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
C = Q/V Capacitance measured in Farads - 1 farad = 1C per V
I = Change in Q / Change in time
Uses for capacitors:
- Flash photography
- 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
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
Simple harmonic motion
Frequency = 1/Time period
- SHM starting from Maximum displacement - x = Acos(2πft)
- SHM starting from the Midpoint - x = Asin(2πft)
- F = kx (k is the spring constant)
- T = 2π x *
- E = 1/2 x kX2
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.