truck roller bushes are also joined by this process.
• It is also used in electrical industries for welding copper and aluminium equipment. 
• Gear levers, drill bits connecting rod also a made by this process. 
• Almost any metal that can be hot forged and is unsuitable for a dry bearing application can be friction welded. 
• Production of marine engine valves, the valves so produced are as good as or superior to those produced by forging.

Friction welding

It is a solid-state welding process that generates heat through mechanical friction between workpieces in relative motion to one another with the use of lateral force and fuses the materials. 
Friction welding is not a fusion welding process because no melting occurs. 

Working principle :

In this process of welding, the heat required for welding is obtained by the friction between the ends of the two parts to be joined. One of the parts to be joined is rotated at a high speed around 3000 RPM and the other part is axially aligned with the second one and pressed tightly against it.

Also, the friction between the two parts raises the temperature of both the ends. After that, the rotation of the part is stopped abruptly and the pressure on the fixed part is increased so that the joining takes place. 

Machine set up :

The machine for friction welding is similar to a centre lathe. Through a centre lathe could be used for smaller sized jobs, the bigger ones required a special welding machine because in a lathe machine power available would not be sufficient. The power requirements of friction welding may be between 25 kVA to 175 kVA, which is far beyond that of the many general-purpose centre lathes. 

Major parameter :

The major parameters in friction welding are the rotational speed and the axial pressure applied. The axial pressure applied depends on the strength and hardness of the metals being joined. 

The pressure may range from 40 Mpa for low carbon steels to as high as 450 Mpa for alloy steels.

The rotational speed may also change the requirement of the pressure. It may be of the order of 1500 to 3000 RPM.  

The other variable that needs to be closely controlled is the time of contact between the two parts. The total welding time that is taken in the friction welding is between 2 to 30 seconds. 

Advantages of friction welding :

• The major advantage of friction welding is the ease with which the joining can take place. 
• Edge cleaning is not a problem since the oxides and contaminants present would easily be removed during the initial rubbing. 
• The heat generated is small and well below the melting temperature, there will be no distortion and warping. 
• The quality of the weld achieved is very high and it is economical in operation. 
• No skilled operator required since it completely automatic in operation. 

Because of the above advantages, the quality of weld obtained is very high so that the friction welding has been widely accepted in the aerospace industry as well as the automobile industry for the welding of critical parts. 

Disadvantages of friction welding :

• This welding process mostly used only for round bars of some cross-section.
• Non-forgeable materiel can not be weld.
• Preparation of workpiece is more critical.
• High machine setup cost. 
• Joint design is limited. 
• It can only be used for smaller parts of machines, big parts are not compatible with it.