1. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Physics I 95.141 LECTURE 12 10/18/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Work Done by a Spring The force exerted by a spring is given by: Hooke’s Law

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Example Problem How much work must I do to compress a spring with k=20N/m 20cm?

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Exam Prep Problem A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). Assume there is a velocity dependent drag force (F D =-10v 2 ). –A) (5pts) What is the Force required to move the rocket at the surface of the Earth? 1,000 km above the Earth’s surface? –B) (5pts) What is the Work done by air resistance over the 1,000km? –(C) (10pts) What is the Work done by Force responsible for moving the rocket over those 1,000km?

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Exam Prep Problem A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). –A) (5pts) What is the Force required to move the rocket at the surface of the Earth? 1,000 km above the Earth’s surface? Ignore air resistance.

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Exam Prep Problem A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). –B) (5pts) What is the Work done by air resistance over the 1,000km?

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Exam Prep Problem A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). –C) (10pts) What is the Work done by Force responsible for moving the rocket over those 1,000km?

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Review of Dot Products Say we have two vectors What is angle between them?

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Outline Work-Energy Theorem Conservative, non-conservative Forces What do we know? –Units –Kinematic equations –Freely falling objects –Vectors –Kinematics + Vectors = Vector Kinematics –Relative motion –Projectile motion –Uniform circular motion –Newton’s Laws –Force of Gravity/Normal Force –Free Body Diagrams –Problem solving –Uniform Circular Motion –Newton’s Law of Universal Gravitation –Weightlessness –Kepler’s Laws –Work by Constant Force –Scalar Product of Vectors –Work done by varying Force

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Energy One of the most powerful concepts in science, used to solve complicated problems in basically all fields of Engineering, Chemistry, Materials Science, Physics… For the purpose of this chapter, we will define Energy as: The ability to do work. –This means something has energy if it can exert a force over a distance We will begin by looking at translational kinetic energy

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Translational Kinetic Energy Kinetic: associated with motion Translational: motion in a line or trajectory (as opposed to circular/rotational motion)

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Moving Car Say a car starts at some velocity v 1, and, with a constant net Force F net applied to it, accelerates to a velocity v 2 over a distance d.

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Kinetic Energy The net work done on the car results in a change of the car’s kinetic energy (K). The car’s energy (also in Joules), changes by an amount equal to the net work done on the car.

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Work Energy Principle The net work done on an object is equal to the change in the object’s kinetic energy.

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Example What is the net Work required to accelerate a 1000kg car from rest to 20 m/s? What about from 20 m/s to 40 m/s?

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Example What about the net Work required to stop this car when it is going 40 m/s?

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Energy of a Spring A spring (k=400N/m) is compressed 10cm, and a mass (m=2kg) is place in front of the spring. How much work does the spring do on the mass after the spring is released? x=-10cm

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Compressed Spring What is the kinetic energy (and velocity) acquired by the mass when it separates from the released spring at x=0?

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 What about Friction? Say we assume a constant frictional force (5N) on the mass as it is pushed by the spring. Does work-energy theorem still hold?

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Spring problem Find spidey-k

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Work Done to Extend Spidey-web d≈500m v o =25m/s M train =181,000

22. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Kinetic Energy of Train

23. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Work-Energy Principle Energy is the ability to do work –Train’s kinetic energy does work on Spiderman’s springs Work and Energy have the same units Kinetic Energy proportional to mass and the square of velocity Both Work and Energy are scalar quantities. Can be applied to a particle, or a mass that can be approximated by a particle…where internal motion is insignificant. Why do we use Work/Energy here and not Kinematic equations?

24. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Conservative and Non-Conservative Forces A Conservative Force: –The work done by the force on an object moving from one point to another depends only on the initial and final positions of the object, and is independent of the particular path taken. A conservative force is only a function of position

25. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Is Gravity a Conservative Force? Imagine two scenarios: h

26. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Alternative Definition A force is conservative if the net work done by the force on an object moving around a closed path is zero.

27. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Conservative Forces The work done by a conservative force is recoverable –The work done by the object (on something else) on a given path is equivalent to the work done by the something else on the object on its return trip. –This means that the net work done on the object over the closed loop is zero, which means, from the work- energy theorem, that the change in energy of the object is zero. –Energy is conserved!

28. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Springs Is the Force exerted by a spring a conservative force?

29. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 What about Friction? Is friction a conservative Force? d d

30. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Non-Conservative Forces For friction, the work done by friction on an object moving around a closed loop will never be zero. This work is not recoverable Work done by friction (or any nonconservative Force) depends on path between two points

31. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 Non-Conservative Forces Work done by non-conservative force depends on path

32. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 What about air resistance? Move from point A to point B, either by path 1 or path 2, at constant velocity (F D =-bv). A B Path 1 Path 2 R

33. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 What about air resistance? Move from point A to point B, same path, but different speeds, (F D =-bv). A B Path 1 2R

34. Department of Physics and Applied Physics 95.141, F2010, Lecture 12 What did we learn today? How we can use Energy/Work to understand physical systems Power of Work/Energy is that we don’t have to know anything about acceleration, or even the complicated kinematic equations that would go with spring/mass systems or air resistance, etc… All we need is energy!