AS & A Level Physics - 9702 Paper 2 2013 Summer Zone 2

(a) Determine the SI base units of power.

SI base units of power ........................................................... [3]

(b) Fig. 1.1 shows a turbine that is used to generate electrical power from the wind.



Fig. 1.1

The power $P$ available from the wind is given by

$P = C L^2 \rho v^3$

where $L$ is the length of each blade of the turbine,
$\rho$ is the density of air,
$v$ is the wind speed,
$C$ is a constant.

(i) Show that $C$ has no units.

[3]

(ii) The length $L$ of each blade of the turbine is 25.0 m and the density $\rho$ of air is 1.30 in SI units. The constant $C$ is 0.931. The efficiency of the turbine is 55% and the electric power output $P$ is $3.50 \times 10^5 W$.
Calculate the wind speed.

wind speed = .............................................. m s$^{-1}$ [3]

(iii) Suggest two reasons why the electrical power output of the turbine is less than the power available from the wind.

1. ..............................................................................................................................
.................................................................................................................................
2. ..............................................................................................................................
................................................................................................................................. [2]

(a) Define force.   [1]

(b) A resultant force \( F \) acts on an object of mass 2.4 kg. The variation with time \( t \) of \( F \) is shown in Fig. 2.1.

The object starts from rest.

(i) On Fig. 2.2, show quantitatively the variation with \( t \) of the acceleration \( a \) of the object. Include appropriate values on the \( y \)-axis.   [4]

(ii) On Fig. 2.3, show quantitatively the variation with \( t \) of the momentum \( p \) of the object. Include appropriate values on the \( y \)-axis.    [5]

(a) Define $\textit{centre of gravity}$.   [2]

(b) A uniform rod AB is attached to a vertical wall at A. The rod is held horizontally by a string attached at B and to point C, as shown in figure.

The angle between the rod and the string at B is $50\degree$. The rod has length $1.2\,m$ and weight $8.5\,N$. An object O of mass \( M \) is hung from the rod at B. The tension \( T \) in the string is $30\,N$.

(i) Use the resolution of forces to calculate the vertical component of \( T \).    [1]

(ii) State the $\textit{principle of moments}$.   [1]

(iii) Use the principle of moments and take moments about A to show that the weight of the object O is $19\,N$.   [3]

(iv) Hence determine the mass \( M \) of the object O.    [1]

(c) Use the concept of equilibrium to explain why a force must act on the rod at A.   [2]

(a) Describe apparatus that demonstrates Brownian motion. Include a diagram.  [2]

(b) Describe the observations made using the apparatus in (a). [2]

(c) State and explain two conclusions about the properties of molecules of a gas that follow from the observations in (b).   [2]

Fig. 5.1 shows a string stretched between two fixed points P and Q.

A vibrator is attached near end P of the string. End Q is fixed to a wall. The vibrator has a frequency of 50 Hz and causes a transverse wave to travel along the string at a speed of 40 ms$^{-1}$.

(a) (i) Calculate the wavelength of the transverse wave on the string.   [2]

(ii) Explain how this arrangement may produce a stationary wave on the string. [2]

(b) The stationary wave produced on PQ at one instant of time $t$ is shown on Fig. 5.2. Each point on the string is at its maximum displacement.

(i) On Fig. 5.2, label all the nodes with the letter N and all the antinodes with the letter A. [2]

(ii) Use your answer in (a)(i) to calculate the length of string PQ.   [1]

(iii) On Fig. 5.2, draw the stationary wave at time $(t + 5.0 ext{ ms})$. Explain your answer.  [3]

(a) Define \textit{charge}.
...........................................................................................................................[1]
(b) A heater is made from a wire of resistance 18.0\,\Omega and is connected to a power supply of 240\,\text{V}. The heater is switched on for 2.60\,\text{Ms}.
Calculate
(i) the power transformed in the heater,

power = ........................................... W [2]
(ii) the current in the heater,

current = .......................................... A [1]
(iii) the charge passing through the heater in this time,

charge = .......................................... C [2]
(iv) the number of electrons per second passing a given point in the heater.

number = .......................................... \text{s}^{-1} [2]

A polonium nucleus $^{210}_{84}Po$ is radioactive and decays with the emission of an $\alpha$-particle. The nuclear reaction for this decay is given by
$^{210}_{84}Po \rightarrow ^{W}_XQ + ^{Y}_Z\alpha.$
(a) (i) State the values of
$W \ldots\ldots\ldots\ldots\ldots\ldots$
$X \ldots\ldots\ldots\ldots\ldots\ldots$
$Y \ldots\ldots\ldots\ldots\ldots\ldots$
$Z \ldots\ldots\ldots\ldots\ldots\ldots$
[2]
(ii) Explain why mass seems not to be conserved in the reaction.
$\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots$
[2]
(b) The reaction is spontaneous. Explain the meaning of \textit{spontaneous}.
$\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots$
[1]