Physics 1010 The Physics of Everyday Life TODAY Conservation Laws Energy Momentum Collisions Work Energy Kinetic Potential Heat 1 Admin Matters Cummulative grades are on the course website listed by clicker number Some clicker s have no names 137097 202054 241566 Some names have no clicker number Please make sure Yu has your name and clicker number 2 Conservation Laws The real power behind Physics Allow us to write equations whatever before whatever after We don t need to know details of how Newton s Laws are conservation of momentum No other science has conservation laws well Chemistry borrowed mass concerv 3 Conservation Laws Momentum p mv Different kinds of energy kinetic potential heat Energy converted from one kind to another but TOTAL energy is unchanged 4 Newton s second law revisited Force gives change of momentum Momentum p mv Acceleration is rate at which velocity changes v a t Force rate at which momentum changes mv Fnet t F dp dt Impulse defined to be Fnet t Impulse is the transfer of momentum mv Impulse of wall on ball is mv 5 Newton s second law revisited Force gives change of momentum Momentum p mv Acceleration is rate at which velocity changes v a t Force rate at which momentum changes mv Fnet t F dp dt Impulse defined to be Fnet t Impulse is the transfer of momentum mv m 0 1kg v 10m s t 0 1s F F D mv Dt 2mv 1 N 2 1 N 20N Impulse of wall on ball is mv 6 Momentum conserved in collisions because of Newton s third law Force ma is rate at which momentum changes Force on red object negative of force on green object Momentum change of first object negative of momentum change on second Momentum sum of momenta of both balls is conserved m1v1 m2v2 before m1v1 m2v2 after 7 Momentum conservation allows us to predict results of collisions A mass of 1 kg is moving a 0 21 m s to the right at 1 m s b 0 33 m s It hits a stationary mass c 1 m s of 0 5 kg and sends it to d 2 m s the right at 1 33 m s m1v1 m2v2 before m1v1b After the collision how fast is the first mass going m1v1a m2v2a m1v1b m1v1 m2v2 before v1a v1b m2 m1 v2a 1m s m1v1 m2v2 after 0 5 1 33m s 0 33 m s 8 Conservation Laws Momentum p mv Different kinds of energy kinetic potential heat Energy converted from one kind to another but TOTAL energy is unchanged 9 Work transfers energy like impulse transfers momentum Impulse F t momentum Work F x energy Lift object human chemical energy to gravitational energy Falling object gravitational potential energy to kinetic energy 10 Work Work Force x Length L F h height Constant Speed Up W FxL 11 The work we have to do to move things up against gravity is independent of how we get there GRAVITY IS A CONSERVATIVE FIELD F hand Con S t n a st p U d e e p h height mg Move straight up Move cart up ramp assuming friction is negligible same accomplishment same work Work Framp x Lramp Fvert x height 12 Push frictionless cart up 1 meter ramp at constant velocity Constant Speed Up F hand h height mg Work Framp x Lramp Fvert x height If want to push up ramp at constant velocity force applied by hand must be a greater than the weight mg of the cart b less than the weight of the cart c the same as the weight of the cart 13 Push frictionless cart up 1 meter ramp at constant velocity Constant Speed Up F hand h height mg Work Framp x Lramp Fvert x height If want to push up ramp at constant velocity force applied by hand must be a greater than the weight mg of the cart b less than the weight of the cart c the same as the weight of the cart 14 How much work force applied x distance did I have to do to push cart along the ramp a distance of 10 meters F hand M 100kg Constant Speed Up 10 m h 1m pick which one is closest a 980 Joule b 9800 Joule d 98 Joule e impossible to tell from this data 1 Joule 1N x 1m unit of energy Work Framp x Lramp Fvert x height 15 How much work force applied x distance did I have to do to push cart along the ramp a distance of 10 meters F hand M 100kg Constant Speed Up 10 m h 1m pick which one is closest a 980 Joule b 9800 Joule d 98 Joule e impossible to tell from this data Work Framp x Lramp Fvert x height 100kg 9 8m s2 1 m 980 N 16 How big a force did I have to exert to push the cart along the ramp a distance of 10 meters F hand M 100kg Constant Speed Up 10 m h 1m pick which one is closest a 980 N b 9800 N d 98 N e impossible to tell from this data Work Framp x Lramp Fvert x height 17 How big a force did I have to exert to push the cart along the ramp a distance of 10 meters F hand M 100kg Constant Speed Up 10 m h 1m pick which one is closest a 980 N b 9800 N d 98 N e impossible to tell from this data Work Framp x Lramp Fvert x height 980 J So Framp 980J 10m 98 N 18 If no conservation law have to do trig oh my Framp f Fg sin theta theta Fg Part of the weight Fg is countered by the ramp Framp The force down the ramp is proportional to the sine of the angle of the ramp 19 Different Kinds of Energy Kinetic Energy the energy in a moving mass Ek 1 2 mv2 Potential Energy the energy stored in a mass pushed up against a force gravity mgh spring 1 2 kx2 Heat The energy stored in a mass by virtue of its temperature kinetic 20 Kinetic energy conversion of work to motion velocity no longer constant Suppose only force along motion is net force Fnet ma vf vi v a x t Fnet m t 1 2 vf vi vf vi Fnet m 1 2 vf vi t 1 2 m vf2 vi2 Fnet x Change of kinetic energy work done Speed one gets falling down a ramp depends on the height loss of potential energy 21 Energy of a spring can be calculated in same way x Push from equilibrium Work on spring F x Fx Work 1 2 Finit Ffinal x Finit 0 Ffinal kx Work 1 2 kx2 22 Now have three forms of energy Kinetic energy 1 2 mv2 Gravitational potential energy mgh Spring energy 1 2 kx2 Through work we can convert any one to any other 23 Now have three forms of energy Kinetic energy 1 2 …