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Springs and Hooke’s Law

Springs and Hooke’s Law. Physics 11. Springs. A mass-spring system is given below. As mass is added to the end of the spring, how would you expect the spring to stretch?. Springs. Springs. 2 times the mass results in a 2 times of the displacement from the equilibrium point…

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Springs and Hooke’s Law

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  1. Springs and Hooke’s Law Physics 11

  2. Springs A mass-spring system is given below. As mass is added to the end of the spring, how would you expect the spring to stretch?

  3. Springs

  4. Springs • 2 times the mass results in a 2 times of the displacement from the equilibrium point… • 3 time the mass… 3 times the displacement…

  5. What kind of energy is this? • Potential Energy • Elastic Potential Energy to be exact!

  6. What else besides springs has elastic potential energy? • Diving boards • Bows (bow and arrows) • Bungee cord

  7. Hooke’s Law Fspring: Applied force X : displacement of the spring from the equilibrium position (units: m) K: the spring constant (units: N/m)

  8. Hooke’s Law • the restoring force is opposite the applied force. (negative sign) • Gravity applied in the negative direction, the restoring force is in the positive direction

  9. Example • An archery bow requires a force of 133N to hold an arrow at “full draw” (pulled back 71cm). Assuming that the bow obeys Hooke’s Law, what is its spring constant?

  10. F = kx • 133 = k(0.71) • k = 133/0.71 • k = 187.32 N/m  190 N/m

  11. Restoring Force • The restoring force is the force that is needed to put the spring back to equilibrium. • Example: If you stretch a spring by 0.5m and you had to use 150N of force, the restoring force is -150N.

  12. Practice Problems • Textbook • Page 258 • 35-37

  13. Elastic Potential Energy of a Spring • Formula: Ee = ½ kx2 • Units: Joules (J)

  14. Example: • A spring with spring constant 75 N/m is resting on a table. • A) If the spring is compressed a distance of 28cm, what is the increase in its potential energy? • B) What force must be applied to hold the spring in this position?

  15. Answer: • A) Ee = ½ kx2 • Ee = ½ (75)(0.28)2 • Ee = 2.9 J • B) F = kx • F= 75(0.28) • F = 21 N

  16. Practice Problems • Page 261, questions 38, 39, 40 • Page 261 (Section Review) • 1, 2, 3, 4, 7

  17. Conservation of Energy with a Spring • Ex. 1: A 4.0 kg block slides across a frictionless table with a velocity of 5.0m/s into a spring with a stiffness of 2500 N/m. How far does the spring compress?

  18. Answer • X = 0.20m

  19. Example 2: • A 70. kg person bungee jumps off a 50.m bridge with his ankles attached to a 15m long bungee cord. Assume the person stops at the edge of the water and he is 2.0m tall, what is the force constant of the bungee cord?

  20. Answer: 64 N/m • Conservation of Energy Worksheet

  21. Practice Problems • Textbook • Page 261 • 38-40 • Section review (p 261) • 1-10

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