1. Physics 106 Lesson #5 Work and Energy Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu

2. First Law: Objects continue their state of motion (rest or constant velocity) unless acted upon by a net external force. Second Law: The action of a net external force on an object is to cause its momentum to change with time. For objects with a constant mass this can be written as F = ma. Third Law: Any object which exerts a force on another object experiences an equal and opposite force from the object it acts upon. Newton’s Laws: Review

3. Newton’s 1st law: Inertia Newton’s 2nd law: Force and Momentum Newton’s 3rd law: Action and Reaction Newton’s Laws: Summary True if Mass is Constant Always True Newton Said: Rocket Cars:

4. Newton’s Second Law Solves Galileo’s Puzzle! All objects fall with the same downward acceleration ! A Falling Object… m Our Hero!

5. Review: Linear Momentum and Newton’s Second Law The Second Law in Newton’s own words: “ The change in the quantity of motion is proportional to the motive force impressed and is made in the direction of the line in which that force is impressed.”

6. Review: Impulse and Momentum If we multiply both sides of Newton’s Second Law by time, we get another way to say it: “The impulse (force x time) delivered by the net force equals the change in an object’s momentum” This is also called the Impulse -- Momentum Theorem This is a vector equation Force X Time = Change in Momentum This is our rocket car experiment

7. Impulse and Momentum: Rocket Car Data The final momentum is constant to ~ 10% The units for impulse and momentum are kg-m/s or N-s

8. We can measure the impulse of our CO 2 rocket engines this way. Rocket Science: Impulse Delivered by a Rocket Engine Force (N) Time (s) Area Under Curve = Impulse In Newton-Seconds (N-s) Thrust vs. Time Impulse = Force x Time

9. In football, the defensive player applies a force for a given amount of time to stop the momentum of the offensive player who has the ball. An object with momentum can be stopped if a force is applied against it for a given amount of time. Impulse in Football F

10. Rocket Science: Thrust Demo: Water Rocket + y Cannot be described with F = ma ! Thrust = Exhaust Speed x (Ejected Mass/Time)

11. Newton’s laws of motion provide a complete description of mechanics. Using Newton’s laws we can: –predict solar eclipses for millennia to come –design suspension bridges –understand the fate of distant galaxy clusters What about quantities that do not change during motion? –energy and momentum are conserved in certain circumstances –these conservation laws transcend Newtonian mechanics and lie at the very core of our understanding of nature –conservation laws enable us to solve many problems without a detailed understanding of the forces that act  simplification The Story So Far...

12. If no net external force acts on the system it is isolated and linear momentum is conserved Newton’s Second Law: Another Trick-Momentum Conservation!

13. Rocket Propulsion: Momentum Conservation Define the system: rocket + fuel Initial momentum of the system is zero Momentum of the system is conserved because the forces are internal Image courtesy NASA p rocket p fuel We are ignoring gravity Demonstration: Cannon Recoil The forward momentum of the rocket must equal the rearward momentum of the fuel!

14. Image courtesy NASA p rocket p fuel We are ignoring gravity Rocket Propulsion: Momentum Conservation The CO 2 canisters eject 4 grams of CO 2 The speed of sound in air is 340 m/s→(275 m/s)/(340 m/s) = Mach 0.8

15. We call many activities “work” Work in physics has a concise definition Definition: Work is the action of a force through a distance Work and Energy F d Example: You exert a horizontal force F to push an object an object through a horizontal displacement d Work is a scalar Energy ≡ the ability to do work

16. Most generally, work is the product of the component of force parallel to the displacement and the magnitude of the displacement: Work and Energy d F θ F║F║ Work has units of N-m ≡ Joules ≡ J Work can be positive or negative. Positive work is done if the force acts in the direction of motion. Negative work is done if the force acts in opposition to the motion. A force which acts perpendicular to the direction of motion does zero work.

17. kinetic energy means “energy of motion” Kinetic Energy and the Work-Energy Theorem The work done by a net force is equal to the change in the kinetic energy of the object on which the net force acts Net work is required for an object to change speed We can either determine the net force and calculate the work it does or calculate the work done be each force and add it up to get the net work done The Work- Energy Theorem Caution Quiz Ahead

18. Concept Test #1 Which statement about work is true? A.Only the component of a force parallel or anti-parallel to the displacement does work. B.The component of a force perpendicular to the displacement does positive work. C.Only the net force on an object does any work. Caution Quiz Ahead

19. Concept Test #2 When you do positive work on an object, its kinetic energy A. decreases. B. increases. C. remains the same. D. need more information about how the work was done

20. Work by Conservative Forces The work a conservative force does on an object in moving it from a point A to a point B is path independent. It depends only on the path’s end points. Conservative Forces: 1.Gravity 2.Elastic (spring) Force 3.Electromagnetic Force The work done by gravity is the same for path A-B-C-D-E as it is for path A-E D B A C E For conservative forces it is possible to define a potential energy function

21. Alternate definition: a conservative force does no work on an object moving around a closed path. Work and Conservative Forces The work done by gravity on the car as is travels in a closed loop from start, around the track and back to start is zero. Caution Quiz Ahead

22. After hiking all day, you return to the trail head from which you departed that morning. The work that gravity has done on you during your hike is: Concept Test #3 A)Positive B)Zero C)Negative Gravity is a conservative force no work done moving in a closed loop.

23. Work Done by the Gravitational Force mg PE=0 h0h0 hfhf mg An object loses gravitational potential energy and gains an equal amount of kinetic energy as it falls toward the Earth. The sum of gravitational potential energy and kinetic energy never changes → total energy is conserved (neglecting air!).

24. A ball dropped from rest that falls a height h looses PE and gains KE With no air resistance, the gain in KE is equal to the loss in PE : Energy can be converted from one form to another Converting PE to KE No friction or air drag h m

25. A Bob-Sled Run

26. Comments on Gravitational Potential Energy Gravitational potential energy is energy that an object possesses by virtue of its position in a gravitational field. We measure the height h with respect to some arbitrary reference point. Therefore, define your choice for the zero potential energy level first. There is no intrinsic significance to the absolute value of an object's gravitational potential energy. It's differences in gravitational potential energy that matter. Gravitational potential energy can be thought of as an energy reserve that you can draw on and convert into kinetic energy and as a form of energy into which kinetic energy can be converted.

27. Total Energy Conservation The principle of conservation of energy: Energy can neither be created nor destroyed, but can only be converted from one form to another. Work-Energy: The Work-Energy Theorem is energy conservation and turns mechanics into accounting. W nc ≡ Work done by nonconservative forces other than gravity → Friction Demo: Downhill Duck The Work-Energy “Balance Sheet” KE ≡ Cash PE ≡ Deposits W friction ≡ Taxes!