Work
\displaystyle \small \bullet When the point of application of force moves in the direction of the applied force, we say that work is done.
Work done = Applied force ✕ Displacement
\displaystyle \small W=Fs\cos \theta
\displaystyle \small \bullet If displacement is zero, then work done will be zero.
\displaystyle \small \bullet Units of Work:
\displaystyle \small \circ Absolute Units
\displaystyle \small \star M.K.S.= 1 Joule = 1 Newton meter = \displaystyle \small 10^{7} ergs
\displaystyle \small \star C.G.S.= 1 erg = 1 Dyne cm
\displaystyle \small \star F.P.S.= 1 foot poundal
\displaystyle \small \circ Gravitational Units
\displaystyle \small \star M.K.S.= 1 kg-m = 9.8 Joules
\displaystyle \small \star C.G.S.= 1 gm-cm
\displaystyle \small \star F.P.S.= 1 ft-lb
Power
\displaystyle \small \bullet It is the rate of doing work or rate at which a machine can perform work.
\displaystyle \small Power=\frac{Work\; Done}{Time}
\displaystyle \small P=\frac{W}{t}=\frac{Fs}{t}=Fv \displaystyle \small \left [\frac{s}{t}=v \right ]
\displaystyle \small \bullet Units of Power:
\displaystyle \small \circ Absolute Units
\displaystyle \small \star M.K.S.= 1 Watt = 1 Joules/sec = \displaystyle \small 10^{7} ergs/sec
\displaystyle \small \star C.G.S.= 1 erg/sec
\displaystyle \small \star F.P.S.= 1 ft poundal/sec
\displaystyle \small \circ Gravitational Units
\displaystyle \small \star M.K.S.= 1 kg-m/sec
\displaystyle \small \star C.G.S.= 1 gm-cm/sec
\displaystyle \small \star F.P.S.= 1 ft-lb/sec
\displaystyle \small \circ Practical Units
\displaystyle \small \star 1 kW = 1000 Watts = 1.34 H.P.
\displaystyle \small \star 1 H.P. = 75 kg-m/sec = 735.5 Watts = 550 ft-lb/sec = 746 Watts
Horse Power of Engines
\displaystyle \small \bullet It is the practical unit of power
\displaystyle \small \bullet One horse power is the amount of work, a standard horse can do in one second.
\displaystyle \small \bullet Torque,T = Applied force ✕ Perpendicular distance
\displaystyle \small H.P.=\frac{2\pi NT}{4500}
\displaystyle \small H.P.=\frac{(T_{1}-T_{2})\times velocity}{4500}
where,
\displaystyle \small T_{1}-T_{2} = net tension in belt
T = torque in kg meters
N = rotational speed in R.P.M.
Indicated Horse Power (I.H.P.)
\displaystyle \small \bullet I.H.P. is the actual power generated in the engine cylinder
\displaystyle \small I.H.P.=\frac{P\times L\times A\times N\times K}{4500}
where,
P = mean effective pressure (\displaystyle \small kg/cm^{2})
L = length of the stroke (m)
A = area of cross section of object (\displaystyle \small cm^{2})
N = number of revolution per minute (R.P.M.)
K = constant = 1, for two stroke engine = 1/2, for four stroke engine
Brake Horse Power (B.H.P.)
\displaystyle \small \bullet All the power generated by engine cylinder is not available for useful work because, part of it is always utilized in overcoming the internal friction of moving parts of the engine.
\displaystyle \small \bullet The net output of the engine is B.H.P.
B.H.P.= I.H.P.- Losses
Mechanical Efficiency
\displaystyle \small \bullet Mechanical efficiency is the ratio of B.H.P. to I.H.P.
\displaystyle \small \bullet Generally expressed in percentage.
Mechanical Efficiency = \displaystyle \small \frac{B.H.P.}{I.H.P.}\times 100
Energy
\displaystyle \small \bullet The capacity of a body to do work is called energy.
\displaystyle \small \bullet Energy can neither be created nor destroyed and can only be converted from on form to another.
\displaystyle \small \bullet If one form of energy disappears, it reappears in another form. This principle is known as law of conservation of energy.
\displaystyle \small \bullet Types of energy
\displaystyle \small \circ Kinetic energy
\displaystyle \small \star Kinetic energy is the energy a body possesses because of its motion
Kinetic energy = \displaystyle \small \frac{1}{2}mv^{2} Joules
Kinetic energy = \displaystyle \small \frac{mv^{2}}{2g} kg meters
where,
m = mass of body (kg)
v = velocity of body (m/s)
g = acceleration due to gravity = 9.8 \displaystyle \small m/s^{2}
\displaystyle \small \star Ex: a body placed at height, water in overhead tank, gas stored in overhead tank, springs of clock etc.
\displaystyle \small \circ Potential energy
\displaystyle \small \star Potential energy is the energy a body possesses because of its position
Potential energy = \displaystyle \small mgh Joules
Potential energy = \displaystyle \small mh kg meters
where,
m = mass of body (kg)
g = acceleration due to gravity = 9.8 \displaystyle \small m/s^{2}
h = height (m)
\displaystyle \small \star Ex: moving train, flowing water, blowing wind, rotating wheels etc.
\displaystyle \small \bullet When the point of application of force moves in the direction of the applied force, we say that work is done.
Work done = Applied force ✕ Displacement
\displaystyle \small W=Fs\cos \theta
\displaystyle \small \bullet If displacement is zero, then work done will be zero.
\displaystyle \small \bullet Units of Work:\displaystyle \small \circ Absolute Units
\displaystyle \small \star M.K.S.= 1 Joule = 1 Newton meter = \displaystyle \small 10^{7} ergs
\displaystyle \small \star C.G.S.= 1 erg = 1 Dyne cm
\displaystyle \small \star F.P.S.= 1 foot poundal
\displaystyle \small \circ Gravitational Units
\displaystyle \small \star M.K.S.= 1 kg-m = 9.8 Joules
\displaystyle \small \star C.G.S.= 1 gm-cm
\displaystyle \small \star F.P.S.= 1 ft-lb
Power
\displaystyle \small \bullet It is the rate of doing work or rate at which a machine can perform work.
\displaystyle \small Power=\frac{Work\; Done}{Time}
\displaystyle \small P=\frac{W}{t}=\frac{Fs}{t}=Fv \displaystyle \small \left [\frac{s}{t}=v \right ]
\displaystyle \small \bullet Units of Power:
\displaystyle \small \circ Absolute Units
\displaystyle \small \star M.K.S.= 1 Watt = 1 Joules/sec = \displaystyle \small 10^{7} ergs/sec
\displaystyle \small \star C.G.S.= 1 erg/sec
\displaystyle \small \star F.P.S.= 1 ft poundal/sec
\displaystyle \small \circ Gravitational Units
\displaystyle \small \star M.K.S.= 1 kg-m/sec
\displaystyle \small \star C.G.S.= 1 gm-cm/sec
\displaystyle \small \star F.P.S.= 1 ft-lb/sec
\displaystyle \small \circ Practical Units
\displaystyle \small \star 1 kW = 1000 Watts = 1.34 H.P.
\displaystyle \small \star 1 H.P. = 75 kg-m/sec = 735.5 Watts = 550 ft-lb/sec = 746 Watts
Horse Power of Engines
\displaystyle \small \bullet It is the practical unit of power
\displaystyle \small \bullet One horse power is the amount of work, a standard horse can do in one second.
\displaystyle \small \bullet Torque,T = Applied force ✕ Perpendicular distance
\displaystyle \small H.P.=\frac{2\pi NT}{4500}
\displaystyle \small H.P.=\frac{(T_{1}-T_{2})\times velocity}{4500}
where,
\displaystyle \small T_{1}-T_{2} = net tension in belt
T = torque in kg meters
N = rotational speed in R.P.M.
Indicated Horse Power (I.H.P.)
\displaystyle \small \bullet I.H.P. is the actual power generated in the engine cylinder
\displaystyle \small I.H.P.=\frac{P\times L\times A\times N\times K}{4500}
where,
P = mean effective pressure (\displaystyle \small kg/cm^{2})
L = length of the stroke (m)
A = area of cross section of object (\displaystyle \small cm^{2})
N = number of revolution per minute (R.P.M.)
K = constant = 1, for two stroke engine = 1/2, for four stroke engine
Brake Horse Power (B.H.P.)
\displaystyle \small \bullet All the power generated by engine cylinder is not available for useful work because, part of it is always utilized in overcoming the internal friction of moving parts of the engine.
\displaystyle \small \bullet The net output of the engine is B.H.P.
B.H.P.= I.H.P.- Losses
Mechanical Efficiency
\displaystyle \small \bullet Mechanical efficiency is the ratio of B.H.P. to I.H.P.
\displaystyle \small \bullet Generally expressed in percentage.
Mechanical Efficiency = \displaystyle \small \frac{B.H.P.}{I.H.P.}\times 100
Energy
\displaystyle \small \bullet The capacity of a body to do work is called energy.
\displaystyle \small \bullet Energy can neither be created nor destroyed and can only be converted from on form to another.
\displaystyle \small \bullet If one form of energy disappears, it reappears in another form. This principle is known as law of conservation of energy.
\displaystyle \small \bullet Types of energy
\displaystyle \small \circ Kinetic energy
\displaystyle \small \star Kinetic energy is the energy a body possesses because of its motion
Kinetic energy = \displaystyle \small \frac{1}{2}mv^{2} Joules
Kinetic energy = \displaystyle \small \frac{mv^{2}}{2g} kg meters
where,
m = mass of body (kg)
v = velocity of body (m/s)
g = acceleration due to gravity = 9.8 \displaystyle \small m/s^{2}
\displaystyle \small \star Ex: a body placed at height, water in overhead tank, gas stored in overhead tank, springs of clock etc.
\displaystyle \small \circ Potential energy
\displaystyle \small \star Potential energy is the energy a body possesses because of its position
Potential energy = \displaystyle \small mgh Joules
Potential energy = \displaystyle \small mh kg meters
where,
m = mass of body (kg)
g = acceleration due to gravity = 9.8 \displaystyle \small m/s^{2}
h = height (m)
\displaystyle \small \star Ex: moving train, flowing water, blowing wind, rotating wheels etc.
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