1 / 23

More applications of Newton’s laws (chapter five)

More applications of Newton’s laws (chapter five). Forces of friction (static, kinetic) Uniform circular motion Nonuniform circular motion Velocity dependent forces Numerical methods Fundamental forces Gravitational field. Friction.

tsalls
Download Presentation

More applications of Newton’s laws (chapter five)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. More applications of Newton’s laws (chapter five) • Forces of friction (static, kinetic) • Uniform circular motion • Nonuniform circular motion • Velocity dependent forces • Numerical methods • Fundamental forces • Gravitational field

  2. Friction • Force acting parallel to an interface that opposes the relative motion • Static – frictional force opposite to applied force - magnitude fs • where s is the coefficient of static friction and n is the magnitude of the normal forces between the surfaces • the equality holds just as the object starts to slip

  3. Friction • Kinetic – frictional force opposite to relative motion – magnitude fk • where k is the coefficient of static friction and n is the magnitude of the normal forces between the surfaces • the kinetic frictional force is constant • s and k are constants that depend on the nature of the surfaces • Usually, s > k

  4. Friction • Note: Static friction is not constant – it is whatever is needed to match the applied force, up to the limit of Sn • As the applied force increases, the static frictional force also increases, until the limit, then the object begins to slide, and the frictional force goes to a constant value

  5. Friction • ConcepTest • Examples • Demo

  6. +y +x m1 m1 m2 m2 Example

  7. Example

  8. Question • What do you call a broken boomerang?

  9. Question • What do you call a broken boomerang? • Answer: A stick.

  10. Newton’s 2nd law applied to uniform circular motion A mass in uniform circular motion (speed v) accelerates according to This acceleration must be caused by some force along a direction towards the center of the radius of curvature (r)

  11. L  r Example: conical pendulum

  12. Uniform circular motion • ConcepTest

  13. R  Nonuniform circular motion • If an object changes its speed while in circular motion, there is both a radial and a tangential component to the acceleration, therefore, there will be a radial and tangential force applied. • Example: mass moving in a vertical circle

  14. Words of wisdom • "If I had only known, I would have been a locksmith."-Albert Einstein • "There is no clearer manifestation of pure evil than teachers giving assignments over holiday breaks."-James Halloran

  15. Velocity dependent forces Two models: 1. Force proprtional to the velocity (viscous, low speed) b is a constant that depends on the object size and shape and the medium 2. Force proportional to the square of the magnitude of the velocity (air, high speed) D: drag coefficient : density of air A: cross sectional area of object

  16. Velocity dependent forces 1. Force proprtional to the velocity

  17. Velocity dependent forces Can solve differential equation where  = m/b is a time constant related to the motion Or, just find terminal speed (a=0)

  18. Velocity dependent forces Force proportional to the square of the magnitude of the velocity Nonlinear differential equation Terminal speed:

  19. Words of wisdom • "I love deadlines. I like the whooshing sound they make as they fly by."-Douglas Adams • "In a survey taken several years ago, all incoming freshman at MIT were asked if they expected to graduate in the top half of their class. Ninety-seven percent responded that they did."-??? • "We made too many wrong mistakes."-Yogi Bera

  20. Numerical representations of particle dynamics Euler method

  21. Fundamental forces of nature Gravitational: force between any two objects where G is the universal gravitational constant Electromagnetic: force between two charged objects (q) where ke is the Coulomb constant Nuclear (strong) – short range Weak – short range

  22. Gravitational field • Field: the effect in a region of space that induces a force on an object • e.g the field (created by a mass) exerts the force on the other masses

  23. Last bad joke for this chapter • An atom walking down the street says to its friend “I think I lost an electron. The friend asks “Are you sure?” to which the first atom repiles “Yea, I’m positive.”

More Related