Springs and Hooke’s Law Physics 11. Newton’s Cradle  Explain this…  0HZ9N9yvcU.

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Presentation transcript:

Springs and Hooke’s Law Physics 11

Newton’s Cradle  Explain this…  0HZ9N9yvcU

Springs A mass-spring system is given below. As mass is added to the end of the spring, what happens to the spring? WHY???

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…

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

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

Hooke’s Law F spring : Applied force 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).

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?

 F = kx  133 = k(0.71)  k = 133/0.71  k = N/m  190 N/m

Practice Problems  Textbook Page 258  35-37

 XnbvZx9iWs

Restoring Force  The restoring force is the force that is needed to put the spring back to equilibrium. Usually it opposes gravity so it is a positive force.  Example: If you stretch a spring by 0.5m and you had to use 150N of force, the restoring force is -150N.

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

Elastic Potential Energy of a Spring  Formula: E e = ½ kx 2  Units: Joules (J)

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?

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

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

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?

Answer  X = 0.20m

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?

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

Practice Problems  Textbook Page 261  Section review (p 261)  1-10