a 2 physics term 22011 answer scheme

8/12/2019 A 2 Physics Term 22011 Answer Scheme

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Name Form Master

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AUCKLAND GRAMMAR SCHOOLCAMBRIDGE A2 PHYSICS EXAM

TERM 2 2011

MARK SCHEME

Time allowed = 2 hourINSTRUCTIONSWrite your name and Masters name in the space provided

on eachsheet.Answer all questions.Write your answers in the spaces provided on the questionpaper.Universal constants and some formulae are provided.The number of marks for each question is given inbrackets [ ] at the end of each question or part question.You will lose marks if you do not show your working,explain the physics or if you do not use appropriate units.

Answer question 12 on a piece of separate Grammar

paper

Induction Q 1Mutual induction and a.c. power Q 2SHM Q 3Gas Laws Q 4X-rays Q 5Ultrasound Q 6Direct sensing Q 7

MRI Q 8Op-Amps Q 9 -11Design Q 12

FOR EXAMINERS USE

Q 1 /21

Q 2 /14

Q 3 /15

Q4 /12

Q5 /16

Q6 /10

Q7 /6

Q8 /16

Q9 /11

Q10 / 8

Q11 / 10

Q12 /15

TOTAL

.........../154

Final %


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Data and Formulae

speed of light in free space, c = 3.00 x 108m s1

permeability of free space, 0= 4x 107H m1

permittivity of free space, 0= 8.85 x 1012F m1

elementary charge, e = 1.60 x 1019C

the Planck constant, h = 6.63 x 1034J s

unified atomic mass constant, u = 1.66 x 1027kg

rest mass of electron, me= 9.11 x 1031kg

rest mass of proton, mp= 1.67 x 1027kg

molar gas constant, R = 8.31 J K1mol1

the Avogadro constant, NA= 6.02 x 1023

mol1

the Boltzmann constant, k = 1.38 x 1023J K1

gravitational constant, G = 6.67 x 1011N m2kg2

acceleration of free fall, g = 9.81 m s2

uniformly accelerated motion, s = ut + at2 , v2= u2 + 2as

work done on/by a gas, W =p V

gravitational potential, = GM / r

simple harmonic motion, a =2x

velocity of particle in s.h.m., v = v0cos t , v = (x02

x2)

resistors in series, R = R1+ R2+ . . .

resistors in parallel, 1/R = 1/R1+ 1/R2+ . . .

electric potential, V = Q / (40r )

capacitors in series, 1/C = 1/C1+ 1/C2+ . . .

capacitors in parallel, C = C1+ C2+ . . .energy of charged capacitor, W = QV

alternating current/voltage, x =x0 sin t

hydrostatic pressure, p = g h

pressure of an ideal gas, p = 1/ 3 Nm / V

radioactive decay, x =x0exp(t )

decay constant, = 0.693 / t


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1. InductionA steel wire is held taut between the poles of a permanent magnet, as illustrated in Fig. 1.1

Fig. 1.1

A cathode-ray oscilloscope (c.r.o.) is connected at the points P and Q.The Y-plate sensitivity is adjusted to 2.0mV cm1and the time base is 5 ms cm1.The wire is plucked at its centre. Fig. 1.2 shows the trace seen on the c.r.o.

Fig. 1.2

(a) Making reference to the laws of induction suggest why,I. an e.m.f. is induced in the wire [2]

Wire cuts through the lines of flux 1

Induced emf proportional to rate of change of flux 1

II. The e.m.f. is alternating [2]The wire moving up and down so cuts flux lines in different directions 1

Induced emf depends on direction of motion 1

(b) Using Fig. 1.2 and the c.r.o. settings determine anequation for the induced alternating e.m.f.

[4]Period of oscillation = T = 30 ms (0.030s) 1Amplitude = 3.0 mV 1

1 1


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(c) Which way would the current be flowing in the wire when the wire is moving downwards? [1]Right ( P to Q ) 1

(d) Would the induced e.m.f. be larger, smaller or the same if the wire was struck without the c.r.o.connected? Explain your answer. [2]

The same (with reasoninduced emf is just to do with rate of change of flux linkage 1

OR

Larger (with reason)As WITH a CRO a small current will be induced to try to oppose themotion of the wire thus giving a smaller velocity and amplitude (and in turn emf). 2

(e) On the graph Fig.1.2 sketch the shape of the trace if the wire was plucked so that it oscillatedat twice the frequency of the original. [2]Greater amplitude 1Period halved 1

(f) If the steel wire was replaced with an aluminium wire would an emf be induced? Explain [2]

Yes, an emf will be induced across all metals moving in a magnetic field 1And induced current will occur if you have a full conducting circuit 1

(g) In a new experiment the magnetic flux density is made to vary with time t (while the wire isstationary) as shown in Fig. 1.3

Sections 1 and 3 straight with emf 1

ASections 2 and 4 zero 1

Sections 1 and 3 opposite 1

Section 1 larger than 3 1

(note section 1 and 3 can be oppositeway around ie 1 negative and 3 positive)Straight copy or inverse zero

Without use of ruler can not get 4/4

Fig. 1.3

Sketch on the graph the resulting e.m.f. across the wire (the wire is connected to the c.r.o.). [4]

(h)State Lenzs Law. [2]

The direction of the induced emf is such that 1

It produces effects to oppose the change causing it 1


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2. Mutual induction and a.c. power(a) Explain why alternating currents are used in transformers? [2]Transformers need change of flux in core 1

Rate of change of flux linkage is proportional to emf 1

(D.C has no change in flux so no induced emf)Or Changing magnetic field is needed to induce current in secondary coil for 1

(b) Why are high voltages used for long distance power transmission? Use equations/ formulae in

your answer. [3]Power = I2 R so to minimise heat loss on wire we need a minimal current 1

Since P = V I if we have a maximum Voltage we have a minimum current 1

Both formula used 1

(c) (i)Explain the difference between the peak and RMS voltage of an a.c. supply

(ii)Why do we use RMS voltages for calculations? [2]RMS is the DC equivalent value, peak is the maximum value of supply 1

RMS allows use of a single number rather than a time variable value 1

(d) Using a c.r.o. a student measures the peak voltage across a 12.0 kresistor connected to amains powered a.c power supply to be 18.0 V.Calculate the rate of transfer of energy in the resistor. [3]

1

(e) Electrical equipment often needs a d.c. voltage to run.

I. What is the name of the process that turns a.c. into d.c.? [1]Rectification 1

II. Place electrical components in the correct places and directions to ensure the a.c. supplywill provide a smoothed d.c. output and that will add to the batteries emf to drive a largercurrent through the bulb.

[3]

Diodes in the correct position 1NO gaps between components 1

Capacitor in the correct position 1


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3. SHM (a) A toy parrot, of mass 0.800 kg, hangs by a long light spring from the ceiling of a room. When the

parrot is in equilibrium the length of spring is 2.23 m. The natural (unstretched) length of thespring is 0.80 m.Calculate the spring constant, k (force per unit extension) [2]

Working 1Answer and unit 1

(b) The parrot is pulled down and released so that it is set oscillating up and down.I. Show clearly that the periodic time of the oscillations is 2.40 s. [2]

Exactly the same working (including answer and unit) 2Missing one bit 1

II. The amplitude of the oscillations is 0.20 m. At time t = 0 theparrots beak is passing through the equilibrium position and moving upwards.

i. Explain what is wrong with this argument: The parrots beak will reach its highestpoint at t = 0.60 s. Therefore at t = 0.30 s it will be at point A, midway betweenthe equilibrium position and the highest position. [2]

The parrot does not move at a constant velocity 1

So doubling/halving the time does not double/half the displacement 1

ii. Use the appropriate simple harmonic motion equation to calculate the actualdisplacement of the beak from the equilibrium position at time t = 0.300 s [3]

1

2(working and answer/unit)

iii. Calculate the maximum speed of the parrot when it is oscillating with anamplitude of 0.200m. [2]

2(working and answer/unit)

iv. State the position (or positions) of the parrot at which it has this speed. [1]

Whenever passing through equilibrium position 1


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(c) If the wings of the parrot are outstretched, the oscillations of the parrot, when displaced andreleased, are noticeably damped. Sketch a possible graph of displacement,x, against time, t, forthese damped oscillations ensuring a maximum displacement at time t=0. [3]

Start at max 1One osc= 2.4 seconds 1Reducing amplitude 1

4. Gas LawsUp to about 12 km from the Earths surface, the temperature and pressure of the atmospheredecrease with height. Typical values are

temperature/ C pressure/10 PaGround level 17 1.00

12km above surface -58 0.19

To simplify calculations, assume air consists only of nitrogen (1 mole of nitrogen = 28g ).Mass of earth = 6.00x1024kg radius of earth = 6380km 1 mole helium = 4g

(a) CalculateI. the volume occupied by 1.00 mole of air at ground level, using the ideal gas equations.

[2]

1

II. the density of air at ground level. [2]

2

(working and answer/unit)

(b) Calculate the r.m.s. speed of the molecules at ground level. [3]

1 1


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(c) Calculate the escape velocity from the earth using the data provided. [3]

1

( ) 1 1

(d) Explain why nitrogen molecules are found in the atmosphere around the earth yet there is littlehelium. [2]

Few molecules have the required escape velocity 1

(helium has a smaller mass higher velocity (or nitrogen larger masss....) 1

5. X-Rays(a) Explain how a beam of X-rays are produced [5]

Electrons accelerated from heated cathode (via thermionic effect) 1

Accelerated through vaccum towards anode 1

When electrons decelerate 1

They lose Ek and emit e-m radiation 1A continuous spectrum since electrons decelerate at different rates 1

(b)I. Why does increasing the filament current not change the energy of the x-ray photon?

[2]Electron energy due to accelerating pd 1

NOT the filament current 1

II. What is the effect of doubling the current through the filament? [2]Additional electrons removed from cathode 1

More electrons travel through tube so more x-rays produced 1

(c) X-ray production produces a continuous spectrum of x-rays, explain how we get a maximumenergy photon? [2]

When all the Ek of an electron is transferred to produce just one photon 1

(some formula to help) 1


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(d)I. X-rays are attenuated in our bodies, what is attenuation? [1]

Reduction in intensity as x-rays are absorbed 1

II. Assuming an arm was made of only one medium with a linear attenuation co-efficient of

4140 cm

-1

and initially x-ray intensity was 9500W m

-2

.What is the maximum thickness that the arm could be if a reading was still made at thedetector (Note a detection can be made if 0.2% of the initial intensity is incident on thedetector). [4]

1

1

1 1

6. Ultrasound Note the speed of sound in air = 330 m s -1

(a) What is the specific acoustic impedance of water, where the density of water is 1g cm -1and thespeed of sound in water is 4.49 faster than in air. [3]

(b) Draw and label an A-scan ultrasound image through your arm taken at the middle of the bicepmuscle. Assume the arm is made up of skin, fat, muscle, bone (in that order) and it goes all theway through to the bone. [3]

labelled peaks 1considered POSITION of peaks (thickness of

muscle) 1Muscle bone peak largest 1

(c) Which regions of the body are difficult to image using ultrasound? [2]Regions which are filled with air (lungs) 1

As almost all intensity is reflected 1

(d) Explain how the piezo-electric crystal in an ultrasound transducer produces a short pulse ofultrasound rather than many high frequency oscillations. [2]

Backing material is placed next to crystal which critically dampens the oscillations once

the ac stops being applied


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7. Direct sensing(a) A strain gauge is set up across a crack in the English block building frames as shown in the

diagram below. What happens to the resistance as the crack closes up (gets smaller) and why?State any assumptions made in your answer. [3]

As the crack closes up the strain gauge wire decreases in length 1

Resistance of a length of wire 1So as length decreases R decreases 1

(the wire will also increase in Area which further decreases Resistance)

(b) The initial resistance of the strain gauge was 340.5 and after some time the resistancechanged to 297.8, whatwas the percentage change of width of the crack [3]


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8. MRI(a) What atom is used in medical MRI imaging for production of [2]

i. The overall picture Hydrogen H................................................................

ii. Contrast in the image Gadolinium Gd...........................................................

(b) Why is a non-uniform magnetic field needed for MRI images to be created? [3]Need a specific point in body with a specific field 1

To isolate these points with a specific larmor frequency 1

Otherwise all atoms will have the same frequency 1

( so impossible to tell where RF radiation is being emitted from)

(c) What is the Larmor frequency? [3]Frequency of precession 1

Of the nucleus 1

About the direction of the applied magnetic field 1

(d) Explain why is a MRI scan safer than a CAT scan? [2]MRI does not have ionising radiation 1

x-rays absorbed by our cells and can be damaged 1

(e) Explain why babies are not usually sent for MRI scans. [2]You must lie still for an MRI scan while it operates 1

Babies are not able to stay very well 1

(f) Explain why it would not be a good idea to send an unconscious person from a car accident foran MRI scan. [2]

It us unknown if the person has metal in their bodies (pacemakers, metal rods, bitsocar) 1

These could heat up or if in soft tissue move while inside MRI machine 1

(g) The room a MRI scanner is placed in is a huge Faraday cage. Explain why this is neededaround the MRI scanner [2]

The Cage will block external Radio waves from entering the room 1

This is important in case RF enters that is being received by the machine to give false

readings 1(do not accept magnetic fields or flux ideas)


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9. Op-Amps(a) In the circuit below, what is the minimum resistance the thermistor can be that will cause the

buzzer to ring (Note, the buzzer requires a voltage of +10V across it to operate, it is not an idealop-amp and the gain is only 500). [5]

1

and use 1 1 1 1

(b) If the buzzer required a large enough power the current generated might blow the op-amp.Redraw the circuit showing how op-amps are protected from these large currents. [1]

Just look at the parts shown above (unless they have added other bits that are not needed)Should also have the 2 added diodes to protect op-amp from back emf

(c) State 5 characteristics of an ideal op-amp [5]

1) Infinite input impedance

2) Zero output impedance

3) Infinite open loop gain

4) Infinite bandwidth

5) Infinite slew rate


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10. (a) By reference to an amplifier, explain what is meant by negative feedback. [2]

Part of the op-amp output is added back into the op-amp input 1

Negative feedback means that a added value will be negative. 1(So the overall circuit gain will be lower than the open loop gain)

(b)An amplifier circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 10.1.

Fig 10.1

The power supply for the op-amp is 9.0 V and the amplifier circuit has to have a gain of 25.

Calculate the resistance of resistor R.

1 1 1

resistance = ........................................... [3]

(c) State the value of the output voltage VOUTof the amplifier in (b) for input voltages VINof

(i)0.08 V,

= - 2 1

VOUT= ............................................ V [1]

(ii) +0.4 V.

= 10V 1

But saturated so 9.0V 1

VOUT= ............................................ V [2]


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11. (a) The circuit for an amplifier incorporating an ideal operational amplifier (op-amp) is shown inFig. 11.1.

(i) State

1. the name of this type of amplifier circuit, [1]Inverting amplifier........................................................................................................................................................

2. Why the point P is referred to as a virtual earth. [3]For the op-amp not to be saturated, the potential at point P must be very close to the 1non-inverting inputs potential........................................................................................................................................................The non-inverting input is held at 0V or earth 1........................................................................................................................................................So point P is is said to be virtually at earth or virtual earth 1........................................................................................................................................................

Fig 11.1

(ii) Show that the gain G of this amplifier circuit is given by the expression [3]

Current through R1 = Current through R2 , as no current passes through op-amp 1

2 marks for correct working for proofR1and R2changed from in book

Explain your working.

(iii) Calculate the value of Voutif R1= 120 k, R2= 10 k and Vin= 1.40 VExplain your answer. [3]

1 1


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12. Design Question(Answer this on a piece of Grammar paper) [15]

Students were investigating a how the magnetic field strength of a solenoid was effected by the crosssectional area of a core placed inside it.

They were told that the formula below related the magnetic field strength to the cross sectional area.

Where B is the magnetic field strength, A is the cross sectional area and & are constants.

You should draw a diagram showing the arrangement of your equipment.(This means a labelled diagram)

In your account you should pay particular attention to

(a) the procedure to be followed,

(b) the measurements to be taken,

(c) the control of variables,

(d) the analysis of the data,

(e) the safety precautions to be taken.

Mark allocationDefining the problem (3 marks)Methods of data collection (5 marks)Method of analysis (2 marks)Safety considerations (1 mark)Additional detail (4 marks)

End.


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A2 Physics 2011 Term 2 Examination Practical design question 12.

Max mark = 15 in 5 sections P, C, A, S, D.

P - Defining the problem 3 marks

1 States independent variable = cross sectional area of the core

2 States dependent variable = magnetic field strength B

3 Identifies variables needed to be kept constant (Control variables) = current in the core (M) , position B

field measured (M), material of core, coil properties eg turns per metre

C - Method of data collection 5 marks

1 Method to measure field strength eg (calibrated) Hall probe

2 Method to measure core area eg vernier callipers and maths

3 Method to measure the control variable current eg ammeter

4 Diagram of the apparatus with dc power supply

5 Suitable connections and apparatus choice for other variables

A - Method of data analysis 2 marks

1 Collect data for field strength and current, with repeat readings averaged2 Plot a graph of ln B vs A ( using at least 6 points ) stating if formula correct the line will be straight line

(negative gradient) and intercept equal to ln(Bo) or equivalent.

S - Safety 1 mark

1 Care with overheating coil, no shorting out of the wires with metal core touching coil turns etc, have a

safety resistor in the circuit to stop excessive current in the core etc.

No marks for use rubber gloves etc, use voltages less that 150 kV !!, use in dry conditions away from water

etc.

D - Additional details 4 marks

1 Specifics on how to measure B, fixed distance and fixed or multiple axis Hall probe orientation

2 Specifics on how to best measure area, state shape of core and relevant maths and use of Vernier calliper /

micrometer with several readings averaged to calculate area

3 Specifics on how to control the current in the core to keep it constant eg use of a variable resistor and

ammeter in series with the core

4 Discussion of the elimination of the Earths magnetic field / need to carry out experiment away from

sources of magnetic field

5 Specifics on repeat readings and how data averaged

6 Use of a smoothed dc supply / battery or checked with a CRO

Do not allow

Use a constant voltage supply, keep pd constant

Keep voltage constant

Measure pd across Hall probe

Measure B with hall probe without additional detail about probe position and orientation

Keep the core the same without the current in the core monitored and kept constant.

Measure force on a magnetic material and say this = B

a 2 physics term 22011 answer scheme

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