1 / 31

Announcements

Announcements. Midterm 2 – Tomorrow (7/30/04) Material from Chapters 7-12 Room where recitation meets Practice Exam available on-line or in Davey library Some good practice problems 7.13, 8.7, 8.21, 9.10, 9.23, 9.35, 10.4, 10.23, 10.29, 11.33, 11.56, 12.19, 12.23, 12.40. Chapter 13.

phila
Download Presentation

Announcements

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. Announcements • Midterm 2 – Tomorrow (7/30/04) • Material from Chapters 7-12 • Room where recitation meets • Practice Exam available on-line or in Davey library • Some good practice problems • 7.13, 8.7, 8.21, 9.10, 9.23, 9.35, 10.4, 10.23, 10.29, 11.33, 11.56, 12.19, 12.23, 12.40

  2. Chapter 13 Equilibrium and Elasticity

  3. Equilibrium An object is in equilibrium if: and Examples: fan blades, ball rolling across the floor… An object is in static equilibrium if it is at rest in our reference frame and Examples: bridges, skyscrapers…

  4. Stable vs. Unstable Static Equilibrium Stable Equilibrium: A small perturbation of the objects position results in the object being pushed back to its original position by restoring forces Unstable Equilibrium: A small perturbation of the objects position results in the object being pushed away from its original position. Neutral Equilibrium: When displaced, the object stays in new position

  5. U x Types of Equilibrium stable neutral unstable

  6. Stable vs Unstable Equilibrium Unstable Equilibrium: easy to knock things over Examples: Dominos or a Rube Goldberg machine

  7. Demo: Equilibrium If I stack two blocks on top of each other, what is the condition for equilibrium? L ½ L Center of mass of top block must be supported by the bottom block

  8. Demo: Equilibrium ½ L What about 3 blocks? CM of top two blocks must be supported by bottom block L ??

  9. Demo: Equilibrium 4 blocks? A pattern is developing…

  10. Demo: Equilibrium This is known as the geometric series, and it never converges! With enough blocks, we can make the overhang as big as we like! Complete overhang! With 5 blocks:

  11. Requirements for Equilibrium If an object is in equilibrium, then: So we can solve statics problems using only the physics we already know!

  12. Problem Solving Strategy: • Draw and label a diagram • Pick an appropriate origin • torques sum to zero about any choice of origin • Sum forces and torques • Solve for unknown quantities

  13. Example: Teeter-Totter A 80 kg parent and a 20 kg child are balancing on a see-saw. If the child sits 2 m from the pivot, where does the parent need to sit, and what is the force on the pivot? D d=2m mg Mg

  14. Example: + D d=2m Pick origin at pivot (makes the torque from the force at the pivot = 0) Fp Mg mg Summing the torques:

  15. Example: D d=2m Fp Summing the forces: Mg mg

  16. Example: Another Way… D=0.5m d=2m Fp Mg mg + Pick dad as origin, then sum torques: Same result!

  17. 10 in T1=? T2=? 5 in 2 in 0.8 N 3 in 2 N 3 N Example: Weights are suspended from a rod which is suspended by two ropes at its ends. Find the tension in these ropes, T1 and T2.

  18. 10 in T1=? T2=? 8 in 5 in 3 in 0.8 N 2 N 3 N + Example: (continued) Pick origin at right edge Sum torques:

  19. 10 in T1=? T2=? 8 in 5 in 3 in 0.8 N 2 N 3 N Example: (continued) Sum forces:

  20. Does it work? T1 T2

  21. Standing on a Ladder FN1 L Mg θ d mg FN2 Ffr A 5 m ladder rests against a frictionless wall at an angle 30º from vertical. The weight of the ladder is 200 N, uniformly distributed along its length. A 1000 N person climbs the ladder. What coefficient of friction must the ladder have with the floor so the ladder does not slip when the person has climbed 4 m along the ladder?

  22. Standing on a Ladder FN1 L Mg d mg FN2 Ffr Pick the origin at the bottom of the ladder: Summing forces in the x-direction: Summing forces in the y-direction:

  23. Standing on a Ladder FN1 L Mg d mg FN2 Ffr Summing the torques:

  24. Towing a Trailer Safely x d=4m N1 N2 Nh ½Mg ½Mg d1=3m d2=5m A trailer hitch has a rated ‘tongue weight’ of 2000 N. A lightweight two-axle trailer, with axles 3 m and 5 m behind the hitch, is pulled behind the vehicle. A 4 m car weighing 10000 N is parked on the trailer. How far back must the car be parked, and what are the forces on the axles?

  25. Towing a Trailer Safely x d=4m N1 N2 Nh ½Mg ½Mg d1=3m d2=5m Pick the hitch as the origin. Sum forces: Sum torques: Don’t know x, N1, N2 2 equations and 3 unknowns! Not enough info!

  26. Indeterminate Structures Sometimes the force and torque equations lead to more unknown forces than equations. Example: Four-legged table Detailed material properties and history determine the forces.

  27. Elasticity When a real object is subjected to a force (or a stress), it will deform (strain). Over a range of deformation, objects usually obey a form of Hooke’s law The “modulus” is like the spring constant. It varies for different materials and different stresses

  28. F A L+DL L Types of Stress Tensile (and compressive): E = Young’s modulus Not all materials are as good under tension as under compression (example: concrete)

  29. Dx F A L V DV Types of Stress Shear stress: G = shear modulus Hydraulic stress: B = Bulk modulus p = pressure

  30. Elasticity Objects return to original shape if deformation is small enough. The point at which a deformation becomes permanent is called the yield strength The point at which on object breaks is called its ultimate strength

  31. Tensile Stress:

More Related