Creating Models

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  • Created by: helena
  • Created on: 28-05-13 12:45

Radioactivity and Exponential Decay

Half life = T1/2 = ln2/ λ

Activity = A= λN where λ is the decay constant and  N is the number of atoms

Number of remaining atoms = N0e-λt where N0 = the initial number of atoms

Activity is measured in Becquerels (Bq)

Activity = 1 decay per second

Change in number of radioactive nuclei in a given amount of time:

dN/dt = -λN

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Capacitors

Q=It where t is time

Capacitance is measured in Farads

C = Q/v

Capacitors are used in flash photography, defibrillators and back up power supplies

The shorter the time taken for the capacitor to discharge, the higher I

E = ½ Qv = ½CV2 = ½Q2/C

The factors affecting time of charge/discharge are capacitance and resistance

The charge decreases exponentially (instant charge, exponential discharge)

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Simple Harmonic Motion

Force = F = kx where k is the spring constant

frequency = f =1/T where T is time period

Displacement

  • SHM from max displacement = x = Acos(2πft)
  • SHM from midpoint = x = Asin(2πft)

Time period = T = 2πx

Energy = E = ½kx2

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Free and Forced Vibrations

Energy of a free oscillating mass on a spring

Etotal = ½ mv2 + ½ k

Dampening happens when energy is lost, and Amplitude is reduced

When the driving frequency approaches the natural frequency the system gains more energy. The amplitude increases rapidly. When this happens the system is resonating

Natural Frequency is the frequency at which a system oscillates when not subjected to a continuous or repeated external force

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