CENTRALE COMMISSIE VOORTENTAMEN NATUURKUNDE

PHYSICS EXAM

Date : Friday 28 April 2017

Time : 13.30 tot 16.30

Number of questions : 5

Number of answer sheets : 1 (for question 1)

Each question must be answered on a separate sheet (because each questionis marked by different examiners).

State your name on every sheet you hand in.

Do not write in pencil and do not use Tipp-Ex or any similar product.

Answers without argumentation will not be deemed correct.

Additional data can be found in the BINAS science data reference book (4th or5th edition).

The standardized scores are:

Question 1 : 18 pointsQuestion 2 : 12 pointsQuestion 3 : 15 pointsQuestion 4 : 8 pointsQuestion 5 : 16 points

The marks are calculated as follows: mark = score/69 x 9 + 1

Information concerning the procedure and progress of the proces of markingsee: www.ccvx.nl > verloop van de correctie

QUESTION 1 - pilot emergency training

An ejector seat is used by fighter pilots who need to evacuate their plane inan emergency situation. There is a specific installation to train pilots for thiseventuality. This installation consists of long, vertical rails along which a pilotin a seat can be launched vertically upwards. This is schematically shown inFigure 1.

The force propelling the pilot and the chair upwards only operates for the first1.81 s immediately after launch. After that time, the only active forces arefriction and, of course, gravity.

Figure 2 shows the v-t graph for the first 6.00 seconds after launch. Anenlarged version of the v-t graph is provided on the answer sheet.

2p a. Calculate the maximum speed reached by the pilot.

3p b. Calculate the height reached by the pilot. (If you were unable tocalculate this part, assume a value of 85 m for the remainder of thisassignment. Please note that is value is incorrect.)

3p c. Calculate the maximum acceleration during the upwards launch.

The pilot and the chair together have a mass of 96 kg.

3p d. Calculate how much work the force with which the pilot is launched exerts on thepilot and chair if there was no friction.

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In reality, there is friction and part of the work is converted into heat.At t = 4.26 s, the graph shows a slight kink.

3p e. Explain this kink.

When coming down, assume that the pilot descends at a constant speed until he hits theground.The v-t graph has only been drawn up to t = 6.00 s but at that time the pilot has notreached the ground.

4p f. Using the v-t graph, calculate whether the pilot hits the ground before or aftert = 8.00 s.

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QUESTION 2 - resonance

A string with a certain lengthl is strung betweentwo fixed points, P and Q. At point P, there is asource that can be used to make the string vibrate.Next to the string, there is a hollow pipe, closed atone end, with a depth (d) of 25.0 cm. The scene isrepresented as a diagram in the figure.The speed of sound in air is 343 m/s.

The air in the cylinder starts resonating.

3p a. Calculate the cylinder’s lowest and secondlowest resonant frequency.(If you have been unable to work out thissection, please assume a value of 400 Hzas the lowest frequency and 1200 Hz as thesecond lowest resonant frequency).

The vibrations in the string are caused by a source with an adjustable frequency. Bothends of the string are attached to a fixed point. The reproduction rate of the waves in thestring is 823 m/s.

3p b. What should the length lof the string be to ensure that resonance occurs at thelowest frequency in section a.?

4p c. Calculate the shortest length the string can have be to ensure that both resonancesunder section a. can occur.

2p d. If resonance occurs initially and the temperature falls subsequently, this resonancewill cease. Explain why.

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QUESTION 3 - hot air gun

A hot air gun is a device in which a fan moves an air flowover a filament between points K, L, M, N and O. The hotair produced can be used to remove old coats of paintfrom a door you want to repaint, for example.

The wiring diagram is shown below. The hot air gun isconnected to an effective alternating current of 220 V.

Some time after switching on, the device enters its “ready to use” mode. At this time, acurrent of 750 mA runs through the fan, and a current of 8.50 A runs through the filamentbetween K, L, M, N and O.

2p a. Calculate the electrical resistance of thefilament (KLMNO) is this situation.

3p b. Calculate the overall power consumed by thedevice in the “ready to use” mode.

Immediately after switching on, the magnitude of thecurrent in the filament is greater than in the “ready touse” mode.

2p c. Explain why.

At a certain moment in time, a short circuit occursbetween points M and O of the filament. The lengthbetween M and O equals 1/2 of the total length of KLMNO.

4p d. Calculate the value of the current intensity immediately after the short circuit: 1) through the filament part KLM 2) through the filament part MNO 3) through the fan motor

In China, mains voltage is 220 V. The Chinese manufacturer of the hot air gun intends tomake the device suitable for use in Europe, where mains voltage is 230 V. This can bedone by placing an additional electrical resistor in the device.

1p e1. Draw a wiring diagram that includes this additional resistor.3p e2. Calculate the value of the additional resistance.

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QUESTION 4 - radioactivity

Two different decay mechanisms are known for the radioactive isotope Cs. 137

See the figure below.

Six percent of the Cs nuclei decay directly to the stable Ba, throwing out an electron137 137

in the process. This electron emission releases 1.18 MeV in the form of kinetic energy ofthe electron.

2p a. Provide the equation for this radioactive decay.

Ninety-four percent of the Cs nuclei decay after an intermediate step. 137

These caesium nuclei first decay to an excited state of barium nuclei, with the emission ofan electron.This releases 0.51 MeV in the form of kinetic energy. This excited state of barium nuclei isreferred to as Ba.137m

From this excited state, the barium nucleus then decays to a ground state, with theemission of ã-radiation (gamma radiation). See the figure again.

Einstein has discovered that mass and energy can be converted into one anotheraccording to the famous formula:

with: E the energy,

m the mass andc the speed of light.

3p b. Calculate the mass difference between a Cs nucleus and a Ba nucleus by137 137

using the data above.

3p c. Calculate the frequency of the ã-radiation produced during the decay from Ba to137m

Ba. 137

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QUESTION 5 - the electron

The ratio between the mass and charge of an electron can be calculated experimentallyusing a setup of which a simplified version is shown in Figure 1.

The electrons released at the cathode are accelerated between the cathode and anode.The electrons pass through the hole in the anode then enter a uniform electric fieldbetween two plates, M and N, with a velocity parallel to these plates. The strength of theelectric field is 2.1·10 V m . The distance between the plates is 1.8 cm. The whole setup4 –1

is in vacuum.

2p a. Calculate the potential difference between plates M and N.

3p b. Demonstrate using a calculation that the effect of gravity on the electrons isnegligible compared to the force experienced by the electrons due to the electricfield between the plates.

The deflection of the electron beam between the plates can be avoided by also creating auniform magnetic field in the area between the plates. The effect of gravity on theelectrons is negligible.

In the figure 1, a point P is shown on the trajectory of the electrons.

4p c. Explain using a drawing on the answer sheet which direction the magnetic field hasat point P.

The speed of the electrons travelling straight through is 3.1·10 m s .7 –1

3p d. Calculate the magnitude of the magnetic induction.

Continued on the next page L

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Next, the magnetic field is switched off. This means the electron beam will be deflected inthe electric field between the plates. This is schematically shown in Figure 2.The length of the plates is 3.5 cm.From this deflection, it can be calculated that the electrons will have a speed with avertical component of 4,2·10 m s once they have passed through the electric field.6 –1

4p e. Calculate the resulting value for the ratio between the mass and charge of anelectron. Hint: first, calculate the vertical acceleration achieved by the electrons inthe electric field. Keep in mind that in the time an electron moves in a horizontaldirection from right to left between the plates, the electron gets the aforementionedvertical component speed of 4,2·10 m s .6 –1

END

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ANSWERSHEET - QUESTION 1

Naam : ...........................................................