work? formula?
The work done on an object is the scalar (or dot) product of force F & displacement d.
W = Fd
Or W = Fd cos θ
θ the angle b/w force & displacement.
how can force be resolved into components?
direction of each component?
effective component?
- force can be resolved into 2
components Fcosθ & Fsineθ. - Fcosθ is the component of force along the direction of displacement which is the effective component.
- Whereas, Fsinθ is the component of force which is perpendicular to the direction of dísplacement & therefore plays no role in doing work.
pg 74
unit of work?
The SI unit of work is the joule (J)
1 joule is equivalent to 1 newton-metre (N m).
1J=1N m
Dependence of Work?
work done depends upon force ‘F’, displacement ‘d’ & the angle
‘e’ b/w them
+ve work?
when the force has a component in the same direction as the displacement (0° ≤ 0 < 90°), cos in above equation is
positive and the work W is positive.
-ve work?
When the force has a component opposite to the displacement (90° <0≤180°), cos 0 is negative and work done by the force will be negative.
zero work?
When the force is perpendicular to the displacement, 0 = 90° then the work done by the force is zero.
The area under the force-displacement graph gives _________.
draw garph for work done by constant force?
work done.
draw a graph for Work Done by Variable Force?
work done by variable force?
pg 76
force field?
The region around a body where it can influence other bodies by a force associated with it.
conservative field?
- A field is said to be conservative if it has 2 imp. properties:
- Work Done is Independent of the Path Taken: If the work done on a particle moving b/w any two points A and B is same for path I and Il
- Work Done around a Closed Path is Zero: If the work done on a particle moving through any closed path (the path in which the beginning & end points are same) gives zero such a field will be conservative.
non conservative field?
field in which work done depends upon the path followed or the work done along a closed path is not zero.
example of non conservative field?
- Frictional field is a non-conservative field, & frictional or drag forces are non-conservative forces cz when an object is moved in frictional field, the work done against frictional force depends upon the path followed.
- Frictional force, viscous drag & air resistance are all examples of non-conservative forces & the fields where they act are termed as non conservative fields.
kinetic energy?
The energy possessed by a body due to its motion.
derive K.E equation?
work done on an object is equal to change in energy i.e. W = AE, where W’ is the work done & AE is the change in energy.
WORK - ENERGY PRINCIPLE formula?
change in K.E is due to?
on what condition is it valid for potential energy?
pg 78
Work - Energy Theorem in Resistive Medium.
what is resistive force?
work done by the object against the resistive force ______?
Input of Mechanical Machine? formula?
The energy supplied to a mechanical machíne is called input.
Input is equal to the product of effort ‘p’ and the distance ‘d’ through which effort acts.
input = px d.
Output of Mechanical Machine
The work done by a mechanical machine
is called output. Output is the product of load ‘W’ and the distance ‘D’
through which the load lifts.
output =WxD
Efficiency? unit? formula? what is never efficinecy?
The efficiency is the ratio of work output to the work input,
and can be expressed in percentage as:
Efficiency is the ratio of similar quantities and therefore has no unit.
The efficiency cannot be greater than 1 (or 100%), in fact it cannot be
equal to 1 (or 100%) for real machines.
Ideal Machine? efficiency?
For an ideal machine only, the input will be equal to output, this means that
no energy is wasted and all energy is converted into useful work. Therefore, the efficiency of
an ideal machine is 100%.
output = input or efficiency = 1
Almost all energy transformation technologies operate at efficiencies less than 100%, most of
the wasted energy becomes thermal energy.
For example, automobiles are highly inefficient. Suppose that an amount of fuel containing
1000 J of chemical potential energy is used by an automobile’s engine. Only 10 percent of the
energy is available to do work.
