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PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101 Plan for Lecture 14:

PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101 Plan for Lecture 14: Chapter 12 – Static equilibrium Balancing forces and torques; stability Center of gravity Will discuss elasticity in Lecture 15 (Chapter 15). Summary of gravity:. R E. m. R ES. F. v. a. M sat.

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PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101 Plan for Lecture 14:

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  1. PHY 113 C General Physics I • 11 AM-12:15 PM MWF Olin 101 • Plan for Lecture 14: • Chapter 12 – Static equilibrium • Balancing forces and torques; stability • Center of gravity • Will discuss elasticity in Lecture 15 (Chapter 15) PHY 113 C Fall 2013 -- Lecture 14

  2. PHY 113 C Fall 2013 -- Lecture 14

  3. Summary of gravity: RE m RES F v a Msat Newton’s law of gravitation: Earth’s gravity: Stable circular orbits of gravitational attracted objects: PHY 113 C Fall 2013 -- Lecture 14

  4. From Webassign Assignment #12: When a falling meteoroid is at a distance above the Earth's surface of 3.40 times the Earth's radius, what is its acceleration due to the Earth's gravitation?m/s2 towards earth m r=4.4RE PHY 113 C Fall 2013 -- Lecture 14

  5. From Webassign Assignment #12: An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 6.79 m/s2. Determine the orbital period of the satellite. r PHY 113 C Fall 2013 -- Lecture 14

  6. From Webassign Assignment #12: How much work is done by the Moon's gravitational field as a 1090 kg meteor comes in from outer space and impacts on the Moon's surface? RM iclicker question W>0 W<0 PHY 113 C Fall 2013 -- Lecture 14

  7. From Webassign Assignment #12: A space probe is fired as a projectile from the Earth's surface with an initial speed of 1.74 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. vi PHY 113 C Fall 2013 -- Lecture 14

  8. From Webassign Assignment #12: Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v = 190 km/s and the orbital period of each is 10.7 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 1030 kg.) PHY 113 C Fall 2013 -- Lecture 14

  9. From Webassign Assignment #12: Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v = 190 km/s and the orbital period of each is 10.7 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 1030 kg.) • iclicker exercise: • Who might pose a question like this? • A mean professor. • A puzzle master. • An observational astronomer. PHY 113 C Fall 2013 -- Lecture 14

  10. Meanwhile – back on the surface of the Earth: Conditions for stable equilibrium PHY 113 C Fall 2013 -- Lecture 14

  11. Stability of “rigid bodies” N mig PHY 113 C Fall 2013 -- Lecture 14

  12. Center-of-mass Torque on an extended object due to gravity (near surface of the earth) is the same as the torque on a point mass M located at the center of mass. mi ri rCM PHY 113 C Fall 2013 -- Lecture 14

  13. Notion of equilibrium: Notion of stability: T- mg cosq = 0 -mg sin q = -maq F=ma  r q T t=I a r mg sin q = mr2 a = mraq mg(-j) Example of stable equilibrium for q» 0. PHY 113 C Fall 2013 -- Lecture 14

  14. Unstable equilibrium: Support aboveCM: Support belowCM: r q T mg(-j) PHY 113 C Fall 2013 -- Lecture 14

  15. NikWallenda walking on high wire across Grand Canyon PHY 113 C Fall 2013 -- Lecture 14

  16. Analysis of stability: PHY 113 C Fall 2013 -- Lecture 14

  17. X ** PHY 113 C Fall 2013 -- Lecture 14

  18. PHY 113 C Fall 2013 -- Lecture 14

  19. RCM X ** Fg1 mg PHY 113 C Fall 2013 -- Lecture 14

  20. iclicker question: F2 F1 L/3 mg Mg L • Consider the above drawing of the two supports for a uniform plank which has a total weight Mg and has a weight mg at its end. What can you say about F1 and F2? • F1 and F2 are both up as shown. • F1 is up but F2 is down. • F1 is down but F2 is up. PHY 113 C Fall 2013 -- Lecture 14

  21. X ** F2 F1 L/3 mg Mg L PHY 113 C Fall 2013 -- Lecture 14

  22. iclicker question: • The fact that we found F1<0 means: • We set up the problem incorrectly • The analysis is correct, but the direction of F1 is opposite to the arrow • Physics makes no sense • iclicker question: • What would happen if we analyzed this problem by placing the pivot point at F1 ?: • The answer would be the same. • The answer would be different. • Physics makes no sense PHY 113 C Fall 2013 -- Lecture 14

  23. X ** T Mg mg PHY 113 C Fall 2013 -- Lecture 14

  24. X ** d PHY 113 C Fall 2013 -- Lecture 14

  25. Mg = 120 N mg = 98 N T < 110 N Fwall X ** mg Mg N T PHY 113 C Fall 2013 -- Lecture 14

  26. A ladder of weight Mg and of length L is supported by the ground with static friction force f and by a frictionless wall as shown. The firefighter has weight mg and is half-way up the ladder. Find the force that the ladder exerts on the wall. X ** x q PHY 113 C Fall 2013 -- Lecture 14

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