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, what happens to the spring? WHY???

3. Answer  Gravitational force (Fg) or the weight of the mass pulls the spring down (stretches spring). This creates potential ELASTIC energy (energy due to the shape of the spring).  The more mass on the end of the spring, the farther it goes down and the more potential energy it has.  The force from the spring is equal to the force of gravity.

4. Springs – What happens when you add more weight?

5. 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…

6. What kind of energy is this?  Potential Energy Elastic Potential Energy to be exact!

7. Compression  Springs can also compress. If you compress a spring it can gain potential energy as well. When you let go, the spring transforms the potential elastic energy into another type of energy (kinetic in the case of the push toys).

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

9. Elastic Energy – Summary Slide  Ee = The potential energy that is stored in elastic/stretchy things like: elastics, springs, diving boards, bungee cords, bows (bow and arrows), etc.  Elastic potential energy is due to the shape of the elastic or spring- either compressed or stretched.

10. Elastic or Spring Force Summary  The force that is used to create the compression or stretch in the spring/elastic.  This equation will be explained soon

11. Restoring Force Summary  The restoring force is the force that is needed to put the spring back to equilibrium. It is in the opposite direction of the force that compressed or stretched the spring to store the energy originally.  Example: If you stretch a spring by 0.5m and you had to use 150N of force, the restoring force is -150N.

12. Hooke’s Law  The restoring force is opposite to the applied force. (negative sign) Gravity applied in the negative direction, the restoring force is in the positive direction

13. Hooke’s Law (summary slide) F spring : Applied force to stretch/compress spring x : displacement of the spring from the equilibrium position (units: m) k: the spring constant (units: N/m) The spring constant is unique to the spring (similar to coefficient of friction). A large spring or coil has a large k value.

14. 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?

15.  F = kx(Hooke’s Law)  133 = k(0.71)(sub in values)  k = 133/0.71(rearrange)  k = 187.32 N/m  190 N/m

16. Practice Problems  Textbook Page 258  35-37

17.  http://www.youtube.com/watch?v=y XnbvZx9iWs

18. Elastic Potential Energy of a Spring (summary)  Formula: E e = ½ kx 2  k is the spring constant  x is the displacement from equilibrium position  Units: Joules (J)

19. 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?

20. Answer:  A) E e = ½ kx 2  E e = ½ (75)(0.28) 2  E e = 2.9 J  B) F = kx  F= 75(0.28)  F = 21 N

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

22. Conservation of Energy  Remember: Energy cannot be created or destroyed.  Using the same equation as before, Ei = Ef, now we can add another type of energy in:  Eg+Ek+Ee (initial)= Eg+Ek+Ee (final) In presence of friction:  Eg+Ek+Ee (initial)= Eg+Ek+Ee (final)+ Q

23. Quick Lab – Spring Constant

24. 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?

25. Answer  X = 0.20m

26. Example 2:  A 70. kg person bungee steps 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?

27.  Answer: 64 N/m  Conservation of Energy Worksheet

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