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Understanding Line Integrals and Potential Energy in Physics

This quiz explores line integrals and their relationship with work and potential energy. It highlights the role of force vectors, path integrals, and the importance of evaluating work done by different forces in overcoming gravity and other influences. Through practical examples, including a skateboarder on a ramp, students learn to analyze how height, angle, and velocity affect potential energy and work done in a conservative force field. This foundational understanding is crucial for mastering the principles of physics.

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Understanding Line Integrals and Potential Energy in Physics

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  1. Honors Physics 1Class 09 Fall 2013 • Quiz 4 • Line integrals • Potential Energy

  2. So what?

  3. Line integrals • Requires force vector, path (in vector form), dot product and integral. • Sometimes you can do several separate integrals over simple steps in the path. • Sometimes you need to relate dx, dy, dz in the path. • Examples follow.

  4. Work by a uniform force

  5. Work done by what on what? • Be careful when evaluating work. • Is it not unusual to focus on one force (the force you apply and neglect others.) • Consider lifting a book from the floor to the table. • You do work FyouH so Wby you = FyouH. • But gravity does work too=-FyouH. • Total work = 0.

  6. Bad force!

  7. Bad force with functional path

  8. Conservative forces and Potential Energy • If the work line integral between two points is independent of the path taken, then the force is conservative.

  9. PHYS1100_F2012 Work and potential energy • Dang!

  10. PHYS1100_F2012 Exercise 9.1_______________Skateboarder Going Up a Ramp • A skateboarder is moving at velocity v and comes • to a ramp at angle theta to the ground. • How high does he get? (Physically.) • On what properties of the system does his height depend? (His mass? The angle? His velocity?) • How long does the ramp have to be so that he doesn’t fall off the end?

  11. PHYS1100_F2012 Example Projectile ProblemSkateboarder Going Up a Ramp • Dude!

  12. PHYS1100_F2012 Example Projectile ProblemSkateboarder Going Up a Ramp • Dang!

  13. PHYS1100_F2012 • Dang!

  14. What potential energy tells us about force

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