Kinetic energy and Work

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CHAPTER-7

• Kinetic energy and Work

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Ch 7-2,3 Kinetic Energy

• Energy a scalar quantity associated with state
  or condition of one or more objects
• Kinetic Energy (K) energy associated with state
  of motion of an object. The faster an object
  moves, greater is its K
• Kmv2/2
• Unit of energy (K or any type of energy) is joule
  (J)
• 1J1 kg. m2/s2

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Ch 7-4 Work

• Work W is energy transferred to or from an object
  by means of a force acting on the object.
• If the object is accelerated by applying a force,
  its kinetic energy K increases. Energy
  transferred to the object is positive work W.
• If you decelerate the object by applying a force,
  you decrease its kinetic energy K. Energy
  transferred from the object is negative work -W.

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Ch 7-5 Work and Kinetic Energy

• Work done in accelerating a bead through a
  distance d along x-axis under a constant force F
  acting at an angle ? with respect to x-axis
• W ?K m(v2-v02)/2 but
• axd(v2-v02)/2
• W ?Km axdFxdFcos ? dF.d
• W FxdFcos ? dF.d
• Positive Work Displacement along force
  direction
• Negative Work Displacement opposite to force
  direction

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Ch 7-5 Work and Kinetic Energy

• Work-Kinetic Energy Theorem
• W ?K Kf-Ki m(v2-v02)/2
• Kf W Ki
• v2 2(WKi)/m

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Ch 5-Check-Point-1

• A particle moves along x-axis. Does its kinetic
  energy increase or decrease , or remain the same
  if the particle velocity changes
• a) from -3 m/s to -2 m/s
• b) -2 m/s to 2 m/s
• c) in each situation the work done on the
  particle is positive, negative or zero?

• ?K m(vf2-vi2)/2
• a) ?K m(vf2-vi2)/2
• m/2(4-9)-5m/2
• ?K is negative
• b) ?K m(vf2-vi2)/2
• m(4-4)/20
• ?K is constant
• c) W is negative
• W is Zero

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Ch 5-Check-Point-2
The figure show four situation in which a box
acts on a box while the box slides rightward a
distance d across a frictionless floor. The
magnitude of the forces is identical their
orientation are as shown. Rank the situation
according to the work done on the box during the
displacement, most positive first
W Fdcos? d) W Fd c) WFdcos? b) W 0 a) W
- Fdcos?
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Ch 7-6 Work Done by Gravitational Force
(Constant Force)

• A tomato, thrown upward, is slowed down from
  initial velocity v0 to v under the effect of
  gravitational force Fg
• Work Wg done by the gravitational force Fg in
  rising objects
• WgFgd cos ?mgd cos ? mgd (-1) - mgd
• Work Wg done by the gravitational force Fg in
  falling objects
• WgFgd cos ?mgd cos ? mgd (1) mgd

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Work done in lifting and objects

• Work Wa done by an applied force F in lifting /
  lowering an object through a distance d
• ?K Kf-Ki Wa Wg
• In lifting object is at rest in initial and final
  position
• ?K Kf-Ki 0 then
• Wa - Wg -mg d cos?
• Lifting ? 180
• Lowering ? 0

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Ch 7-7 Work done by a spring Force- (Variable
Force)

• Relaxed state of a spring ( Fig. a) Spring
  neither compressed nor extended
• Spring Fore Fx (Restoring Forces) acts to restore
  the spring to its relaxed state
• Fx-kx (Hookes Law)
• where k is spring constant ( force constant) and
  x is compression or extension in the relaxed
  length of the spring
• -ve Fx for ve value of x
• ve Fx for -ve value of x

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Ch 7-7 Work done by a spring Force (Variable
Force)

• Work done by a spring force Ws
• Ws?xixfFx dx ?xixf(-kx) dx k(xi2-xf2)/2
• Ws -kx2/2 (if xi0 and xfx)
• Work done by an applied force Wa in
  stretching/compressing a spring
• ?K WaWs
• If the block is initially and finally at rest
• then ?K 0 and
• Wa - Ws

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Ch 5-Check-Point-4
For three situations the initial and final
position respectively , along x-axis for the
block is a) -3 cm, 2cm b) 2 cm, 3 cm c) -2 cm, 2
cm. In each situation the work done by the spring
force on the block is positive, negative , or
zero.

• Work done by spring force is
• Wsk(xi2-xf2)/2
• Ws k(9-4)/25k/2 J
• Ws k(4-9)/2-5k/2 J
• Ws k(4-4)/20 J

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Ch 7-8 Work done by a General Variable Force

• W ?xixfFx dx
• Work done by a variable force is equal to area
  between F(x) curve and the x-axis , between the
  limits xi and xf
• Work-Kinetic Enegy Theorem for a variable force
• ?K Kf-KiW ?xixfFx dx

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Ch 7-9 Power

• Power P Time rate of doing work of a force
• Average Power Pavg W/?t
• Instantaneous Power P dW/dt d/dt (Fcos ? dx)
• P Fcos ? vF.v
• Unit of power 1 watt 1 W 1J/s