Chapter 10 - Creating models

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

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

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

Frequency = 1/Time period

Displacement:

• 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
• 
  

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.