Chapter 10 - Creating models

revision cards for chapter 10 - creating models

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Radioactivity and Exponential Decay

Activity = decay constant x number of atoms

or A = λN

Activity is measured in becquerels (Bq) = 1 decay per second 

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

dN/dt = -λN

Half life = ln2/λ

Number of remaining atoms = N0e-λt

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C = Q/V Capacitance measured in Farads - 1 farad = 1C per V

I = Change in Q / Change in time

Uses for capacitors:

  • Flash photography
  • Defibrillators
  • Back up power supplies

the shorter the time taken for the capacitor to release the higher the current!

E = 1/2 x Q x V

E = 1/2 x CV2

  • Q = I x t
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Charging and Discharging

Factors affecting time of charge or discharge:

  • capacitance of capacitor, affects the amount of charge that can be transferred at a given voltage.
  • resistance of the circuit affects the current that can flow through the circuit.

The charge of a capacitor decreases exponentially.

Time constant τ = RC

Q = Q0e-1

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Simple harmonic motion

Frequency = 1/Time period


  • SHM starting from Maximum displacement - x = Acos(2πft)
  • SHM starting from the Midpoint - x = Asin(2πft)

Harmonic Oscillators:

  • F = kx (k is the spring constant)
  • T = 2π x *
  • E = 1/2 x kX2

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Free and forced vibrations

The total energy of a free oscillating mass on a spring:

Etotal = 1/2mv + 1/2k

  • a system can be forced to vibrate by a periodic external force
  • when the driving frequency approaches the natural frequency, the system gains more energy from the driving force and vibrates with a rapidly increasing amplitude
  • when this happens the system is resonating.
  • Damping happens when energy is lost to surroundings due to damping forces such as air. Amplitude reduced over time.
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