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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.

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Adv Physics

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  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?

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