Conservative vs. Non-conservative forces Gravitational Potential Energy. Work done by non-conservative forces and changes in mechanical energy

Transcription

1 Next topic Conservative vs. Non-conservative forces Gravitational Potential Energy Mechanical Energy Conservation of Mechanical energy Work done by non-conservative forces and changes in mechanical energy 1

2 Motivation Why do we learn about potential energy and conservation of mechanical energy? 2

3 iclicker Quiz Work done by a gravity force h 1 4 m Mass =1 kg Mass =1 kg h 1 4 m h h m m vs. + h 4 1 m Fg mg h 4 1 m (Work along h 1 ->h 2 ->h 3 ->h 4 ) vs (Work along h 1 ->h 4 ) Which work is greater? A) Work along h 1 ->h 2 ->h 3 ->h 4 B) They are equal C) Work along h 1 ->h 4 D) Not enough information 3

4 iclicker Quiz Work done by a gravity force x1=0 m x2=4 m h 1 3 m Mass =1 kg vs. vs. Fg mg h 4 0 m (Work along red arrows) vs (Work along green arrows) vs (work along blue arrow) Which work is the greatest? A) Work along green arrows B) Work along blue arrow C) Work along red arrows D) Work along red and green are equal and greater than work along blue arrow E) They are all equal 4

5 Conservative force If the work done by a force depends only on initial and final positions, not on the path between them, the force is called a conservative force. Gravity force is a conservative force. 5

6 iclicker Q: Work done by friction force Position 1m 2m 3m 4m vs. x f 1N : opposite to - m x4 4m k displacement - In which case, the work by friction is more negative? A) Top B) Bottom C) They are equal D) N.E.I. Is friction force a conservative force? 6

7 Non-Conservative force If the work done by a force depends not only on initial and final positions, but also on the path between them, the force is called a non-conservative force. Example: Friction force,tension, normal force, and force applied by a person. 7

8 Conservative forces in Phys 102: Gravity, Spring force(to be studied in future) Non-Conservative forces in Phys 102: Friction, Normal force, Tension, Other applied forces 8

9 height=10 m Mass=1 kg Can you find the work done by the gravity force along the path? A) Yes, of course. B) Please No. C) Not enough information height=2 m 9

10 Gravitational Potential Energy h i (Work done by gravity on object with mass m ) W mg( h h ) g i f Fg mg mgh i mgh f h f U where U g, i g, f U g mgh U g = Gravitational Potential Energy", which depends on position only. Energy related to position, which potentially converted to kinetic energy. W U U ( U U ) U g g, i g, f g, f g, i g Work done by gravity is negative of gravity Potential Energy change 10

11 Height: h Gravitational Potential Energy Mass m Gravitational Potential Energy: U g mgh (Note: Height, h, should be measured along vertical direction.) The higher and the heavier an object is, the greater the gravitational potential energy is. 11

12 A U mgh mgh mg( h h ) mg h g A B A B B iclciker: True or false? (a), (b), and (c) have the same answer. A) True B) False C) N.E.I. 12

13 Example: Bungee Jump and Gravitational potential energy (a) Is that, by any chance, uh Prof. Ahn? (b) Suppose that the person s mass is 70 kg and the height of the bridge from the water surface is 120 m. What is the person s gravitational potential energy when the person starts to jump? The height and the potential energy is measured from the water surface. New Zealand, 2004

14 initial m= 3 kg 10 m final 30 deg iclicker Quiz The change in gravitational potential energy is (a)3 x 9.8 x 10 J (b) 3 x 9.8 x (-10) J (c) something else 14

15 initial m= 3 kg 10 m final 30 deg Example: The change in gravitational potential energy is J 15

16 initial m= 3 kg 10 m final 30 deg Example: The work done by gravity is 16

17 W U U ( U U ) U g g, i g, f g, f g, i g Work done by gravity force is negative of gravitational potential energy change If gravitational force is the only force that does work, net g, then, from Work-Energy theorem,,and above. K U g K U g K U g 0 does not change. W net K W W 17

18 Conservation of Mechanical Energy with gravity force Define Mechanical energy : W mech W If net g E K U g mv mgh or, if gravity force is the only forces that does work, E E mech, f mech, i : Mechanical energy does not change. Mechanical energy is conserved. In general, if conservative forces are the only forces that do work, mechanical energy is conserved. : Conservation of mechanical energy 18

19 Conservation of Mechanical Energy If conservative forces only cause energy changes, the kinetic and potential energy can change, but their sum, the mechanical energy E mec of the system, cannot change. Example: Falling ball Height h 1 v 1 Less kinetic energy, but More potential energy h 2 v 2 More kinetic energy, but Less potential energy 0

20 Conservation of Mechanical Energy If conservative forces only cause energy changes, the kinetic and potential energy can change, but their sum, the mechanical energy E mec of the system, cannot change. Example: Falling ball Height h 1 v 1 Mechanical energy Emech mv mgh h 2 v 2 Conservation of mechanical energy 1 mv mgh 1 mv mgh

21 iclicker Quiz A person throws a ball 30 degree from horizontal from the top of a 20 m high building. Neglect the air resistance. True or false? If he throws the ball at a different angle but with the same speed, the ball would hit the ground at a different speed. (a) True (b) False 21

22 Example: Pendulum 2 m rope V_i=0 30 degree What is the speed at the bottom? 22

23 Example. A car with its engine off costs along a straight highway, which goes uphill. How far along the highway will the car go before its stops, if its initial speed was 30 m/s, and the slope is 15 o? The tires roll, not skid. 23

24 Work done on a system by non-conservative force If non-conservative forces do work on an object, in addition to conservative forces, Mechanical energy changes by the amount of work done by the non-conservative force. E E E W mech mech, f mech, i non conservative E mech K U

25 Example: Surface with friction K 1 0 J Displacement = 5 m Height change = 3 m K 2? Mass of the dog = 10 kg Friction force = 10 N Find the final kinetic energy, K 2?

26 Example: A skier stars from rest at the top of a frictionless incline of height 20 m. At the bottom of the incline, the skier encounters a horizontal surface where the m k =0.21. How far does the skier travel on the horizontal surface before coming to rest? iclicker 1: In this problem, work done by normal force is. iclicker 2: In this problem, work done by gravity force is. iclicker 3: In this problem, work done by friction force is. (a) positive, (b)zero, (c)negative 26

27 7. A person pulls a sled with load from rest. The total mass of the sled with load is 50kg, and the person exerts a force of 1.2x10 2 N on the sled by pulling on the rope with angle 30 degree. (u_ k =0.2) What is the kinetic energy of the sled after he pulls the sled 5 m? iclicker Quiz In this problem, Magnitude of the normal force is mg. (A) true (B) false 27

28 A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. How much work is done by the dissipative (air) resistive force, which is a nonconservative force, on the projectile during this ascent? 28