Power

Power

 

                 Power is the rate of work done or rate of energy consumed. We can manually pedal a wheel of bicycle at 1 revolution per second. If we want to turn the same wheel with 10 revolutions per second, we need more power and will use engine. 

Power is the time rate of doing work (or expending energy).

P    =       W/t      

      =       Fd/t   

      =      mgh/t

The SI power unit is called watt (W) in honor of James Watt (1736-1819), a Scottish engineer who developed one of the first practical steam engines. A common unit of electrical power is the kilowatt (kW). Power tells you how fast work is being done or how fast energy is transferred.

The SI unit for power is watt. 
One watt is equal to 1 Newton-meter per second (Nm/s). 

If you were pushing on something with a force of 1 N, and it moved at a speed of 1 m/s, your power requirement would be 1 watt. 

British unit of power is horsepower.

The conversion is as follows: SI:

  Watts (W) 1000 W = 1 kW Kilowatt (kW) 
                      1kW = 1.341 hp Horsepower (hp)
                      1 hp = 0.746 kW

 

Work

 

Work is the application of a force over a distance. When we lift an object from the ground and put it on the shelf, we do work. The force is the weight of the object and distance is the height of the shelf. Similarly, when we push an object and moves it, we do work. The distance taken for calculating work has to be in the direction of force applied. 

Example: a weight of 50kg. is lifted to height of 5 meter. Calculate the work done. Work = force ´ distance through force is applied = (W kg ´ 9.8) ´ h (W = 50kg, h = 3m) = 50 ´ 9.8 ´ 3 = 1470 Nm
When we push an object and it moves through a distance L,
the work done is calculated as follows:
Work = force ´ distance through which force is applied 
W = F ´ L (unit of force is N, distance is in meter) 
W = F (N) ´ L (m) 
    = F ´ L (Nm) 

When we do work, we use energy. Work and Energy are closely related. Work is measured in the same unit of energy.

 

Torque

 

                    Torque is a force that tends to rotate or turn things. You generate a torque whenever, you apply a force to turn handle of diesel engine.

Torque = Force ´ Distance from the center. 

Unit of Torque = N ´ m = Nm. 

It is common experience, that a nut which is hard to move by hand can be easily rotated when a spanner of longer length is used. Increasing length of application of force from the center of shaft increases torque applied.

 

Mass and Weight

 Mass and Weight

                         Mass is defined as the measure of how much matter an object or body contains. It is measured in Gram (g). More the mass of object more is the gravitational force on the object. If we drop an object from a height, earth pulls it at the acceleration of 9.8m/s2

                            

                               Weight is the amount of force that earth exerts on us.

  

                                Acceleration is the rate of change of speed. This means speed of an object will increase by 9.8m every second. This means, if an object falls from a height to reach earth, after 10 second it would have achieve speed of 9.8 ×10 = 98 m/s. · Force causes acceleration, 

Sir Isaac Newton’s Second Law states that the acceleration (a) of an object is directly proportional to the force (F) applied, and inversely proportional to the object’s mass (m) Newton’s Second Law is usually summarized in equation form: 

 a = F/m, 

or F = ma 

Unit of force is derived as follows -

Unit of force F = m (Kg) × a (m/s2) 

                    = Kg m/s2 

                    = N 

To honor Newton’s achievement, the standard unit of force i.e kg m/s2 in the SI system is named as Newton (N). One Newton (N) of force is enough to accelerate 1 kilogram (kg) of mass at a rate of 1 meter per second square (m/s2). A kilogram is the amount of weight at which 1 N of force will accelerate at a rate of 1 m/s2. In practice, we measure weight, in terms of gms. or Kgs. But when weight is used as force, we must remember to measure it in terms of Newton.

Electric Charge

Electric Charge

a)    1 ab-coulomb         = 0.00278 ampere-hour 

                                    = 10 coulomb 

                                    = 6.24151x10¹⁹  electronic charge 

                                    = 1.03632x10^-4  faraday (chem) 

                                    = 2.99792x10¹⁰  stat coulomb

b)    1 ampere hour       = 360 ab  coulomb

                                   = 3600   coulomb 

                                   = 0.03731  faraday (chem)

c)    1 coulomb              = 0.1 ab coulomb 

                                    = 0.000278 ampere hour 

                                    = 1 ampere second 

                                    = 1.00015002 coulomb (Int)

                                    = 1.0363x10^-5  faraday (chem) 

                                    = 1.0360x10^-5 faraday (phys)

                                    = 2.9979x10⁹ stat coulomb

Density

Density

kg/cubic meter, gram/centimeter³,  lbm/cubic inch, lbm  /cubic foot, slug/cubic foot, kilogram/cubic meter, lbm/gallon (US liq)

Density Water

a)      1000 kg/m³ = 62.43 Lbs./Cu.Ft 
                           = 8.33 Lbs./Gal. 
                           = 0.1337 Cu.Ft./Gal.

 
b)       1 lb/ft³ = 16.018 kg/m³ 
                     = 0.016 g/cm³ 
                     = 0.00926 oz/in³ 
                     = 2.57 oz/gal (Imperial)
                     = 2.139 oz/gal (U.S.) 
                     = 0.0005787 lb/in³ 
                     = 27 lb/yd³ 
                     = 0.161 lb/gal (Imperial) 
                     = 0.134 lb/gal (U.S)
                     = 0.0121 ton/yd³
 

c)          1 slug/ft³ = 515.379 kg/m³


 
d)          1 kg/l = 62.43 lb/ft³
 

e)           1 kg/m³ = 0.001 g/cm³ 
                          = 1 g/ml
                          = 0.0005780 oz/in³ 
                          = 0.16036 oz/gal (Imperial) 
                          = 0.1335 oz/gal (U.S.) 
                          = 0.0624 lb/ft³ 
                          = 0.000036127 lb/in³
                                = 1.6856 lb/yd³ 
                          = 0.010022 lb/gal (Imperial) 
                          = 0.008345 lb/gal (U.S)
                          = 0.0007525 ton/yd³

Capacitance, Conductance, Current

Capacitance

a)   1 ab farad = 1x10⁹ farad 
                    = 1x10¹⁵ microfarad
                    = 8.98755x10²⁰ stat farad
 

b)   1 farad = 1x10^-9 ab farad 
                 = 1.00049 farads (Int)
                 = 1x10⁶ microfarad 
                 = 8.98755x10¹¹ stat farad 

 

Conductance

       1 abmho = 1000 megamho  

                    = 1x10⁹ mho

                    = 8.98755x10²⁰ statmho

 

Current

a)      1 ab ampere = 10 ampere

                           = 1.03638x10^-4 Faraday/sec(chem) 

                           = 2.99792x10¹⁰ stat ampere 

                           = 1 biot

 

b)       1 ampere = 0.1 ab ampere.

                        = 1.00015 ampere (Int) 

                        = 1 coulomb/sec

                        = 1.03638x10^-5 Faraday/sec (chem) 1x10⁶ micro ampere 

                        = 1000 milli ampere 

                        = 2.99792x10⁹ stat ampere

 

c)          1 ampere (Int) = 0.99985 ampere

 

d)          1 biot = 10 ampere

Area

Area

acre, are, barn, sq.ft., sq.in., foot², hectare, inch², mile², section, meter², township, yard², hectares

a)  1 m² = 1550 in² 

             = 10.764 ft² 

             = 1.1968 yd² 

             = 3.861x10^-7 mile²

b)   1 ft² = 0.0929 m² 

             = 144 in² 

             = 0.1111 yd² 

             = 3.587x10^-8 mile²

c)   1 in² = 6.452 cm² 

              = 6.452x10^-4 m² 

              = 6.944x10^-3 ft² 

              = 7.716x10^-4 yd² 

              = 2.491x10^-10 mile²

d)    1 yd² = 0.8361 m² 

                = 1296 in² 

                = 9 ft² 

                = 0.3228x10^-6 mile²

e)    1 mile² = 2.590x10⁶ m² 

                  = 0.4015x10¹⁰ in² 

                  = 2.788x10⁷ ft² 

                  = 3.098x10⁶ yd² 

                  =640 Acres

f)   1 acre = 1/640 square mile 

               = 0.404686 ha (Hectares) 

               = 4046.86 m² 

               = 43560.174 Sq.Ft. (Int)

               = 43560 Sq.Ft. (US Survey) 

               = 4840 Sq.Yds. 

               = 40.46873 are
 

g)   1 km² = 10² ha² 

               = 10⁶ m² 

               = 10¹⁰ cm² 

               = 10¹² mm²

h)   1 ha (Hectare)  = 10⁴ m² 

                            = 10⁸ cm² 

                            = 10¹⁰ mm² 

                            = 2.471 Acres
 

i)      1 cm² = 10^-4 m² 

                 = 0.155 in²

j)      1 mm² = 1.55x10^-3in²

k)     1 township = 36 square mile 

                        = 23040 acre 

                        = 36 section 

                        = 9.323957 10⁷ m² 

                        = 9324 hectare

                        = 93.24 square kilometer

 

l)     1 section = 1 square mile

                     = 2.59 10⁶ m² 

                     = 2.59 square kilometer 

                     = 259 hectare

                     = 3.0976 10⁶ square yards

                     = 640 acre 

 
 

m)    1 are = 0.024711 acre (Int) 

                = 1 sq dekameter 

                = 1076.39 sq foot 

                = 100 sq meter 

                = 3.86102x10^-5 sq mile 

                = 119.599 sq yard
 

n)      1 barn = 1x10^-24 sq cm
 

o)      1 centiare = 0.01 are 

                        = 10.764 sq foot  

                        = 1550 sq inch

                        = 1 sq meter

                        = 1.19599 sq yard

 

p)      1 circular mil = 1x10^-6 circular inch 

                           = 5.06707x10^-6 sq cm

                           = 7.85398x10^-7 sq inch

                           = 0.000507 sq mm

                           = 0.7854 sq mill

q)     1 hectare = 2.471 acre  

                      = 100 are

                      = 1x10⁸ sq cm

                      = 107639.1 sq foot

                      = 10000 sq meter

                      = 0.00386 sq mile

                      = 395.367 sq rod

r)      1 rood = 1/4 acre 

                   = 1011.5 m² 

                   = 40 sq rods 

                   = 40 sq perches
 

s)      1 sq rod = 1 sq perch

                      = 30¼ sq yards 

                      = 25.2928 m²

                           = 1/160 acre
 

t)       1 arpent = about 0.85 acre

                      = 3439.1 m²
 

u)     1 Marla = 30.25 Sq. Yards 

                   = 25.2928 Sq. Metres

                   = 272.25 Sq. Feet 

                   = 0.00625 Acre 

                   = 0.05 Kanal

Angle

Angle

i)   1 circle = 360 degrees 

                = 400 grades 

                = 21600 minutes 

                = 6.28318 radians 

                = 12 signs

ii)  1 circumference = 360 degrees 

                            = 6.28318 radians

iii) 1 radian = 0.15915 circumference 

                 = 57.29578 degree

                 = 3437.747 minute 

                 = 0.63662 quadrant

                 = 0.15915 revolution 

                 = 206265 second

Acceleration

Acceleration

        foot/second², meter/second², gal, galileo, inch/second²

i)  1 m/s² = 3.28084 ft/s²  
               = 100 cm/s²     
               = 39.37 inch per second squared (inch/s²) .

ii)  1 ft/s² = 0.3048 m/s²    
               = 30.48 cm/s²




iii)  1 g      = 9.80665 m/s²  
               = 32.17405 ft/s² 
                   = 386.1 in/s² 
                   = 35 kph/s 
               = 22 mph/s

SI units

Introduction :

The SI system (International System of Units) is the modern metric system of measurement and the dominant system of international commerce and trade. SI units are gradually replacing Imperial and USCS units.

The SI is maintained by the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures) in Paris.
The SI system is founded on the

• SI base units
• SI derived units described in terms of acceptable SI units
• SI derived units with special names and symbols acceptable in SI
• SI Prefixes

SI Base Units

The core of the SI system is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. The International System of Units (SI) is founded on seven base units.

 

SI Derived Units with Special Names and Symbols acceptable in SI

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.


 

 

SI Derived Units described in Terms of acceptable SI Units

Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.

SI Prefixes

 

 

The prefixes provide an order of magnitude: Ex.

• 16600 m = 16.6 10³ m = 16.6 km
• 1 mm³ = (10^-3 m)³ = 10-9 m³