• 9702 November 2012 Paper 41 & 42 Worked Solutions | A-Level Physics

Paper 41 and 42 are similar.

SECTION A

Question 1

(a)

Newton’s law of gravitation states that the force between two point masses is proportional to the product of the masses and inversely proportional to the square of the separation, provided that the separation is much larger than the sizes of the masses.

(b)

(i)

Considering gravitational force on satellite and centripetal force, kinetic energy E_k can be expressed as:

Gravitational force provides the centripetal force.

mv²/r = GMm/r²          and E_k = ½ mv²

Hence, E_k = GMm / 2r

(ii)

Satellite mass, m = 620kg

Initial orbit = 7.34x10⁶m

(Resistive forces causes) New orbit = 7.30x10⁶m

For satellite,

1.

Change in E_k

ΔE_k = ½ x 4.00x10¹⁴ x 620 x ({7.30x10⁶}^-1 – {7.34x10⁶}^-1)

ΔE_k = 9.26x10⁷J (ignore any sign in answer)

2.

Change in gravitational potential energy

ΔE_p = – GMm / r

ΔE_p = 4.00x10¹⁴ x 620 x ({7.30x10⁶}^-1 – {7.34x10⁶}^-1)

ΔE_p = 1.85x10⁸J (ignore any sign in answer)

(iii)

Explain whether linear speed of satellite increases, decreases or remains unchanged when radius of orbit decreases:

Either ({7.30x10⁶}^-1 – {7.34x10⁶}^-1) or ΔE_k is positive / E_k increased.

Speed has increased.

Question 2

Student: when an ideal heated from 100^oC to 200^oC, internal energy of gas is doubled

(a)

(i)

Internal energy is the sum of potential energy and kinetic energy of atoms / molecules / particles which are in random motion.

(ii)

By reference to one assumption of kinetic theory of gases, internal energy of ideal gas:

For an ideal gas, it is assumed that there are no intermolecular forces, and so, the potential energy of the molecules is zero. Therefore, internal energy of an ideal gas is the kinetic energy (from the random motion) of the molecules.

(b)

Is student’s suggestion correct?:

Kinetic energy is proportional to the thermodynamic temperature.

Either Since the temperature is given in Celsius and not in Kelvin, it is incorrect.

Or Temperature in kelvin is not doubled

Question 3

An electric water heater contains a tube through which water flows at a constant rate.

Question 4

(a)

Explain features of Fig 4.2 that indicate that motion is simple harmonic:

The straight line passing through the origin shows that the acceleration is proportional to the displacement. The negative gradient shows that the gradient and displacement are in opposite directions.

(b)

For oscillation of ball:

(i)

Amplitude = 2.8cm

(ii)

Frequency:

Either gradient = ω² and ω = 2πf       or a = - ω²x and ω = 2πf

Gradient = 13.5 / (2.8x10^-2) = 482

ω = 22rads^-1

Frequency = 22 / (2π) = 3.5Hz

(c)

Line AB is now vertical. Ball now oscillates. Ball now oscillates in vertical plane. One reason why oscillations may no longer be simple harmonic:

e.g. Lower spring may not be extended.

e.g. Upper spring may exceed limit of proportional / elastic limit

Question 5

{Detailed explanations for this question is available as Solution 706 at Physics 9702 Doubts | Help Page 143 - http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-143.html}

Question 6

(a)

(i)

Condition for charged particle to experience a force in magnetic field:

The particle must be moving with a component of velocity normal to the magnetic field.

(ii)

Expression for magnetic force F acting on charged particle in magnetic field flux density B:

F = Bqvsinθ

Where q is the charge of the particle, v is the velocity of the particle and θ is the angle between the direction of motion and magnetic field

(b)

(i)

Face where electrons tend to move due to force:

Face BCGF shaded

(ii)

Movement of electrons in magnetic field causes potential difference between 2 faces of conductor. State these faces:

Between face BCGF and face ADHE

(c)

Why potential difference causes an additional force on moving electrons in conductor:

The potential difference gives rise to an electric field.

Either F_E = qE (no need to explain symbols)

Or The electric field gives rise to a force (on the electrons).

Question 7

(a)

Lenz’s law states that the induced e.m.f / current produces effects / acts in such a direction / tends to oppose the change causing it.

(b)

Why core is:

(i)

1.

Made of iron:

The core is made of iron to reduce flux losses / increase flux linkage / easily magnetized and demagnetized.

2.

Laminated:

To reduce energy / heat losses caused by eddy currents.

(ii)

Emf induced in secondary coil of transformer. Explain how current in primary coil gives rise to this induced emf:

The alternating current / voltage gives rise to a (changing) flux in the core.  This flux links the secondary coil. (By Faraday’s law), the changing flux induces an e.m.f (in secondary coil).

Question 8

(a)

A photon is a discrete quantity / packet / quantum of energy of electromagnetic radiation. Energy of photon = Planck constant x frequency

(b)

Where photoelectric emission of electrons take place, there is negligible time delay between illumination of surface and emission of electron. 3 other evidence provided by photoelectric effect for particulate nature of EM radiation:

Choose any 3:

Threshold frequency (of electromagnetic radiation required for emission of electrons.)

Rate of emission is proportional to intensity.

Maximum kinetic energy of electron dependent on frequency.

Maximum kinetic energy independent of intensity.

(c)

Work function of metal surface = 3.5eV.

Wavelength of light incident = 450nm

Determine whether electrons will be emitted by photoelectric effect from surface:

Either

E = hc /λ

λ = 450nm to give Energy = 4.4x10^-19 or 2.8eV

2.8eV < 3.5eV so no emission

Or

hc /λ = eV

Work function of 3.5eV to give λ = 355nm

355nm < 450nm so no emission

Or

Work function = 3.5eV

[E=hf] Threshold frequency = 8.45x10¹⁴Hz

Wavelength of 450nm = 6.67x10¹⁴Hz

6.67x10¹⁴Hz < 8.45x10¹⁴Hz so no emission

SECTION B

Question 9

An operational amplifier (op-amp) may be used as part of the processing unit in an electronic sensor.

Question 10

Principle of CT scanning:

X-ray images taken from different angles / X-rays directed from different angles

of one section / slice.

All the images are in the same plane

The images are combined to give an (2D) image of the section / slice

The (2D) images of successive sections / slices are combined

and a (3D) image is formed using a computer.

The image formed can be rotated / viewed from different angles.

Question 11

{Detailed explanations for this question is available as Solution 668 at Physics 9702 Doubts | Help Page 134 - http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-134.html}

Question 12

(a)

(i)

Cross-linking in the wire pair occurs when the signal in one wire (pair) is picked up by a neighboring wire (pair).

(ii)

Why cross-linking in coaxial cables is much less than in wire pairs:

The outer braid of coaxial cables is earthed and it shields the core from noise / external signals.

(b)

Length of wire pair = 1.4km

Constant noise power in wire pair = 3.8 x 10^-8W

For input signal to wire pair of (P₂=) 3.0x10^-3W, signal-to-noise ratio at receiver = 25dB.

Attenuation per unit length for wire pair:

Attenuation per unit length = (1/L) x 10lg(P₂/P₁)

Signal power at receiver, P₁ = 10^2.5 x 3.8x10^-8 = 1.2x10^-5W

Attenuation in wire pair = 10 lg({3.0x10^-3}/{1.2x10^-5}) = 24dB

Attenuation per unit length = (1/1.4) x 24 = 17dBkm^-1