Classical Mechanics Lecture 8

Transcription

1 Classical Mechanics Lecture 8 Name St.No. - Date(YY/MM/DD) / / Section Today's Concepts: a) Poten)al Energy b) Mechanical Energy UNIT 11: ENERGY CONSERVATION Approximate Classroom Time: Two 100 minute sessions In order to understand the equivalence of mass and energy, we must go back to two conservation principles which... held a high place in pre-relativity physics. These were the principle of the conservation of energy and the principle of the conservation of mass. Albert Einstein OBJECTIVES 1. To understand the concepts of potential energy and kinetic energy. Mechanics Lecture 8, Slide 1 2. To investigate the conditions under which mechanical

2 Stuff asked about last year: Gravity is the law. violators will be brought down. How were these equa)ons derived? I don't want to have to memorize, I would like a logical explana)on of these equa)ons. Why is the poten)al energy of a spring hanging ver)cally 1 / 2 ky 2? I thought poten)al energy was always defined as mgh. What is the easiest way to understand these rates/ ra)os? The rela)onship of KE, W tot and and mechanical energy is really confusing. please explain. Ques)on 1. Why shoo)ng the ball horizontally gives the same speed as shoo)ng up or down. I seriously cannot stand springs!!! >:[ let's discuss polar bears ea)ng green beans The whole thing with seung a point on a spring equal to h=0 My cat's name is MiXens. Mechanics Lecture 8, Slide 2

3 Stuff you asked about this year: Doesn't maxer what I type here cuz they don't go up on the slide anymore... integrals and integrals of deriva)ves, or how to fake understanding them. So my girlfriend told me she needs )me and distance. Is she calcula)ng velocity? I found the idea of normal force doing work on the object to be puzzling. My cat's name is MiXens. Mechanics Lecture 8, Slide 2

4 Summary Lecture 7 Work KineCc Energy theorem Lecture 8 For springs & gravity (conservacve forces) Total Mechanical Energy E = KineCc + PotenCal Work done by any force other than gravity and springs will change E Mechanics Lecture 8, Slide 3

5 Relax. There is nothing new here It s just re-wricng the work-ke theorem: everything except gravity and springs If other forces aren't doing work Mechanics Lecture 8, Slide 4

6 Finding the potential energy change: Use formulas to find the magnitude Check the sign by understanding the problem Mechanics Lecture 8, Slide 5

7 CheckPoint Three balls of equal mass are fired simultaneously with equal speeds from the same height h above the ground. Ball 1 is fired straight up, ball 2 is fired straight down, and ball 3 is fired horizontally. Rank in order from largest to smallest their speeds v 1, v 2, and v 3 just before each ball hits the ground. A) v 1 > v 2 > v 3 2 B) v 3 > v 2 > v 1 C) v 2 > v 3 > v 1 h 1 3 D) v 1 = v 2 = v 3 Mechanics Lecture 8, Slide 6

8 Clicker Question Which of the following quancces is NOT the same for the three balls as they move from height h to the floor: h A) The change in their kinecc energies B) The change in their potencal energies C) The Cme taken to hit the ground Mechanics Lecture 8, Slide 8

9 Clicker Question A block of mass m is launched up a fricconless ramp with an inical speed v and reaches a maximum verccal height h. A second block having twice the mass (2m) is launched up the same ramp with the same inical speed (v). What is the maximum verccal height reached by the second block? A) h B) h C) 2h D) 4h v m h Mechanics Lecture 8, Slide 9

10 Clicker Question A block acached to a spring is oscillacng between point x (fully compressed) and point y (fully stretched). The spring is un-stretched at point o. At point o, which of the following quancces is at its maximum value? A) The block s kinecc energy B) The spring potencal energy C) Both A and B x o y Mechanics Lecture 8, Slide 10

11 Clicker Question A block acached to a spring is oscillacng between point x (fully compressed) and point y (fully stretched). The spring is un-stretched at point o. At point x, which of the following quancces is at its maximum value? A) The block s kinecc energy B) The spring potencal energy C) Both A and B x o y Mechanics Lecture 8, Slide 11

12 Clicker Question A block acached to a spring is oscillacng between point x (fully compressed) and point y (fully stretched). The spring is un-stretched at point o. At which point is the acceleracon of the block zero? A) At x B) At o C) At y x o y Mechanics Lecture 8, Slide 12

13 CheckPoint A box sliding on a horizontal fric3onless surface runs into a fixed spring, compressing it a distance x 1 from its relaxed posi3on while momentarily coming to rest. If the ini3al speed of the box were doubled, how far x 2 would the spring compress? A) B) C) x Mechanics Lecture 8, Slide 13

14 CheckPoint x A) B) C) A) the formula is 1/2kX 2 so it would be the square root of two when the equa)on is rearranged B) Since both the velocity and distance variables are squared in the kine)c energy and spring poten)al energy equa)on, double velocity also doubles extension. C) The velocity is squared so it will be 4 )mes more distance. Mechanics Lecture 8, Slide 14

15 Spring Summary M kx 2 x Mechanics Lecture 8, Slide 15

16 CheckPoint In Case 1 we release an object from a height above the surface of the earth equal to 1 earth radius, and we measure its kine)c energy just before it hits the earth to be K 1. In Case 2 we release an object from a height above the surface of the earth equal to 2 earth radii, and we measure its kine)c energy just before it hits the earth to be K 2. Compare K 1 and K 2. A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 wrong Case 1 Case 2 Mechanics Lecture 8, Slide 16

17 Clicker Question For gravity: +U 0 What is the poten)al energy of an object of mass m on the earths surface: A) B) C) U surface = U surface = U surface = GM e m 0 GM e m R E GM e m 2R E R E Mechanics Lecture 8, Slide 17

18 Clicker Question What is the poten)al energy of a object star)ng at the height of Case 1? A) B) C) Case 1 Case 2 R E Mechanics Lecture 8, Slide 18

19 Clicker Question What is the poten)al energy of a object star)ng at the height of Case 2? A) B) C) Case 1 Case 2 R E Mechanics Lecture 8, Slide 19

20 What is the change in poten)al in Case 1? A) ΔU case1 = GM em = 2Re R e GM em R e B) ΔU case1 = GM em = Re 2R e GM em 2R e Case 1 Case 2 R E Mechanics Lecture 8, Slide 20

21 What is the change in potential in Case 2? What is the change in poten)al in Case 2? A) ΔU! R e case2 = GM em = Re 3 R e e GM R e e m B) ΔU case2 = GM em = Re 3R e GM R e e m Case 1 Case 2 R E Mechanics Lecture 8, Slide 21

22 Draw U r 0 U Mechanics Lecture 8, Slide 22

23 What is the ra)o A) 2 B) 4 C) 4/3 D) 3/2 Case 1 Case 2 Mechanics Lecture 8, Slide 23

24 In Case 1 we release an object from a height above the surface of the earth equal to 1 earth radius, and we measure its kine)c energy just before it hits the earth to be K 1. In Case 2 we release an object from a height above the surface of the earth equal to 2 earth radii, and we measure its kine)c energy just before it hits the earth to be K 2. Compare K 1 and K 2. CheckPoint A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 Case 1 Case 2 Mechanics Lecture 8, Slide 24

25 Dangers to Earthlings by Jason s