Work And Power
In our daily life work implies an activity resulting in muscular or mental exertioan. However, in physics the term work is used when a particle is displaced by the action of a force. Thus, work is a scalar quantity; itsSI unit is joule, CGS unit erg.
ij = 107 erg
dW = F ds
W = F . S = Fs cos θ (if F is constant)
W = ∫F . ds (if F is variable)
Work can be positive or negative as θ is acute or obtuse. Positive work means parallel to displacement and negative work means opposite to displacement.
Work done in lifting a body upwards from the ground is positive but the work done by the force of gravity (downwards) is negative.
When a body is pulled on a rough surface the work done by the pulling force is positive while work done against frictional force is negative
If a body is in static or dynamic equilibrium
Work done = 0 because ∑F = 0
Work done is zero if displacement is zero or displacement is in direction perpendicular to the applied force. Thus work done by the centripetal force and work done by a moving charged particle in a magnetic field
[(F = q(v x B )] is zero.
Work done depends upon the frame of reference because with change in frame of reference displacement may change,. Hence the work done will be different in different frame of references.
In a conservative field, work done is path independent in F versus s curve work done is the area under the curve. The algebraic sum is to be made as illustrated in
W = ∫v2v1 p. dV area under p – V curve is work.
W = ∫F. ds = ∫ma. ds = ∫m dv/dt. Ds
∫mdv. ds / dt = ∫mv. dv
Work done on particle by the resultant force acting on it is always equal to change in KE >
Thus for positive work KEfinal > KEinitial
This theorem is valid for all types of forces (external or internal conservative or non conservative) and is called work energy theorem
W = ?PE (change in potential energy) (for conservatives forces)
W = ½ kx2
Where k is spring constant and x is displacement. It could be extension or compression in case of spring.
W = 1/2 stress x strain x volume (in elastic bodies)
Since work is independent of time, the time rate of doing work is defined as power.
P = dW / dt P average = W / t
If force is constant
P = dW / dt = d / dt (F. s) = F. ds / dt = F. v
Power is a scalar quantity. Its SI unit is watt or j/s. practical unit HP, 1 HP = 746W = 550 ft – Ib/s.
W = ∫P. dt or area under P – t curve.
Practical unit of work or energy is KWH (kilowatt-hour)
1 KWH = 3.6 x 1010 j
Kinetic energy can never be negative.
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