Springs and Hooke

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Springs and Hookes Law

• Physics 11

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Check Your Understanding

• In a well known lecture demonstration, a bowling
  ball is hung from a ceiling by a steel wire. The
  lecturer pulls the ball back and stands against
  the wall of the room with the ball against his
  nose.
• a) If the lecturer simply releases the ball, he
  will not be injured. Why not?
• b) If the lecturer pushes the ball, when it
  returns it will likely hit him and cause injury.
  Why?

3

• http//www.youtube.com/watch?v0ASLLiuejAo

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Solution

• a) When the ball is released, it is not initially
  moving so all of its energy is potential. As it
  swings over and back, its total energy must
  remain the same (or decrease if it loses any
  energy) even though the energy gets converted
  into kinetic energy and back into potential
  energy. When it returns back to its starting
  point, all of the energy returns to potential
  energy. Since it cant have more energy than it
  started with, it cannot go any higher than it
  started. It therefore cannot hit the person.
• b) If the ball is given a push, its initial
  energy is the sum of its initial potential and
  kinetic energies. After it swings across the room
  and returns to its starting point, it still has
  kinetic energy left so it can continue above its
  starting point. This extra energy that the push
  gave the ball allows it to swing higher than its
  original height so it keeps going and hits the
  person.

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Newtons Cradle

• http//www.youtube.com/watch?vd0HZ9N9yvcU

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Springs

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

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Springs
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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

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What kind of energy is this?

• Potential Energy
• Elastic Potential Energy to be exact!

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What else besides springs has elastic potential
energy?

• Diving boards
• Bows (bow and arrows)
• Bungee cord

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Hookes Law

• Fspring 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).

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Example

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

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• F kx
• 133 k(0.71)
• k 133/0.71
• k 187.32 N/m ? 190 N/m

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Practice Problems

• Textbook
• Page 258
• 35-37

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• http//www.youtube.com/watch?vyXnbvZx9iWs

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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.

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Hookes 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

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Elastic Potential Energy of a Spring

• Formula Ee ½ kx2
• Units Joules (J)

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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?

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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

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Practice Problems

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

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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?

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Answer

• X 0.20m

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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?

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• Answer 64 N/m
• Conservation of Energy Worksheet

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Practice Problems

• Textbook
• Page 261
• 38-40
• Section review (p 261)
• 1-10