Mechanical Energy PDF

 Energy: A system has energy if it is able to produce work The kinetic energy  Kinetic energy is the energy that every moving body has.  In an accident for the same speed, the damage caused by a truck is greater than for a car: kinetic energy depends on the mass of the body.  During a...

 Energy: A system has energy if it is able to produce work The kinetic energy  Kinetic energy is the energy that every moving body has.  In an accident for the same speed, the damage caused by a truck is greater than for a car: kinetic energy depends on the mass of the body.  During a "crash test", the damage caused is greater when the speed increases: kinetic energy depends on the speed of the body.  A solid of mass m, animated by a translational motion of speed V, has an energy, called kinetic energy: Existence of mass m with speed v = existence of KE KE(J) ; m(kg) ; V(m.s-1) How to convert km/h to m/s ?? 1km 1000m 1m 1 1 km.h = -1    m.s-1 1h 3600 , s 3,6s 3,6 V (km.h-1) / 3,6 = V (m.s-1) V (m.s-1) x 3,6 = V (km.h-1) Calculation of the kinetic energy of a 50 t truck traveling at 100 km.h-1 1 3 100 2 50.10 ( )  KE = 2.107 J 2 3,6 What would be the speed of a 1000 kg car with this kinetic energy? 7 2 2.10 200 m.s -1 3  10 V = 720 km.h-1  The gravitational potential energy  An object of mass m, at altitude z gives work when it falls so it has a gravitational potential energy : Existence of mass m with height z = existence of GPE GPE(J) ; m(kg) ; z(m)  The gravitational potential energy depends on the chosen reference level: EX: A stone is located 20 m above a 10 m deep well → its gravitational potential energy is : GPE = mgz Where z = 20 m If the reference level is the ground z = 30 m If the reference level is the well  Remark : Below the reference level GPE = - mgh On the reference level GPE = 0 Above the reference level GPE = mgh Z = height of the center of gravity of an object which has big dimensions  Elastic potential energy The elastic potential energy Epe is associated with the reversible deformations of a solid. A compressed or elongated spring can do work when it returns to its natural length so it has an Epe For the system ( solid , spring, earth ) PE = GPE + EPE  Mechanical energy  A moving object at altitude z has mechanical energy: ME = EP + KE ME(J) ; PE(J) ; KE(J) A tennis ball of mass 58.0 g is struck on serve by a player; this ball starts from 2.50 m above the ground with a speed of 180 km.h-1 1 E m E c  E p  m V 2  m g z 2 1 180 2 E m  0,058 ( )  0,058 9,8 2,5  74 J 2 3,6  Conservation of mechanical energy KE ME PE  During the motion of an object, its potential energy is converted into kinetic energy and vice versa.  If we neglect the friction and without motive force (traction of the motor) during motion, the variations of potential and kinetic energy are compensated: KE = - PE  Mechanical energy is conserved ME(initial) = ME(final)  EC Em Ep  With friction → mechanical energy is not conserved but it decreases  The lost mechanical energy (The variation of mechanical energy) is transformed into thermal energy, or heat.  Em = Em (final) - Em (initial) = Wf = -f  d = Work of friction  With traction F and friction Em = -f  d + F×d = (F – f ) d Example: A car is released without initial speed in A  Mechanical energy at A MEA = KEA + GPEA VA = 0 => KEA = 0 MEA = mghA  What can we say about the mechanical energies at B, C and D if we neglect the friction  MEA = MEB =MEC =MED  Calculate the speed of the car at B EmA EmB 1 m g Z A m g Z B  m VB2 2 1 g Z A g Z B  VB2 2 VB  2 g ( Z A  Z B )  2 10 9  13 m.s-1 = 47 km.h-1 VB  2 g ( Z A  Z B )  Calculate the speeds of the car at C and D VC  2 g ( Z A  Z C )  2 10 12  15 m.s-1 = 54 km.h-1 VD  2 g ( Z A  Z D )  2 10 4  8,9 m.s -1 = 32km.h-1