WORK-ENERGY-POWER

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WORK-ENERGY-POWER
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(i) WORK- Work done by a force is the
product of the force and the distance moved by
the point of application in the direction of the
force. It is a scalar quantity.  
Unit Nm ( Joule )
F
F
a
a
A
B
s
Work doneF cosa s
a angle of inclination of force with the
direction of motion sdisplacement of force from
A to B
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2
(ii) POWER- It is defined as the time rate
of doing work. Power work done /Time
(force distance) /Time  
force velocity
Unit (Nm)/s watt
(kN m)/s kilo watt
1 metric H.P735.75 watts.

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• Energy-
• It is defined as the capacity to do work. It is
  a scalar quantity.
•  
• Unit - N m (Joule)

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Work-Energy relation for translation
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•  From Newtons second law of motion
• ? F (W/g) a -----------(1)
• Also a dv/dt ( dv/ds) ( ds/dt) v dv/ds
• sub in (1)
• ? F( W/g ) v dv/ds
• F ds (W/g ) v dv ------------------(2)
  
• Let the initial velocity be u and the final
  velocity after it moves through a distance s
  be v

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Integrating both sides, we get s
v ? F ? ds (W/g) ? v dv
0 u
V ? F s
( W/g ) v2/2
u
? F s (W/2g) v2-u2
Therefore work done by a system of forces acting
on a body while causing a displacement is equal
to the change in kinetic energy of the body
during the displacement.
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Work done by a spring
s
Fk(s)
The force required to cause unit deformation
of the spring is called the spring modulus
denoted by the symbol k. The force required to
deform a spring is given by F ks. Work
done by the force on a spring is the product of
the average force and the deformation s.
W -ks2/2. The negative sign indicates that
whenever spring is deformed the force of spring
is in the opposite direction of deformation.







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IMPULSE MOMENTUM
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Momentum- Quantity of motion possessed by a body
is called momentum. It is the product of mass and
velocity. It is a vector quantity.   Unit- N
s.
Impulse of a Force-  It is defined as the
product of force and the time over which it acts.
It is a vector quantity.   Unit- N s.
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Impulse-momentum relationship
Force Rate of change of momentum   F ( mv
mu) /t Force causing impulse  Ft
mv mu   Impulse final momentum Initial
momentum   The component of the resultant linear
impulse along any direction is equal to change in
the component of momentum in that direction.
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Law of Conservation of momentum
The law of conservation of momentum may be
stated as , momentum is conserved in a system
in which resultant force is zero. In other
words, in a system if the resultant is zero,
Initial momentum is equal to Final
momentum m1u1m2u2 m1v1m2v2
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ASSIGNMENT 1.A small block starts from rest at
point a and slides down the inclined plane. At
what distance along the horizontal will it travel
before coming to rest . Take µk0.3 Ans s6m
5m
A
3
C
4
B
s
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2.The system starts from rest in the position
shown . How much further will block A move
up the incline after block B hits the ground .
assume the pulley to be frictionless and massless
and µ is 0.2 .WA1000N, WB2000N. Answer s
1.27m
A
B
3
4
3m
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3.Two bodies a and b weighing 2000N and
5200N are connected as shown in the figure . find
the further distance moved by block a after the
block b hits block c . Answer s1.34m
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A
5
B
3m
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4.A 1500Kg automobile travels at a uniform rate
of 50kmph to 75kmph . During the entire motion,
the automobile is traveling on a level horizontal
road and rolling resistance is 2 of weight of
automobile . Find (i) maximum power developed
(ii) power required to maintain a constant speed
of 75kmph. ANSWER power developed 6.131KN
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5.A spring is used to stop 60kg pack age which
is sliding on a horizontal surface . the spring
has a constant k which is 20kN/m and is held by
cable such that it is initially compressed at
120mm. knowing that the package has a velocity of
2.5m/s in position shown and maximum additional
displacement of spring is 40mm . Determine the
co-eff of kinetic friction between package and
surface. (Answer µk0.2)
2.5 m/s
60kg
600m
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6. The system shown in figure has a rightward
velocity of 4m/s, just before force P is applied.
Determine the value of P that will give a
leftward velocity of 6m/s in a time interval of
20sec. Take µ 0.2 assume ideal pulley.
Answer P645.41N
P
1000N
400N
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7. A locomotive of weight 500kN pulls a train of
weight of 2500kN. The tractive resistance, due to
friction is 10N/kN. The train can go with a
maximum speed of 27kmph on a grade of 1in100.
Determine (a) Power of the locomotive. (b)
Maximum speed it can attain on a straight level
track with the tractive resistance remaining
same. Answer (a) Power 450kN (b) v15m/s
8.A wagon weighing 400kN starts from rest, runs
30m down a 1 grade strikes a post. If the
rolling resistance of the track is 5N/kN, find
the velocity of the wagon when it strikes the
post. If the impact is to be cushioned by means
of one bumper string, which compresses 1mm per 20
kN weight, determine how much the bumper spring
will be compressed. Answer v1.4m/s, x63.21mm
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9. A car weighing 11,100 N running at 10m/s
holds 3 men each weighing 700N. The men jumps off
from the back end gaining a relative velocity of
5m/s with the car if the three men jumps off (i)
in succession, (ii) all together. Answer (i)
v10.85m/s. (ii) v10.8m/s.
10. A gun weighing 300kN fires a 5kN projectile
with a velocity of 300m/s. With what velocity
will the gun recoil? If the recoil velocity is
over come by an average force of 600N, how far
will the gun travel how long will it travel.
Answer v-5m/s s0.637m/s t0.255s