Note-A-Rific: Mechanical Kinetic You ve probably heard of inetic energy in previous courses using the following definition and forula Any object that is oving has inetic energy. E ½ v 2 E inetic energy (J) ass (g) v velocity (/s) We re going to eep on using that basic forula, but we do need to clear up the definition a little bit. First, what is any object? Any object just refers to anything that we can easure as having a ass. This covers everything fro sall subatoic particles lie electrons all the way up to galaxies. Second, when they say oving we need to as Moving relative to what? Right now you re sitting otionless at a coputer screen, so you have no inetic energy, right? o This is true relative to the reference frae of the roo you re in. Isn t the earth spinning on its axis? Isn t the whole planet oving around the sun? You need to ae sure that you are always sure about what your easureents are being taen in relation to. o Most of the tie we easure stuff relative to the surface of the earth, so things are easier, but be careful. Exaple: A pop can with a ass of 312g is sitting in the cup holder of y car as I drive down Yellowhead at 68 /h. a) How uch inetic energy does it have relative to e in the car? E ½ v 2 But relative to e the pop can s velocity is zero, so E 0 J b) How uch inetic energy does it have relative to soeone standing on the side of the road? E ½ v 2 ½ (0.312 g) (19 /s) 2 E 56 J
Also, be ready to anipulate this forula to solve for other variables Exaple: What is the velocity of a 150 g cart if it has 3.60 x 10 J of inetic energy? First, see if you can correctly solve the forula for v. This is one of the anipulations that students coonly ix up! You should get v 2(3.60x10 150g J) 21.9 / s The concept of inetic energy can also coe in handy if you need to perfor calculations of the wor done, as the following exaple shows Exaple: I a driving y 2500 g Caaro down the street at 52 /h. I notice that there is a school zone ahead, so I hit the braes to slow down to 2 /h. If I slowed down over a distance 15, what was the average force applied by the braes? First, you ll need to change those velocities fro /h into /s v i 52 /h 1 /s (reeber to eep the whole nuber 1. fro your calculator written down on scrap paper that s the nuber you want to use in your calculations before rounding off at the end of the proble. v f 2 /h 6.7 /s Next, calculate the change in inetic energy of the car as it slowed down You could just do a regular calculation of the inetic energy before and subtract it fro a regular calculation of the inetic energy after. Or, you can use a forula derived this way: E E f E i ½ v f 2 ½ v i 2 ½ (v f 2 v i 2 ) E ½ (v f 2 v i 2 ) ½ 2500g [(6.7/s) 2 (1/s) 2 ] E -2.1 x 10 5 J Since wor is a change in energy W E, but wor also equals F d. E W E Fd F E / d (-2.1 x 10 5 J) / (15) F -1. x 10 3 N The negative sign just shows that the force is being exerted in the opposite direction to the velocity of the object.
The fact that wor is equal to the change in energy in a situation is usually called the Wor- Theore It basically just eans that you can do calculations lie the ones we did above and you ll get the right answer. It will go even further once we have looed at potential energy. Potential Potential energy is another concept that you have already studied. You were probably told Potential energy is stored energy that is able to do wor later. E p gh E p potential energy (J) ass (g) g gravity (/s 2 ) h height () This definition is pretty good, but the forula is a bit of a proble in that it refers to one specific ind on potential energy: Gravitational. Gravitational potential energy is by far the ost coon, so it s no big surprise that it s the one everybody thins about. For now we will only exaine this one, but eep in ind that there are other fors of potential energy lie elastic potential energy & cheical potential energy. In the forula E p gh watch out how you use the variables. 1. is the ass of the object being held up. If an apple is being held above the ground, use the ass of the apple in your calculations, not the earth s ass. 2. g is the acceleration due to gravity. Since we will ost often be doing questions that relate to earth, you can use 9.81/s 2, but every so often questions will appear that are not on earth, so ae sure to use the appropriate value. 3. h is the height of the object above soe reference point, which should be whatever the object will hit if it is dropped. If you re holding an apple above a table, don t use the earth as a reference point, use the table top. The weird part is that you can change the gravitational potential energy of an object by oving it horizontally (no change in its actual vertical position) because of reference points Held above the tabletop, we see that the apple doesn t have a lot of E p.
We are NOT creating energy when we do this. Instead, we are just changing the proportion of E p versus other fors of energy. Anyways, at soe point, soehow, that apple reached that height and wor was done to get it there. Therodynaics Conservation of energy actually grows out of two ain ideas in physics the First and Second Laws of Therodynaics. 1. can not be created or destroyed, only changed fro one for to another. This just basically eans the if one thing loses energy, soething else ust be gaining energy. The opposite is also true. In an ideal situation this transfer of energy would be perfect and coplete, but when was the last tie you reeber our universe being perfect? This leads us to the second idea 2. In any energy conversion, there will always be soe waste energy released as heat into the surrounding environent. Because it is ipossible to perfectly transfer energy fro one for to another in the real universe, does that ean we are breaing the first law? No, in fact we recognize that the total energy can still be accounted for, it s just that soe of the energy is released as unusable heat. A large branch of physics called Therodynaics studies the liits of just how close to perfect any device could be in transferring energy. There is a lot ore to the laws of therodynaics, but what you ve just read are the basics that you need to now. Here s an exaple 100 J of waste heat 100 J of waste heat A battery stores 1000 J of Cheical E p running a little otor Motor does 900 J of Wor to ove a box pulling box across floor Box has 800 J of E as it oves across the floor
Although there is a loss of energy at each step, we can still account for the energy being lost to the surroundings. You started with 1000 J of total energy. As you changed energy to other fors you lost a total of 200 J to the environent, but still had 800 J at the end a total of 1000 J still! In ost of the wor we do, we assue that we are living in a perfect universe. This eans that for the ost part we will obey the first law, but ignore the second. There will be soe situations when we give you enough inforation to use the second law, but we will be pretty specific about telling you. o Most of the tie we will say soething about the friction involved, since this is the ost coon source for heat loss in your probles. Total Mechanical A large nuber of questions you will do involve the Total Mechanical of a syste. Total echanical energy is just the total of inetic plus potential energy. As long as there are no outside forces unaccounted for, we now that the totals before and after will be equal. E + E p E + E p Note: the little just eans after. Exaple: A person is sitting on a toboggan at the top of a 23.7 tall hill. If the person and toboggan have a total ass of 37.3 g how fast will they be going when they reach the botto of the hill? Assue there is no friction. At the top of the hill the person isn t oving, so E will be zero. At the botto of the hill the E p will be zero. E + E p E + E p ½ v 2 + gh ½ v 2 + gh 0 + (37.3g) (9.81/s 2 ) (23.7) ½ (37.3g) v 2 + 0 8.67x10 3 J 18.7 v 2 v 21.6 /s Notice how in this exaple all of the potential energy the object had at the top of the hill has been turned copletely into inetic energy at the botto. It s also possible to analyze how the potential energy steadily changes into inetic energy during a fall
Exaple: Wille E. Coyote is trying to drop a boulder off a cliff to hit the Roadrunner eating a bowl of birdseed. He wants to now the speed of the boulder at various points. He supplies you with the following blueprint The Coyote wants you to calculate the velocity of the boulder at several different heights above the ground, assuing no air resistance a) 5 b) 30 c) 10 d) 0 a) Well, this one ain t so tough! Since it s sitting at the top of the cliff, its velocity is 0 /s. It ight be handy at this point to calculate how uch E p the boulder has. 200g h 5 E p gh 200g (9.81/s 2 ) (5) 88290 J 8.8 x 10 J b) First, as yourself how uch E p the boulder still has at 30 above the ground. E p gh 200g (9.81/s 2 ) (30) 58860 J 5.9 x 10 J That eans that 8.8 x 10 J - 5.9 x 10 J 2.9 x 10 J is issing, right? Wrong! According to the conservation of echanical energy, that energy ust now be inetic! E ½ v 2 v 2(2.9x10 200g J) 17 / s c) Again, calculate how uch E p you have at this new height of 10
E p gh 200g (9.81/s 2 ) (10) 19620 J 2.0 x 10 J That eans that I have changed 6.9 x 10 J of energy into other fors we ll assue it all changed into inetic energy. E ½ v 2 v 2(6.9x10 J) 26 / s 200g d) By the tie the boulder has reached the ground, all of its potential energy is gone (it s zero etres above the ground!). We all now that when it actually hits the ground it will coe to rest, but we are concerned with how fast it s going when it is right at ground level but hasn t actually touched the ground yet. We can assue that all of the potential energy the boulder had at the top is now inetic energy at the botto E ½ v 2 v 2(8.8x10 J) 30 / s 200g You could be finding the sae answers based on ineatics forulas fro Physics 20. In fact, you ll find that conservation of energy gives you new ways to do any probles that you did with ineatics forulas