TEST CODE 002472
FORM TP 22246 CARIBBEAN
MAY/JUNE 2OO2
EXAMINATIONS
COUNCIL
ADVANCED PROFICIENCY EXAMINATION PHYSICS UNIT 01 - Paper 02 2 hoursand 15 minutes
READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1.
This paperconsistsof NINE questions.
2.
SectionA consistsof THREE questions.Candidatesmust attemptALL questions in thissection.Answersfor thissectionmustbe writtenin this answerbooklet.
3.
SectionB consistsof SIX questions.Candidatesmust attemptTHREE questionsin this section,ONE questionfrom EACH Module. Answers for this sectionmustbe written in the answerbookletprovided.
4.
All working MUST be CLEARLY shown.
5.
The useof non-prograrrunable calculatorsis permitted.
Copyright@ 2002CaribbeanExaminationsCouncil All rightsreserved.
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NOTHING HAS BEEN OMITTED.
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-3 LIST OF PHYSICAL CONSTANTS Universal gravitational constant
G
6.67x 10-rtN -t kg',
Acceleration due to gravity
g
9.80m s-2
Radius of the Earth
RE
6380km
Mass of the Earth
ME
5.98x l02akg
Mass of the Moon
MM
7.35x 1022kg
1 Atmosphere
Atm
1.00x lOsN m-z
Boltzmann'sconstant
k
l.38xlo-23JK-r
Density of water
1.00x 103kg m-r
Thermal conductivity of copper
400W m-r K-r
Specific heat capacity of aluminium
910J kg-t 11-t
Specific heat capacity of copper
387J kg-t 11't
Specific heat capacity of water
4200J kg-r K- I
Specific latent heat of fusion of ice
3.34x 10sJ kg-t
Specific latent heat of vaporization of water
2 . 2 6 xl 0 6 J k g - t
Avogadro's number
NA
6.02x 1023per mole
Molar gas constant
R
8.31J K-r mol-r
Stefan-Boltzmannconstant
o
5.67x 10-8w m'2K-4
Speedof light in vacuum
c
3 . 0 xl 0 8 m s - l
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2002 002472|CAPE
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SECTION A Attempt ALL questions. You MUST write in this answer booklet. You must NOT spend more than 30 minutes on this section. 1.
Figure I below shows a piece of lead which fits snugly into a glasstube of length 4 metres. The lead sits on a column of compressedair. The valve at B can be releasedso that the air can expand rapidly and the water can rush in and together they can acceleratethe lead.
Compressed air
Figure I The tablebelow showshow the net force on the leadvarieswith the distancetravelledup the glasstubeafterthe valueis released.
(a)
Force (N)
Distance(m)
t220
0
I 193
0.4
tr32
0.8
1045
t.2
906
1.6
740
2.0
557
2.4
400
2.8
261
3.2
t22
3.6
0
4.0
Using the values in the table above, plot a graph on page 5 of force against distance. [4 marks]
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002472|CAPE 2002
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1.
(b)
Use the graph you have plotted on page 5 to estimate the work done on the lead to bring it to the surface.
[2 marks] (c)
Stating any assumptionsyou made, calculate the speed at which the lead of-mass I kg exits the glass tube.
[4 marks] Total 10 marks
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2.
(a)
(i)
Describean experimentto investigatetheeffectof dampingon the amplitudeof a mass-springsystem.
[4 marks] (ii)
What adjustmentscan you make to the experiment in order to investigatewhether the damping is constant or not?
[1 mark 1 GO ON TO THE NEXT PAGE
2002 002472|CAPE
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2.
o) Amplitude of forced Vibrations lm
1.3
r:4
l'5 po..il!6F..q,r"n cy r:Hz
Figure 2 The graphin Figure2 showsthe amplituderesponsecurves for a mass-spring system when it is subjectedto forcedoscillationsand damping. (i)
The masshasvalue 250 gand the springconstantis 20 Nm-r. Given that the naturalfrequency,fo, of the systemis given by
f-o --rli 2n\'l /m Calculate the value of fr.
[3 marks] (ii)
what is the value of the natural frequency on the graph?
[1 mark 1 (i ii)
What effect occurs at this position?
[1 mark I Total l0 marks
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3.
(a)
A thermocouple can be made by carefully placing a cold junction in melting ice and heating the hot junction. (i)
Draw a suitable circuit diagram to show how the thermocouple is constructed.
[3 marks] (ii)
Why is it suitableto taketemperature readingsof a substance whenit is cooling down ratherthanwhile it is heatingup?
[1 mark ] (iii)
How can the thermocouple thermometer be made to respond better to changes in temperature?
[2 marksJ
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-10A Graphof Emf / mV vs0 /"C E /mV
250
ptr
0 /"c
- l1-
3.
(b)
(i)
The graph on page l0 shows how the e.m.f. of a thermocouple varies with temperature. The thermocouple measured 6.@ mV when the hot junction was placed in boiling water at 100 oC. From the graph find the temperature of the hot junction when the e.m.f. is l4 mV.
I
[1 mark ] (ii)
It is found that the Celsius temperaturecan be calculated from
e-
E,
-Eo
E,*
- Eo
x 100'C
g, where E, , E andE o ,* are the respectivee.m.f.s at the unknown temperature the ice point and the steam point. Use this formula to calculate the temperaturewhen the e.m.f. is 14 m V.
[2 marksl (ii)
Accountfor the differentvaluesof temperature in (b) (i) and(b) (ii).
[1 mark ] Total 10 marks
t I
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2001 002472/CAPE
-12SECTIONB You must attempt THR-EEquestionsfrom this section. choose oNE questionEACH from Module l' 2 and'3' YouMusT write your answers in the answerbookletpnovided. MODULE T AnswerEITHER euestion4 OR euestion5. 4.
(a)
state the difference between scalar and vector quantities and give oNE example of EACH.
[4 marks]
(b)
Tlvo tugs, P and Q, tow a ship along the direction Bo at constantspeed,asseenin Figure3' Tug P exertsa force or gs [N at an angleof 20o to Bo. Tug e pulls with a force of 20 kN at an angleg to BO. Tbg P
Figure 3 (i) (ii)
If the resultantforce actsalong Bo, find the angle g. Calculatea valueof this resultantforce.
[6 marks]
(c)
The ship is travelling at 1.5 m/s when it is being is the v towed. what rs lrrv velocity '"'"tttiu of rug p and rug Q? marksl
(d)
If both cables break simultaneously and it is observed that the two tugs speedup while the ship slows down, explain what principle is observed and why energy is NoT conseryed. t4 marksl Total 20 marks
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5.
(a)
Our solar systemis in the Milky Way galaxy. In anothergalaxy a planet, p, has a circular orbit equalto that of the Earth's,that is, the orbits have the sameradius. The massesof the sunsin the two galaxiesare56 andS, respectivelyandplanetP completes its orbit in half the time it takesthe Earth. (i)
(ii)
Show that the massof the Sun in the Earth'sorbit is four times the massof the sunin PlanetP's orbit. Show that the periodof the planet,P, is given b.y. T = zn\f&, Y the massof the planetand r the radiusof the orbit.
whereM, is [8 marks]
(b)
The distancebetweenEarth and planet, P, is 2.0 x 1021m. If the mass of the-planet,p, is 7 x l02a kg, calculate the gravitational force of attraction. [2 marks]
(c)
Calculate the distancebetween the planet and its sun.
(d)
Calculate a value for g'the accelerationdue to graviry on planet P given that the radius
[3 marks]
of the planetP is 8500km. (e)
[4 marks]
An astronautweighs585 N on earth. What will he weighon planetP? [3 marks] ':
Total 20 marks
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MODULE 2 Answer EITHER Question6 OR Question7. 6.
(a)
Define the term 'principalfocusof a lens'.
(b)
Draw a ray diagram to illustrate the formation of the image of an extended object by a convex lens when the object is at a distancefrom the lens, greater than the focal length of the lens, but less than twice the focal length. [2 marks]
(c)
(i) (ii)
(d)
[2 marks]
Draw a ray diagram to show how an image is formed in a diverging lens. Compare the images formed in (b) and (c) (i).
[4 inarks]
An overheadprojector lens has a focal length of 35 cm. The image of a transparencyis formed 2 m from the lens, that is, the total path length from lens to screenis 2.0 m.
Figure 4
(e)
(i)
How far above the transparencymust the lens be held in order for the image to be formed on the screen?
(ii)
What is the magnifying power of the lens and how does this affect image formed? [6 marks]
The focal length of a lens can be found by measuring several values of image distance V corresponding to different values of the object distanceU, using a pin or no parallax method. Explain how, by plotting a suitable graph, the focal length of the lens could be determined from the data collected. Include a sketch of the graph you would expect to obtain. [6 marks]
Total 20 marks
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2002 002472/CAPE
-157.
(a)
(b)
It is observedthat fifteen crestsof water wavespassa certain point in 2l5 s. The distancebetweentwo successive crestsis 4.10 m. What is the speedof the wave? [4 marks] (i)
(ii)
Describe,with the aid of a labelled diagram,an experimentto demonstrate interferenceof soundwaves. Why aresoundwavesdescribedasprogressive longitudinalwaves? [8 marks]
(c)
(i)
The velociryof a transversewave on a wire stretchedbetweentwo fixed points is
v= 1Tl, where T is the tensionof the wave and u is its massper unit length. A piano wire is 75 cm long and of mass 7 .5 g. The wire is stretchedwith a tension of 400 N. Use the equation above to calculate the velocity of a wave along the string.
(ii)
If the wire has length l, the fundamental frequency is given by f = *,Z L where v is the velocity of the wave. .: Calculate this frequency. What can you say about the wavelength of the wave?
(iii)
Calculate the change in the intensity level when the power output from a piano
changesfrom 100mW to 200 mW.
[8 marks] Total 20 marks
2002 002472|CAPE
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-16-
MODULE 3 Answer EITHER Question8 OR Question9. 8.
Figure 5 shows a piece of equipmentwhich allows steamat a very high temperatureto be blown throughthe pipe at A and eventuallycausingthe light frictionlesspiston at D to just pushon the switchat E. Originallythe equipmentis at 25"C,thensteamis blown throughthe pipe at A.
Switch
/l
(A) Pipe
Figure 5 (a)
(b)
(i)
Name the processby which heat is supplied to the gas at C via the copper rod at B.
(ii)
Use the kinetic theory to explain why the piston at D eventually pusheson the switch at E.
(iii)
Why must the copper rod be lagged and the piston light and frictionless? [8 marks]
126 J of heat is supplied to the gas at C via the copper rod at B. 90 J of the energy supplied to the gas is used up as work done by the gas to push back the piston. (i)
Calculate an estimate for the change of internal energy of the gas at C.
(ii)
Why is the actual value for the change of internal energy of the gas at C lower than the value you calculatedin (b) (i) above.
(iii)
Helium gasis containedin the vessel.The gasoccupiesa volume of 1.0 x 10-3m3 at a pressureof 1.0 x 105Pa and temperatureof 25oC. Calculate the
(c)
a)
number of moles of helium atoms in the container
b)
total kinetic energy of the helium atoms.
[9 marksJ
When the piston at D pushes on the switch at E, the flow of hot steam is turned off. Explain what happensto the piston at D and why. t3 marksl
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2002 002472{CAPE
t79.
'tensile
stress' and 'tensile strain'.
(a)
Define
(b)
A wire is stretchedby a force, F, which causesan extension, e. Hooke's law relates F to eby
[2 marksl
F=ke Show how is k relatedto the Young'sModulusE of the wire. (c)
[3 marks]
A load of 30 N is hung from a copper wire 5 m long and 1.0 mm in diameter to keep it taut as shown in Figure 6. The position of the lower end of the wire was read on a scale.
Figure 6 Weights are then added and the corresponding increase in lengths is read off from the scale. The readings were recorded in the table below.
Weieht(N) Extension/ m x 10-3 (i) (ii)
30
40
50
60
70
80
90
100 105 1 1 0
1.40 1.80 2.35 2.80 3.25 3.70 4.30 4.85 5.05 5.25
Plot a graph of load against extension using the values from the table. Use the graph plotted in (c) (i) to calculate the Young Modulus of Copper.
(iii)
What is the maximum load that can be supported by the wire?
(iv)
What was the stressat the proportional limit?
(v)
Calculate the elastic energy stored in the wire just before the wire became perrnanently stretched. [15 marks]
Total 20 marks END OF TEST
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