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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