# Physics 9702 Doubts | Help Page 202

__Question 976: [Vectors]__
The speed of an aeroplane in still
air is 200 km h

^{–1}. The wind blows from the west at a speed of 85.0 km h^{–1}.
In which direction must the pilot
steer the aeroplane in order to fly due north?

A 23.0° east of north

B 23.0° west of north

C 25.2° east of north

D 25.2° west of north

**Reference:**

*Past Exam Paper – June 2015 Paper 13 Q3*

__Solution 976:__**Answer: D.**

For such a question, we need to properly
identify the data we have, and what we are seeking.

With the wind blowing, it will cause
the direction of the aeroplane to change during its motion. Along with this
change, the pilot would need to steer in an appropriate direction in order to
fly due north. Thus, the resultant of our vectors
should be north.

The wind is blowing from the west.
So, the vector representing the wind would be horizontal.

Let the angle that the pilot needs
to steer in order to fly due north (with the wind blowing) be at an angle θ west of the north. {We
don’t know the value of this angle. If the direction was to the east of the
north, instead of west, the angle would be greater than 90°. But by just
imagining the situation with the wind blowing from the west, we know that the
aeroplane cannot be to the east due to north for it to have a resultant north
direction.}

The speed of the aeroplane is still 200km
h

^{-1}– we are more interested with its direction.
The vector diagram below shows the
situation.

The angle θ is given by 85.0 = 200
sin θ.

Angle θ = sin

So,
the aeroplane needs to be travelling at an angle of 25.2° west due to north so that its resultant
direction would be north when the wind blows.^{-1}(85/200) = 25.2°

__Question 977: [Work, Energy and Power]__
The diagram shows a hydroelectric
power station.

The reservoir is linked to the
turbines by a pipe of uniform cross-sectional area. Water flows from the
reservoir, through the pipe and through the turbines at a constant rate.

Which statement about the change of
energy of the water as it moves from X to Y is correct?

A It gains both gravitational potential
energy and kinetic energy.

B It loses gravitational potential
energy and gains elastic potential energy.

C It loses gravitational potential
energy and gains kinetic energy.

D It loses both elastic potential
energy and gravitational potential energy.

**Reference:**

*Past Exam Paper – November 2012 Paper 13 Q21*

__Solution 977:__**Answer: B.**

X is at a higher position than Y –
so as the water moves from X to Y, it is losing gravitational potential energy
(E

_{P}= mgh). [A is incorrect]
The kinetic energy of the water cannot
increase as the pipe is sealed and full of water, and it is stated that the
water flows at

**constant rate**along the pipe. This means that its speed is constant, and hence its kinetic energy is constant (E_{K}= ½ mv^{2}). [C is incorrect]
The water is gaining elastic potential
energy as its pressure increases between X and Y. {The
pressure at a point in the pipe depends on the length of the column of liquid above that
point.}

Choice D goes against the law of
conservation of energy.

__Question 978: [Current of Electricity > Resistance]__**(a)**A metal wire of constant resistance is used in an electric heater.

In order not to overload the circuit
for the heater, the supply voltage to the heater is reduced from 230 V to 220
V.

Determine the percentage reduction
in the power output of the heater.

**(b)**A uniform wire AB of length 100 cm is connected between the terminals of a cell of e.m.f. 1.5 V and negligible internal resistance, as shown in Fig. 6.1.

An ammeter of internal resistance
5.0 Ω is connected to end A of the wire and to a contact C that can be moved
along the wire.

Determine the reading on the ammeter
for the contact C placed

(i) at A,

(ii) at B

**(c)**Using the circuit in (b), the ammeter reading I is recorded for different distances L of the contact C from end A of the wire. Some data points are shown on Fig. 6.2.

(i) Use your answers in (b) to plot
data points on Fig. 6.2 corresponding to the contact C placed at end A and at
end B of the wire.

(ii) Draw a line of best fit for all
of the data points and hence determine the ammeter reading for contact C placed
at the midpoint of the wire.

(iii) Use your answer in (ii) to
calculate the potential difference between A and the contact C for the contact
placed at the midpoint of AB.

**(d)**Explain why, although the contact C is at the midpoint of wire AB, the answer in (c)(iii) is not numerically equal to one half of the e.m.f. of the cell.

**Reference:**

*Past Exam Paper – June 2010 Paper 22 Q6*

__Solution 978:__**(a)**

Either Power, P ∝
V

^{2}OR P = V^{2}/R
Percentage reduction = [(230

^{2}– 220^{2}) / 230^{2}] × 100% = 8.5%**(b)**

(i) Zero

{Since the ammeter has
some resistance, the reading on it would correspond to the current through the
ammeter, not the wire. When the contact is placed at A, the wire has zero
resistance. So, all current would flow through the wire [for wire, R = 0, I = V
/ R = 1.5 / 0 = infinity – that is, all current flow though wire] and no
current in the ammeter.}

(ii) Current = 1.5 / 5 = 0.3(0)A

{The ammeter has some
internal resistance and is connected in parallel with the wire. So, the p.d.
across the ammeter is the same as that across the wire (= 1.5V). Hence, the
current can be directly obtained by I = V / R = 1.5 / 5}

**(c)**

(i)

(point (0, 0) and point
(100, 0.3))

The plots must be correct to within ±
1mm

__reasonable line/curve__through the points giving current as 0.12A for contact at midpoint {50cm} of wire.

(iii) V = IR = 0.12 × 5.0 = 0.6(0)V

**(d)**

The circuit acts as a potential
divider / current divides / current in AC is not the same as current BC.

The resistance between A and C is
not equal to the resistance between C and B

OR The
current in wire AC × R is not equal to the current in wire BC × R

{The resistance of the ammeter
has an effect on the total resistance for that section of the wire. These
resistances are in parallel for that section of the wire.}

__Question 979: [Matter > States of Matter]__
The diagram shows an ice cube
floating in water.

Both the ice cube and the water are
at 0 °C.

Which statement correctly compares
the molecular properties of the ice and those of the water?

A The mean inter-molecular potential
energies are the same for both the ice molecules and the water molecules.

B The mean inter-molecular
separations are the same for both the ice and the water.

C The mean kinetic energies are the
same for both the ice molecules and the water molecules.

D The mean total energies are the
same for both the ice molecules and the water molecules.

**Reference:**

*Past Exam Paper – November 2009 Paper 11 Q17 & Paper 12 Q16 & June 2013 Paper 12 Q19*

__Solution 979:__**Answer: C.**

Temperature depends only on the
average speed of molecules.

Molecules in ice at 0°C
and molecules in water at 0°C have the same average speed and therefore the same average
kinetic energy.

The mean inter-molecular potential
energies for the ice molecules and for the water molecules are different since
the ice is a solid and water is a liquid. As a result of this difference in
inter-molecular potential energy, the mean inter-molecular separations are
different for ice and water. The ice molecules are closer to each other than
are the water molecules. [A and B are incorrect]

For the mean total energy, we need
to consider the kinetic energy of the molecules and the inter-molecular
potential energy of the molecules. Since both are at the same temperature, they
have the same kinetic energy. But their inter-molecular potential energies are
different, so the mean total energies are also different. [D is incorrect]

Please consider answering ALL of the following questions:

ReplyDelete4/O/N/02 Q.5(b),Q.6(c)(i)

6/O/N/02 Q.11(a)(b)

6/O/N/03 Q.9

04/M/J/04 Q.8(a),(b)(i),(ii)1.

06/M/J/04 Q.9(b)(iii),Q.11(b)

06/O/N/04 Q.3(b)(i)1.,Q.4(a),Q.6(b),Q.8(a)(i)

04/M/J/05 Q.7(a)

06/O/N/05 Q.8(b),Q.10(a)

04/M/J/06 Q.6(a),(c),Q.7(b)

06/M/J/06 Q.14(b)

04/O/N/06 Q.3(c)

06/O/N/06 Q.3(b)

05/M/J/07 Q.2(d)

04/O/N/07 Q.7(b)(i),(c),Q.10(c)

04/M/J/08 Q.5(b),Q.9(b),Q.11(a)(ii)

04/O/N/08 Q.7(c)

41/O/N/09 Q.6(a),(b)(i),Q.10

41/M/J/10 Q.6(a),Q.7(a)

51/M/J/10 Q.2(d)

41/M/J/11 Q.8(a)

For 41/M/J/11 Q.8(a), see solution 981 at

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