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Elastic Potential Energy and Simple Harmonic Motion

Elastic Potential Energy and Simple Harmonic Motion. Hooke’s Law. In the late 1600s, Robert Hooke stated that “The power of any springy body is in the same proportion with the extension." Hooke's law has remained valid today but we’ve replaced power with force .

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Elastic Potential Energy and Simple Harmonic Motion

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  1. Elastic Potential Energy and Simple Harmonic Motion

  2. Hooke’s Law In the late 1600s, Robert Hooke stated that “The power of any springy body is in the same proportion with the extension." Hooke's law has remained valid today but we’ve replaced power with force. - Spring’s compression/expansion is directly proportional to the magnitude of the force exerted by the spring

  3. Hooke’s Law: F= -k * Δx Δx = distance a spring has been stretch F = restoring force exerted by the spring k = spring constant (characterizes elastic properties of the spring's material) Ideal Spring: A spring that obeys Hooke’s Law because it experiences no internal or external friction Animation: http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/HookesLaw/HookesLaw.html

  4. The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

  5. Graph of Stretching Force - Extension Gradient = Spring constant (k=F/Δx) NOTE: Δx will be negative for a compression, positive for a stretch

  6. Elastic Potential Energy The energy stored in an object that is stretched, compressed, bent or twisted.

  7. Example 1 You stretch a spring horizontally a distance of 24 mm by applying a force of 0.21N [E]. a) Determine the force constant k of the spring. b) What is the force exerted by the spring on you? b) Force exerted by the spring is 0.21N [W] (Newton’s 3rd Law) a) k = ?

  8. Simple Harmonic Motion SHM: oscillatory (periodic) motion, mass at the end of a spring Displacement Vs Time: http://www.acoustics.salford.ac.uk/feschools/waves/shm.htm Spinning Disk: http://www.acoustics.salford.ac.uk/feschools/waves/shm2.htm#damping At amplitude (A): speed of mass is zero and mass changes direction. At equilibrium (x=0) the mass is moving fastest.

  9. Remember from circular motion… Stretched to it’s maximum when x=A/-A, or r=A for disk. (Let r=x)

  10. Use Hooke’s Law. Force exerted by spring changes as compressed or stretched. Period (seconds): Acceleration depends on x! (Opposite direction of displacement) Frequency (Hertz):

  11. Example 2 A 0.39 kg mass is attached to a spring The mass spring is placed horizontally on a frictionless surface. The mass is displaced 14cm, and is then released. Determine the period and frequency of the Simple Harmonic Motion. The force constant of spring is 1. Period 2. Frequency The period is about 0.37seconds. The frequency is about 2.7 Hz.

  12. Practice Problems (For next 2 days) • Pg. 206-207 #1-4,6 • Pg. 214-215 #17,18,21 • Pg. 211 # 8,10,12,15 • Pg. 218-219 #1,4,5,12,13,16 • Chapter 4 Review pg. 226-229

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