AS & A Level Physics - 9702 Paper 4 2011 Summer Zone 3

(a) State what is meant by a field of force. [1]

(b) Gravitational fields and electric fields are two examples of fields of force. State one similarity and one difference between these two fields of force.
similarity, difference. [2]

(c) Two protons are isolated in space. Their centres are separated by a distance $R$. Each proton may be considered to be a point mass with point charge. Determine the magnitude of the ratio. [2]
$$\frac{\text{force between protons due to electric field}}{\text{force between protons due to gravitational field}}.$$

(a) State what is meant by a mole.  [2]

(b) Two containers A and B are joined by a tube of negligible volume, as illustrated in Fig. 2.1.

The containers are filled with an ideal gas at a pressure of $2.3 \times 10^5 \text{Pa}$.

The gas in container A has volume $3.1 \times 10^3 \text{cm}^3$ and is at a temperature of $17^\circ \text{C}$.

The gas in container B has volume $4.6 \times 10^3 \text{cm}^3$ and is at a temperature of $30^\circ \text{C}$.

Calculate the total amount of gas, in mol, in the containers.   [4]

A capacitor consists of two metal plates separated by an insulator, as shown in Fig. 3.1.

The potential difference between the plates is $V$. The variation with $V$ of the magnitude of the charge $Q$ on one plate is shown in Fig. 3.2.

(a) Explain why the capacitor stores energy but not charge.
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(b) Use Fig. 3.2 to determine
(i) the capacitance of the capacitor,
capacitance = ..................... µF [2]
(ii) the loss in energy stored in the capacitor when the potential difference $V$ is reduced from 10.0 V to 7.5 V.
energy = ..................... mJ [2]
(c) Three capacitors $X$, $Y$ and $Z$, each of capacitance 10 µF, are connected as shown in Fig. 3.3.

Initially, the capacitors are uncharged.
A potential difference of 12 V is applied between points $A$ and $B$.
Determine the magnitude of the charge on one plate of capacitor $X$.
charge = ................................ µC [3]

(a) The first law of thermodynamics may be expressed in the form $\Delta U = q + w$.

Explain the symbols in this expression.  [3]

• + $\Delta U$
• + $q$
• + $w$

(b) (i) State what is meant by specific latent heat.   [3]

(ii) Use the first law of thermodynamics to explain why the specific latent heat of vaporisation is greater than the specific latent heat of fusion for a particular substance.  [3]

A bar magnet is suspended vertically from the free end of a helical spring, as shown in Fig. 5.1.

One pole of the magnet is situated in a coil. The coil is connected in series with a high-resistance voltmeter. The magnet is displaced vertically and then released. The variation with time $t$ of the reading $V$ of the voltmeter is shown in Fig. 5.2.

(a) (i) State Faraday’s law of electromagnetic induction.   [2]

(ii) Use Faraday’s law to explain why

1. there is a reading on the voltmeter,   [1]
2. this reading varies in magnitude,   [1]
3. the reading has both positive and negative values.   [1]

(b) Use Fig. 5.2 to determine the frequency $f_0$ of the oscillations of the magnet.   [2]

(c) The magnet is now brought to rest and the voltmeter is replaced by a variable frequency alternating current supply that produces a constant r.m.s. current in the coil. The frequency of the supply is gradually increased from $0.7f_0$ to $1.3f_0$, where $f_0$ is the frequency calculated in (b).

On the axes of Fig. 5.3, sketch a graph to show the variation with frequency $f$ of the amplitude $A$ of the new oscillations of the bar magnet.  [2]

(d) (i) Name the phenomenon illustrated on your completed graph of Fig. 5.3.   [1]

(ii) State one situation where the phenomenon named in (i) is useful.   [1]

An alternating current supply is connected in series with a resistor R, as shown in Fig. 6.1.

The variation with time $t$ (measured in seconds) of the current $I$ (measured in amps) in the resistor is given by the expression

$I = 9.9 \sin(380t)$.

(a) For the current in the resistor R, determine

(i) the frequency,  [2]

(ii) the r.m.s. current.  [2]

(b) To prevent over-heating, the mean power dissipated in resistor R must not exceed 400W.

Calculate the minimum resistance of R.  [2]

(a) State what is meant by the \textit{de Broglie wavelength}.
\text{............................................................................................................}
\text{............................................................................................................}
\text{............................................................................................................} [2]

(b) An electron is accelerated in a vacuum from rest through a potential difference of 850V.

(i) Show that the final momentum of the electron is $1.6 \times 10^{-23}$ Ns.

[2]

(ii) Calculate the de Broglie wavelength of this electron.

wavelength = \text{........................................} m [2]

(c) Describe an experiment to demonstrate the wave nature of electrons.
You may draw a diagram if you wish.
\text{............................................................................................................}
\text{............................................................................................................}
\text{............................................................................................................}
\text{............................................................................................................}
\text{............................................................................................................} [5]

(a) State what is meant by the \textit{binding energy} of a nucleus. \text{..............................................................} \text{..............................................................} \text{..............................................................} [2]

(b) Show that the energy equivalence of 1.0 u is 930 MeV. [3]

(c) Data for the masses of some particles and nuclei are given in Fig. 8.1. \begin{center} \begin{tabular}{|c|c|} \hline \text{mass / u} & \\ \hline \text{proton} & 1.0073 \\ \text{neutron} & 1.0087 \\ \text{deuterium }(_{1}^{2}\text{H}) & 2.0141 \\ \text{zirconium }(_{40}^{97}\text{Zr}) & 97.0980 \\ \hline \end{tabular} \text{Fig. 8.1} \end{center} Use data from Fig. 8.1 and information from (b) to determine, in MeV,
(i) the binding energy of deuterium,
\text{binding energy = ................................................ MeV [2]} (ii) the binding energy \textit{per nucleon} of zirconium.
\text{binding energy per nucleon = .......................................... MeV [3]}

(a) Describe the structure of a metal wire strain gauge. You may draw a diagram if you wish.
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[3]

(b) A strain gauge S is connected into the circuit of Fig. 9.1.



Fig. 9.1

The operational amplifier (op-amp) is ideal.
The output potential $V_{OUT}$ of the circuit is given by the expression

$$V_{OUT} = \frac{R_F}{R} \times (V_2 - V_1).$$

(i) State the name given to the ratio $\frac{R_F}{R}$.
.................................................................................................................................
[1]

(ii) The strain gauge S has resistance 125 $\Omega$ when not under strain.
Calculate the magnitude of $V_1$ such that, when the strain gauge S is not strained,
the output $V_{OUT}$ is zero.

$V_1 = ..................................................$ V [3]

(iii) In a particular test, the resistance of S increases to 128 $\Omega$. $V_1$ is unchanged.
The ratio $\frac{R_F}{R}$ is 12.
Calculate the magnitude of $V_{OUT}$.

$V_{OUT} = ..................................................$ V [2]

Explain briefly the main principles of the use of magnetic resonance to obtain diagnostic information about internal body structures.

The use of ionospheric reflection of radio waves for long-distance communication has, to a great extent, been replaced by satellite communication.
(a) State and explain two reasons why this change has occurred.
1. ..........................................................................................................................
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2. ..........................................................................................................................
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(b) The radio link between a geostationary satellite and Earth may be attenuated by as much as 190 dB.
Suggest why, as a result of this attenuation, the uplink and downlink frequencies must be different.
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(a) The signal-to-noise ratio in an optic fibre must not fall below 24 dB. The average noise power in the fibre is $5.6 \times 10^{-19}$ W.
(i) Calculate the minimum effective signal power in the optic fibre.
power = ....................................... W [3]

(ii) The fibre has an attenuation per unit length of $1.9 \text{ dB km}^{-1}$. Calculate the maximum uninterrupted length of fibre for an input signal of power 3.5 mW.
length = ....................................... km [3]

(b) Suggest why infra-red radiation, rather than ultraviolet radiation, is used for long-distance communication using optic fibres.
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