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Transcript
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=mv2/2 Unit of energy (K or any type of energy) is joule (J) 1J=1 kg. m2/s2 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. 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 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 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)/2=0 K is constant c) W is negative W is Zero 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 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: 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 Work done in 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 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 Ch 7-7: Work done by a spring Force (Variable Force) Work done by a spring force Ws xf Ws=xi Fx dx = xf xi (-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 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 Ws=k(xi2-xf2)/2 a) Ws= k(9-4)/2=+5k/2 J b) Ws= k(4-9)/2=-5k/2 J c) Ws= k(4-4)/2=0 J Ch 7-8: Work done by a General Variable Force xf W= xi Fx 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 xf K= Kf-Ki=W= xi Fx dx 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