1 / 14

Energy And SHM

Energy And SHM. Energy of Spring. Spring has elastic potential energy PE = ½ kx 2 If assuming no friction, the total energy at any point is the sum of its KE and PE E = ½ mv 2 + ½ kx 2. At Extreme. Stops moving before starts back, so all energy is PE and x is max extension (A)

kesia
Download Presentation

Energy And SHM

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Energy And SHM

  2. Energy of Spring • Spring has elastic potential energy PE = ½ kx2 • If assuming no friction, the total energy at any point is the sum of its KE and PE E = ½ mv2 + ½ kx2

  3. At Extreme • Stops moving before starts back, so all energy is PE and x is max extension (A) E = ½ k A2 • At equilibrium, all energy is KE and vo is the max velocity E = ½ m vo2

  4. Algebraic Manipulation • ½ mv2 + ½ kx2 = ½ k A2

  5. Example • If a spring is stretched to 2A what happens to a) the energy of the system? B) maximum velocity? C) maximum acceleration?

  6. Example • A spring stretches .150m when a .300kg mass is hung from it. The spring is stretched and additional .100m from its equilibrium point then released. Determine a) k b) the amplitude c) the max velocity d) the velocity when .050 m from equilibrium e) the max acceleration f) the total energy

  7. Period of Vibration • Time for one oscillation depends on the stiffness of the spring • Does not depend on the A • SHM can be thought of similar to an object moving around a circle • Time for one oscillation is the time for one revolution

  8. v = 2r/ T • At max displacement r = A • vo = 2A/T • T= 2A/ vo • ½ kA2 = ½ mvo2 • A/vo = (m/k) • T = 2(m/k)

  9. Period of oscillation depends on m and k but not on the amplitude • Greater mass means more inertia so a slower response time and longer period • Greater k means more force required, more force causes greater acceleration and shorter period

  10. Example • How long will it take an oscillating spring (k = 25 N/m) to make one complete cycle when: a) a 10g mass is attached b) a 100g mass is attached

  11. Pendulum • Small object (the bob) suspended from the end of a lightweight cord • Motion of pendulum very close to SHM if the amplitude of oscillation is fairly small • Restoring force is the component of the bobs weight – depends on the weight and the angle

  12. Period of Pendulum • T = 2√(L/ g) • Period does not depend on the mass • Period does not depend on the amplitude

  13. Example • Estimate the length of the pendulum in a grandfather clock that ticks once every second. B) what would the period of a clock with a 1.0m length be?

  14. Example • Will a grandfather clock keep the same time everywhere? What will a clock be off if taken to the moon where gravity is 1/6 that of the earth’s?

More Related