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CHAPTER-7

CHAPTER-7. Kinetic Energy and Work. 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 K=mv 2 /2

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CHAPTER-7

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  1. CHAPTER-7 Kinetic Energy and Work

  2. 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 K=mv2/2 • Unit of energy (K or any type of energy) is joule (J) 1J=1 kg. m2/s2

  3. 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.

  4. 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= K=m axd=Fxd=Fcos  d=F.d W= Fxd=Fcos  d=F.d • Positive Work : Displacement along force direction • Negative Work: Displacement opposite to force direction

  5. Ch 7-5 Work and Kinetic Energy Work-Kinetic Energy Theorem W= K = Kf-Ki= m(v2-v02)/2 Kf = W+ Ki v2 =2(W+Ki)/m

  6. 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)/2=0 K is constant c) W is negative W is Zero Ch 5-Check-Point-1

  7. 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) W=Fdcos b) W= 0 a) W = - Fdcos

  8. 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 Wgdoneby the gravitational force Fg in rising objects: • Wg=Fgd cos =mgd cos = mgd (-1)= - mgd • Work Wg done by the gravitational force Fg in falling objects : • Wg=Fgd cos =mgd cos = mgd (+1)= + mgd

  9. Workdonein lifting an object • 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

  10. 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 (Hooke’s 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

  11. 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 xi=0 and xf=x) • Work done by an applied force Wa in stretching/compressing a spring K = Wa+Ws • If the block is initially and finally at rest then K =0 and Wa= -Ws

  12. Work done by spring force is Ws=k(xi2-xf2)/2 Ws= k(9-4)/2=+5k/2 J Ws= k(4-9)/2=-5k/2 J Ws= k(4-4)/2=0 J 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.

  13. 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-Ki=W= xixfFx dx

  14. 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  v=F.v • Unit of power : 1 watt= 1 W= 1J/s

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