Chapter 10 Flashcards
What is the percolation model?
The idea of a ‘critical density’ in something. E.g. if trees in a forest are below this density, a fire won’t spread all the way through it; if it is above this, then they will. Same concept found in oil cracks
What is an exponential change?
A change in which the rate of change is proportional to the amount of that something there is
How do you calculate radioactivity?
A = (lambda)N, where lambda is the decay constant (probability of decay in a fixed time period), and N is the number of unstable nuclei. A is number decaying per second
How can radioactive decay be described mathematically?
dN/dt = -(lambda)N = -A where dN/dt is change in number of nuclei with respect to time, and lambda is the decay constant. N/N(0) = e^(-lambda t)
How does carbon dating work?
Organic matter absorbs carbon from environment; small amount of this is radioactive C-14. Whilst alive, constantly replenished, so C-12:C-14 ratio constant; when dies, C-14 concentrations decrease as it decays. Half life of C-14 is 5730 years
What is half life?
The time for half of a radioactive sample to decay. Calculated by t(1/2) = ln2/(lambda), where lambda is the decay constant and calculated by activity/no. nuclei
How do you calculate the age of an object with carbon dating?
Measure activity which is proportional to number of nuclei, N remaining. Find factor F by which activity has been reduced. Calculate number of half lives passed, L by 2^L = F. Age=t(1/2)*L
What is a capacitor?
A device for storing electrical charge. It is a pair of electrical conductors, one positively charged and one negatively charged
Define capacitance
C=Q/V charge stored per volt; units of farads or CF(-1)
What is the rate of flow of charge proportional to?
dQ/dt = -Q/RC where R is resistance and C is capacitance
What is the exponential equation for capacitor discharge?
Q/Q(0) = e^(-t/RC)
What is the time constant of a discharge circuit?
RC
How do you calculate energy stored on a capacitor?
E=1/2 QV; E=1/2 CV^2; E=1/2 Q^2/C
What are the properties of a harmonic oscillator?
It is accelerated to the equilibrium point by a spring like force that always pulls towards the equilibrium point
At the equilibrium point, there is no net force, so no net acceleration
It stores energy: as potential energy at the extremes and kinetic energy through the equilibrium position
Resistive forces gradually take energy from the oscillator, so amplitude decreases
The time trace is a sinusoidal curve
How is acceleration calculated for harmonic oscillators>
a= -ks/m where m is mass, k is spring constant and s is displacement
How do you calculate the time period of a pendulum?
T=2pi*sqrt(L/g)
What are the equations for s,v and a for harmonic oscillators?
s=Acos(2pift)
v=-2piftAsin(2pift)
a=-(2pift)^2cos(2pift)=-(2pift)^2 s
How do you calculate the frequency of a harmonic oscillator?
2pif=sqrt(k/m) where k is spring constant and m is mass
How do you calculate energy stored in a spring?
E=1/2 kx^2
What is resonance?
If a driving force is applied at the same frequency that the object oscillates at naturally, the oscillations increase, storing more and more energy until they break apart.
What is damping?
How easily energy leaks away from an oscillator
What is the relationship between damping and resonance?
Low damping gives a large maximum resonance response, but a narrow peak range
High damping gives a small maximum resonance response but a broad range across which it occurs
