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# Chapter 10

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1. Chapter 10 Energy

2. What is Energy? • "It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount." -Richard Feynman "Lectures on Physics" AP Physics C

3. What is Energy? Con’t • Energy - A measure of being able to do work…..–NASA.gov AP Physics C

4. Matter and Energy • The combination of matter and energy makes up the universe. Matter is substance and energy is the mover of substance. • -Paul Hewitt AP Physics C

5. Definition • Energy is an abstract quantity with the ability to effect physical change in matter. • Energy is the substance from which all things in the Universe are made up. AP Physics C

6. Forms of Energy • Two broad categories of energy: • Potential: Stored Energy • Chemical – Stored in chemical bonds • Mechanical – Stored in objects by tension • Nuclear – Stored in nucleus of atoms • Gravitational – Stored based on height and weight • Electrical – Stored in batteries • Kinetic: Energy due to motion • Radiant – electromagnetic • Thermal - Heat • Motion – Moving objects • Sound – motion of air and other media by sound waves AP Physics C

7. Conservation of Energy • Energy Conservation during freefall: AP Physics C

8. Calculus Approach Lets look at the freefall of a mass, m, from N2L and calculus: AP Physics C

9. Kinetic Energy AP Physics C

10. Gravitational Potential Energy Similar concept to kinetic energy except that the orientation is vertical and the force is gravity. Think KE which has not been created. M d mg AP Physics C

11. Mechanical Energy AP Physics C

12. Problem 1 • A boy reaches out of a window and tosses a ball straight up with a speed of 10 m/s. The ball is 20 m above the ground as he releases it. Use energy to find: • a. The ball’s maximum height above the ground. • b. The ball’s speed as it passes the window on its way down. • c. The speed of impact on the ground. Analysis: Use Kf + Uf = Ki + Ui to solve for y1, v2 and v3. a. At y1, v1 = 0; at y0, v0 = 10 and y0 = 0 AP Physics C

13. Problem 1 con’t b. At y0, v0 = 10; at y2=0, find v2 Speed up = speed down. c. At y0 = 0, v0 = 10; At y3 = -20, find v3. AP Physics C

14. Energy Bar Charts Bar chart modeling a rock thrown upward and returning to same elevation: AP Physics C

15. Zero of Potential Energy Our earlier calculus based derivation of The following expression represented the change in potential energy: The initial position was considered to be zero and resulted in U = mgyf U will vary based on where the zero potential energy level is placed. ΔU will always be the same regardless of the location of the zero level. AP Physics C

16. Non-Freefall Ug • Horizontal surface: no change in gravitational potential energy • Slanted/undulating surface: define s-axis parallel to surface of movement. AP Physics C

17. Ballistic Pedulum • A 10 g bullet is fired into a 1200 g wood block hanging from a 150 cm long string. The bullet embeds itself into the block and the block swings out to an angle of 40°. What was the speed of the bullet? Analysis: Two part problem: The impact of the bullet with the block is inelastic. Momentum is conserved. After the collision the block swings as a pendulum. The sum of the kinetic and potential energies before and after do not change as the block swings to its largest angle. AP Physics C

18. Ballistic Pendulum con’t Collision/Momentum calculations: If we can calculate v1x from swing/energy relationships, we can calculate the speed of the bullet. V2 = 0 and dividing by (mW + mB) gives: or AP Physics C

19. Restoring Forces Restoring Force Elastic Equilibrium Length, L0 Displacement, Δs Δs = L - L0 Fsp = k Δs Spring constant, k AP Physics C

20. Hooke’s Law AP Physics C

21. Hooke’s Law Problem You need to make a spring scale for measuring mass. You want each 1.0 cm length along the scale to correspond to a mass difference of 100 g. What should be the value of the spring constant? AP Physics C

22. Elastic Potential Energy Is the force applied to the ball constant? Describe the mechanical energy in both situations; before and after. AP Physics C

23. Elastic Potential Energy con’t N2L for the ball is: By Hooke’s law, (Fnet)s = -k(s – se), substituting gives: Using the chain rule: Substituting gives: Integrating from initial to final conditions: AP Physics C

24. Elastic Potential Energy con’t From previous slide: Substituting and rewriting gives: ½ mv2 is obviously the kinetic energy. is the elastic potential energy, Us AP Physics C

25. Elastic Potential Energy Problem How far must you stretch a spring with k = 1000 N/m to store 200 J of energy? Elastic potential energy is defined as: Solving for ∆s: AP Physics C

26. Elastic Collisions Perfectly Elastic Collision: A collision in which mechanical energy is conserved. Must conserve momentum and mechanical energy Not possible where friction is involved If only one object, m1, initially moving and all motion is along a line: Solving the first equation for (vfx)1 and substituting into the second gives: AP Physics C

27. Elastic Collisions con’t Squaring and simplifying gives: There are two solutions, (vfx)2 = 0 which is trivial and: Substituting this into the momentum equation gives These allow us to compute the final velocity of each object in terms of the initial velocity of m1 and the relative masses of each object AP Physics C

28. Elastic Collision Problem A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision? Analysis: Expect that v1 will decrease and v2 will significantly increase. Laws conservation of Momentum and ME will be observed. AP Physics C

29. Using Reference Frames AP Physics C

30. Energy Diagrams Energy Diagram: A graph showing a system’s potential energy and total energy as a function of position. AP Physics C

31. Energy Diagram for a Spring AP Physics C

32. Generalized Energy Diagram AP Physics C

33. Stable and Unstable Equilibrium AP Physics C