A2 revision U5-U11 and practicals

U5 FURTHER MECHANICS Only one statement is correct or incorrect. Identify which one.

• The equal and opposite force of the centripetal force of rotation is called centrifugal force.

• Two objects are moving to the right. After an elastic collision the momentum is conserved and both objects must continue moving to the right but can do so at different speeds.

• If I calculate the direction of momentum of an object I can calculate the direction on velocity of this object.

• I can calculate the work applied to an object if I am given it's impulse during that time.

Answer explanation

Centrifugal does not exist (only used as a construct when choosing the rotating object as frame of reference to justify the inertia away from the center of rotation) - the opposite would be eg the tension on the string so FALSE; in the collision supposing right=positive, conservation could be p start(>0 + >0)=p end(<0+>>0) so one could go backwards if properly compensated so FALSE; momentum is vectorial so (p→)=(m)·(v→) so the direction is the same as it's velocity so TRUE; work=∆E=∆0.5·mv²=∆0.5p²/m=Ft=mat... all need mass at least, so FALSE.

U6 ELECTROMAGNETIC FIELDS Only one statement is correct or incorrect. Identify which one.

• In the equation E=kq/r², k is the permittivity of free space.

• The time constant of a capacitor is equal to RC and shows the time it takes for the current to fall 50%.

• A static charge situated close to a magnetic field suffers no effect from this field.

• Flux linkage of a solenoid is measured in Webers

Answer explanation

k is Coulomb´s constant and ε0 is permittivity of free space so FALSE; time constant RC corresponds to e^-1=36% so FALSE; flux linkage is measured in Wb-turns (=ϕN) so FALSE; a static charge (not moving) does not suffer any force from the magnetic field until it moves, so TRUE.

U7 PARTICLE PHYSICS Only one statement is correct or incorrect. Identify which one.

• In a beta-plus decay, a proton turns into a neutron and an Up turns into a Down.

• We can create matter from empty space.

• Hadrons are any particle that contain quarks.

• In a synchrotron the frequency of a particle will be f=Bq√[1-v²/c²]/(2πm)

Answer explanation

Beta plus is the opposite of the more common beta minus, it is TRUE; empty space does not mean empty energy so we can have pair production of particles so TRUE; hadrons need to have at least 2quarks so eg a UpQuark-TauLepton (if it existed) would not be a Hadron so FALSE; the synchrotron uses magnetism to curve the particle so mv²/r=Bqv so v/r=Bq/m and so f=w/2π=v/r2π=Bq/2πm applying relativistic mass f=Bq/2πmɣ=Bq√[1-v²/c²]/2πm so TRUE

U8 THERMODYNAMICS Only one statement is correct or incorrect. Identify which one.

• The maximum kinetic energy of the particles due to temperature is proportional to thermal energy.

• √<c²>=∑v/N

• Charles's law shows that a P/T graph has a linear relation in an ideal gas at constant Volume.

• A substance with a higher specific heat capacity will, given the same heating conditions, increase temperature more slowly.

Answer explanation

There is no maximum kinetic energy on a Maxwell-Boltzmann graph due to thermal energy (although the probability is smaller and smaller...) so FALSE; root mean square velocity √<c²>=√∑v²/N so FALSE; Charles's law is V/T=ct at constant Pressure, the one described is Gay-Lussac's law so FALSE; given mcΔθ=ΔE, more c=more ΔE, and given P=E/t and a constant heating power P, more E=more t, so TRUE.

U9 NUCLEAR DECAY Only one statement is correct or incorrect. Identify which one.

• 1u=9.3·10²MeV

• A rock contains 1000 unstable nucleus and in 4hours 4nucleus decay. The time for 700 to decay is 50days.

• U235 has a binding energy of 1786MeV and Po210 a binding energy of 1634. Therefore Polonium is more stable than Uranium.

• A GM tube fixed to the ground and pointing at a fixed beta-radioactive sample cannot measure separately the background radiation and the artificial radiation.

Answer explanation

The conversion of u to eV is not in the constant list but we can use eV-J and u-kg linked by E=mc² so 1.66·10^-27·c²/1.6·10^-19=933MeV so TRUE; λ=∆N/∆tNaverage=4/4·60·60·998(approx) and t=ln(N₀/N)/λ=ln(1000/300)/(λ·60·60·24)= 50.06days so TRUE; stability comes from binding energy per nucleon so Po=1634/210=7,78>U=1786/235=7.6 so TRUE; if we block the radiation with a sheet of metal only background radiation arrives from the sides so FALSE

U10 OSCILLATIONS Only one statement is correct or incorrect. Identify which one.

• A pendulum of 2kg and length 5m is separated 50cm from the center. The restorative force will be 2N.

• A SHM with an amplitude of 4m and an angular velocity of 2rad/s will after 10s present an acceleration of -15m/s².

• The mechanical energy of a spring without friction or heat dissipation is constant.

• The fastest way of making a SHM stop at it's equilibrium point is to overdamp it.

Answer explanation

From the equation T=2π√L/g=(SHM) 2π√m/k then L/g=m/k so k=mg/L=2·9.81/5=3.9kg/s² so F=kx=3.9·0.5=1.96≈2N TRUE; w²x=2²·4cos(2·10)=15 so TRUE; mechanical energy=Ekinetic+Epotential=constant so TRUE; overdamping stops it before it reaches equilibrium so it actually takes a longer time than with critical damping, so FALSE

U11 ASTROPHYSICS Only one statement is correct or incorrect. Identify which one.

• We can calculate the gravitational constant G by using data from the Earth as G=rv²/m

• An astronaut of 60kg while falling the last 50m on an asteroid records that the gravitational potential increases from 23 to 24J/kg. The gravitational acceleration on the surface is 1.2m/s².

• The main sequence stars gradient on a Hertzsprung-Russell diagram show that Temperature and Luminosity are inversely proportional.

• Thanks to the red shift of star's light we have calculated the age of the universe.

Answer explanation

The centripetal force is from eg the Moon so mₘvₘ²/r=Gmₘmₑ/r² and simplifying G=rvₘ²/mₑ therefore we need data from an orbiting body so FALSE; g=∆V/∆x=1/50=0.02Nm/kg (mass in unecessary, g is per mass) so FALSE; the Hertzsprung-Russell diagram has Temperature flipped negative, so the gradient of the graph is numerically positive, so FALSE; red shift indicates velocity/distance which indicates the time from distance zero which is the age of the universe so TRUE.

PRACTICALS Only one statement is correct or incorrect. Identify which one.

• 
• A thermostat circuit is calibrated using a variable resistor and a thermistor and measuring current over voltage.

• We demonstrate Boyle's law by using a manometer and plotting pressure over inverse length.

• When investigating frequency of resonance as we increase the amplitude we must find a sudden peak in frequency.

Answer explanation

The circuit is missing another branch that can discharge parallel to the capacitor so FALSE; the thermostat is calibrated to a certain base temperature (level of thermostat) with a fixed resistor, then we can insert a variable resistor - moreover it is calibrated with a Vcell vs Vmotor graph, so FALSE; Boyle's law would be P∝1/V and in a manometer V∝tube length to TRUE; resonance happens at certain frequencies not amplotudes, and the effect is a peak in amplitude (not frequency) so FALSE.