Chapter 10

Question 1

What is the percolation model?

Answer 1

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

Question 2

What is an exponential change?

Answer 2

A change in which the rate of change is proportional to the amount of that something there is

Question 3

How do you calculate radioactivity?

Answer 3

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

Question 4

How can radioactive decay be described mathematically?

Answer 4

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)

Question 5

How does carbon dating work?

Answer 5

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

Question 6

What is half life?

Answer 6

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

Question 7

How do you calculate the age of an object with carbon dating?

Answer 7

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

Question 8

What is a capacitor?

Answer 8

A device for storing electrical charge. It is a pair of electrical conductors, one positively charged and one negatively charged

Question 9

Define capacitance

Answer 9

C=Q/V charge stored per volt; units of farads or CF(-1)

Question 10

What is the rate of flow of charge proportional to?

Answer 10

dQ/dt = -Q/RC where R is resistance and C is capacitance

Question 11

What is the exponential equation for capacitor discharge?

Answer 11

Q/Q(0) = e^(-t/RC)

Question 12

What is the time constant of a discharge circuit?

Answer 12

RC

Question 13

How do you calculate energy stored on a capacitor?

Answer 13

E=1/2 QV; E=1/2 CV^2; E=1/2 Q^2/C

Question 14

What are the properties of a harmonic oscillator?

Answer 14

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

Question 15

How is acceleration calculated for harmonic oscillators>

Answer 15

a= -ks/m where m is mass, k is spring constant and s is displacement

Question 16

How do you calculate the time period of a pendulum?

Answer 16

T=2pi*sqrt(L/g)

Question 17

What are the equations for s,v and a for harmonic oscillators?

Answer 17

s=Acos(2pift)
v=-2piftAsin(2pift)
a=-(2pift)^2cos(2pift)=-(2pift)^2 s

Question 18

How do you calculate the frequency of a harmonic oscillator?

Answer 18

2pif=sqrt(k/m) where k is spring constant and m is mass

Question 19

How do you calculate energy stored in a spring?

Answer 19

E=1/2 kx^2

Question 20

What is resonance?

Answer 20

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.

Question 21

What is damping?

Answer 21

How easily energy leaks away from an oscillator

Question 22

What is the relationship between damping and resonance?

Answer 22

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