1 / 14

Adv Physics

Adv Physics. Chapter 13 Sections 1 & 2. Simple Harmonic Motion. Any motion that repeats itself over the same path in a fixed time due to a restoring force ex – simple pendulum (gravity) mass on spring (force of spring) - restoring force is proportional to displacement.

primo
Download Presentation

Adv Physics

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. Adv Physics Chapter 13 Sections 1 & 2

  2. Simple Harmonic Motion • Any motion that repeats itself over the same path in a fixed time due to a restoring force ex – simple pendulum (gravity) mass on spring (force of spring) - restoring force is proportional to displacement

  3. Hooke’s Law • For small displacements from equilibrium, a spring applies a force to a mass that is proportional to its displacement from equilibrium and opposite in direction

  4. Hooke’s Law cont’d. F = -kx where F = force k = spring constant (-indicates stiffness of spring) x = displacement Negative in equation since force is always opposite the direction of displacement

  5. Sample Problem A 76 N crate is attached to a spring (k = 450 N/m). How much displacement is caused by the weight of this crate?

  6. Sample Problem A spring of k = 1962 N/m loses its elasticity if stretched more than 50 cm. What is the mass of the heaviest object the spring can support without being damaged?

  7. Sample Problem If a mass of 0.55 kg attached to a vertical spring stretches the spring 2 cm from its original equilibrium position, what is the spring constant?

  8. Simple Harmonic Oscillators • All SHOs cycle through acceleration, velocity, force and energy • Pendulum at release pt.(max amplitude) – max F - max PE, min KE -max a -min v (v=0)

  9. Simple Harmonic Oscillators bottom of swing - min F (F=0) (amp = 0) - min PE, max KE - min a (a=0) - max v max swing - max F (max amp) - max PE, min KE - max a - min v (v=0)

  10. Terms to Know • Period – time it takes to complete one cycle of motion T = time/#cycles [T] = sec • Frequency – number of cycles per second f = #cycles/time [f] = 1/sec = Hertz, Hz

  11. Periods • Period of simple pendulum ____ T = 2π √ (l/g) • Period depends on length and accel due to g • Period does not depend on mass or how far you pull it back (if Θ < 15 degrees)

  12. Periods • Period of a mass-spring oscillator _____ T = 2π √ (m/k) • Period depends on stiffness of spring and mass on spring • Period does not depend on how far you pull it back

  13. Mass Spring Oscillators Us = ½ kx2 KE = ½ mv2 Total energy = ½ kA2 ___________ Since E = Us + KE v=√ (k/m) (A2 – x2) ____ Max v when x = 0 so vmax=√ (k/m)A

  14. Sample Problem A mass spring system is in SHM in the horizontal direction. If the mass is 0.25 kg, the spring constant is 12 N/m, and the amplitude is 15 cm, (a) what would be the maximum speed of the mass, and (b) where would this occur? (c) What would be the speed at a half amplitude position?

More Related