Monday, September 22, 2014

9702 November 2007 Paper 4 Worked Solutions | A-Level Physics

  • 9702 November 2007 Paper 4 Worked Solutions | A-Level Physics

Paper 4


SECTION A

Question 1
(a)
(i)
A radian is the angle subtended at the centre of a circle such that the arc is equal in length to the radius.

(ii)
Why 1 complete revolution is equivalent to angular displacement of 2π rad:
Length of arc = rθ and for one revolution, the length of arc formed (= circumference) = 2πr. So, θ = 2πr / r = 2π

(b)
Elastic cord has unextended length of 13.0cm. One end of cord attached to fixed point C. Small mass of weight 5.0N is hung from free end of cord. Cord extends to length of 14.8cm, as shown.
Cord and mass are now made to rotate at constant angular speed ω in vertical plane about point C. When cord is vertical and above C, its length is the unextended length of 13.0cm, as shown.
(i)
Show that angular speed ω of cord and mass = 8.7rads-1:
EITHER The weight provides / equals the centripetal force OR The acceleration of free fall is the centripetal acceleration.
(a = rω2)
9.8 = 0.13ω2
ω = 8.7 rads-1

(ii)
Cord and mass rotate so that cord is vertically below C, as shown. Length L of cord, assuming it obeys Hooke’s law:

{When the cord and mass is vertically below C, the centripetal force {FC} is provided by the resultant force from the force in the cord [tension in the cord {T} – which is upwards] and the weight [W - which is downwards]. (T should be greater than W so that the mass remains attached to that cord) So, FC = T – W giving T = W + FC}
Force in the cord = Weight + Centripetal force

{To know the force in the cord, the spring constant, which is always constant should be found first. Hooke’s law: Force, F = kx. Extension, x = L – 13 and spring constant, k = F /x. When F = 5.0N, x = 14.8 – 13 = 1.8cm, k = spring constant [this always constant] = 5.0 / 1.8} 
Force in the cord = (L – 13) x 5/1.8    or force constant = 5.0 / 1.8


{Force constant mentioned above = spring constant}

{Weight = 5.0N, Centripetal force = m rω2. Since only the weight is given, we need to find the mass to calculate the centripetal force. Mass, m = weight / g = 5.0 / 9.8}

{Force in the cord = Weight + Centripetal force}
(L – 13) x 5/1.8 = 5.0 + (5/9.8) (L x 10-2) (8.72)
Length of cord, L = 17.2cm



Question 2
(a)
Amount of 1.00mol of Helium-4 gas contained in cylinder at pressure of 1.02x105Pa and temperature of 27oC.
(i)
Volume of gas in cylinder:
pV = nRT
(T = 273 + 27 = 300)
V = (nRT/p =) (8.31 x 300) / (1.02x105) = 0.0244m3

(ii)
Show that average separation of gas atoms in cylinder is approximately 3.4x10-9m:
Volume occupied by 1 atom = 0.0244 / (6.02x1023) = 4.06x10-26m3
Separation ≈ (4.06x10-26)1/3 = 3.44x10-9m

(b)
(i)
Gravitational force between 2 Helium-4 atoms that are separated by distance of 3.4x10-9m:
Force = GMm / r2 = [(6.67x10-11) (4{1.66x10-27})2] / (3.44x10-9)2 = 2.49x10-46N

(ii)
Ratio of weight of a Helium-4 atom to gravitational force between 2 Helium-4 atoms that with separation 3.4x10-9m:
Ratio = [4(1.66x10-27) x 9.8] / (2.49x10-46) = 2.6x1020

(c)
Comment on answer to (b)(ii) with reference to 1of the assumptions of kinetic theory of gases:
One assumption of the kinetic theory of gases is that the forces between the atoms are negligible.
Comment: e.g
The ratio shows the gravitational force to be very small
The force is very much less than the weight
If there are forces, they are not gravitational forces.





Question 3
{Detailed explanations for this question is available as Solution 1125 at Physics 9702 Doubts | Help Page 243 - http://physics-ref.blogspot.com/2016/10/physics-9702-doubts-help-page-243.html}

 



Question 4
{Detailed explanations for this question is available as Solution 714 at Physics 9702 Doubts | Help Page 144 - http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-144.html}
 

 



Question 5
(a)
1 function of capacitors in simple circuits:
Example:
They separate charges
They store energy
For smoothing circuit

(b)
Capacitor is charged to potential difference of 15V and then connected in series with switch, a resistor of resistance 12kΩ and sensitive ammeter, as shown. Switch is closed and variation with time t of current I in circuit shown.
(i)
Relation between current in circuit and charge that passes a point in circuit:
Charge = current x time

(ii)
Area below graph line of Fig represents charge. Use Fig to determine initial charge stored in capacitor:
Area under graph = 21.2cm2   (allow ± 0.5cm2)
1.0cm2 represents (0.125x10-3 x 1.25 =) 156μC
So, charge = 3300μC

(iii)
Initially, potential difference across capacitor was 15V. Capacitance of capacitor:
Capacitance = Q / V = (3300x10-6) / 15 = 220μF

(c)
Capacitor in (b) discharges one half of its initial energy. New potential difference across capacitor:
EITHER energy = ½ CV2       OR energy = ½ QV and C = Q/V
½ x C x 152 = 2 [½ x C x V2]
V = 10.6V






Question 6
A straight conductor carrying a current I isat an angle θ to a uniform magnetic field of flux density B, as shown in Fig.6.1. ... 



  
Question 7
{Detailed explanations for this question is available as Solution 1029 at Physics 9702 Doubts | Help Page 215 - http://physics-ref.blogspot.com/2015/10/physics-9702-doubts-help-page-215.html}






SECTION B

Question 8
(a)
Fig shows circuit incorporating ideal operational amplifier (op-amp). Voltages applied to inverting and non-inverting inputs are V1 and V2 respectively. State value of output voltage VOUT when
(i)
V1 > V2: -9V

(ii)
V1 < V2: +9V

(b)
Circuit of Fig used to monitor input voltage VIN. At point A, potential of 5.0V is maintained. At point B, potential of 3.0V is maintained. Complete Fig by indicating with tick the light-emitting diodes (LEDs) that are conducting for input voltages VIN shown. Also, mark with cross LEDs that are not conducting:

VIN / V             red LED          green LED
+2.0                 cross                cross
+4.0                 tick                  cross
+6.0                 tick                  tick

(c)
Input voltage VIN in (b) provided by sensor circuit.
(i)
Complete Fig to show sensor circuit that will provide voltage output that increases as temperature of sensor decreases.  Show clearly output connections from circuit:
A thermistor and a resistor is shown in series. The output connections are across the thermistor.

(ii)
Operation of sensor circuit:
As the temperature decreases, the thermistor resistance increases. The potential difference across the thermistor = V x [RT / (R+RT)]. So, as RT increases, the output increases.

 

Question 9
(a)
Acoustic impedance is the product of density (of the medium) and the speed of sound (in the medium).

(b)
Why acoustic impedance is important when considering reflection of ultrasound at boundary between 2 media:
The difference in acoustic impedance determines the fraction of incident intensity that is reflected / amount of reflection.

(c)
Principles behind use of ultrasound to obtain diagnostic information about structures within body:
A pulse of ultrasound (which is directed into the body) is reflected at the boundary (between the tissues). (The reflected pulse is) detected and processed. The time for return of the echo gives (information on the) depth and the amount of reflection gives information on the tissue structures.




Question 10
 Fig shows variation with frequency f of power P of radio signal.
(a)
Name
(i)
Type of modulation of radio signal:
Amplitude (modulated)

(ii)
Component of frequency 50kHz:
Carrier (frequency / wave)

(iii)
Components of frequencies 45kHz and 55kHz:
Sideband (frequency)

(b)
Bandwidth of radio signal:
Bandwidth = 10kHz

(c)
On axes of Fig, sketch graph to show variation with time t of signal voltage of Fig:
The sketch should have a general shape, i.e. any wave that is amplitude modulated with a correct period for the modulating waveform (200μs) and a correct period for the carrier waveform (20μs)


 
Question 11
In cellular phone network, country is divided into a number of cells, each with its own base station. Fig shows a number of these base stations and their connection to cellular exchange.
(a)
Explain why country is divided into a number of cells:
The carrier frequencies can be re-used (simultaneously without interference) so that the number of handsets possible is increased.
OR
Any sensible e.g. UHF used, so ‘line of sight’

(b)
What happens at base station and cellular exchange when mobile phone handset is switched on, before call is made?:
The handset sends out an (identifying) signal which is communicated by the base stations to (the computer at) the exchange. The computer selects a base station with the strongest signal and allocates a (carrier) frequency.


18 comments:

  1. asalamualaikum.
    Can you please explain Q3 part b(ii)? How do you find the amplitude using the graph and/or otherwise?

    ReplyDelete
    Replies
    1. Wa`alaikum-us-salaam.
      I have added some details. See it you understand now

      Delete
  2. 04/m/j/07 q4c(ii) pls

    ReplyDelete
    Replies
    1. details have been added for that part

      Delete
  3. s06 qp 4, question 8 b ii) v(velocity)= electric potential/ magnetic force, as the velocity increases shouldn't the magnetic field decrease ;since, they are inversely proportional? meaning the E should increase as the velocity increases but why is that not the case?

    ReplyDelete
    Replies
    1. It's explained as solution 654 at
      http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-130.html

      Delete
  4. M/J 07 Q3(b) and 4(b) and (c) please. Thank you :)

    ReplyDelete
    Replies
    1. For question 3, see solution 26 at
      http://physics-ref.blogspot.com/2014/10/physics-9702-doubts-help-page-4.html

      Delete
    2. For question 4, see solution 699 at
      http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-141.html

      Delete
  5. Can you explain why is the answer for question 4(d.) ? MJ 2007

    ReplyDelete
    Replies
    1. See question 699 at
      http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-141.html

      Delete
  6. Can you explain ON2007 q4(d)? Thank you.**

    ReplyDelete
  7. MJ 2007 7(b) ,can you explain what's the function of resistor and how to draw the graph? Thank you :) thank you

    ReplyDelete
    Replies
    1. Check question 106 at
      http://physics-ref.blogspot.com/2014/11/physics-9702-doubts-help-page-20.html

      Delete
  8. May Allah bless you for your kindness!!

    ReplyDelete

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