16-19 sample answers drawn from a number of different files

The questions are shown in black type with the answers in bold blue.

1. Explain why it is possible for an object travelling in a circle at a constant speed to have an acceleration.
The direction of motion is changing and therefore there is a change in velocity (velocity is a vector) and so there will be an acceleration.

2. A ball mass 2 kg moving left to right at 1.5 ms^-1 collides with a ball of mass 3 kg that is moving from right to left at 0.2 ms^-1. After the collision the 2 kg ball moves from left to right at 1 ms^-1.
Calculate:
(a) the change of momentum of the 2 kg ball
(b) the momentum of the 3 kg ball after the collision
(c) the velocity of the 3 kg ball after the collision
(d) the loss of kinetic energy of the 3 kg ball
(a) Momentum change = m[v – u] = 2[1 - 1.5] = -1 Ns
(b) Momentum of 3 kg ball after collision = -3x0.2 + 1 = 0.4 Ns
(c) Velocity of 3 kg ball = 0.4/3 = 0.13 ms^-1
(d) Loss of kinetic energy of 3kg ball = 0.5x3x0.2² – 0.5x3x0.13² = 0.06 – 0.02535 = 0.035 J


3. A diffraction grating has 300 lines per mm.
Calculate:
(a) the angle of diffraction for the first order image for light of wavelength 550 nm
(b) the highest order possible with this grating at this wavelength
(c) the number of images of the source
Grating spacing (d) = 1/300x10³ = 3.33x10⁶ m
(a) nl = dsinq sin q = 550x10^-9/3.33x10^-6 = 0.165 therefore q = 9.5^o
(b) Highest possible order occurs when the angle of diffraction (q) = 90^o and therefore sin q = sin 90 = 1
n = dsin90/l = 6.06 highest order possible = 6 (you cannot have part of an order)
(c) 13 images – six on each side of the centre line and one in the middle

4. A 5 kg mass is hung on a 2.5m length of copper wire of diameter 0.5 mm. If the Young modulus for copper is 1.2x10¹¹ Pa calculate:
(a) the extension produced.
e = FL/EA A = p d²/4 = 1.96x10^-7 m²   Therefore: e = 5.2x10^-3 m = 5.3 mm
(b) the elastic energy stored in the wire Energy = ½ Fe = ½ x 9.8x5x5.2x10^-3 = 0.255J

5. How could the strength of an electromagnet be increased?
Increase current, number and closeness of coils, bend poles closer, have an iron core

6. Describe and explain an experiment to distinguish between the Plum Pudding model of the atom and the Nuclear model.
Rutherford or alpha particle scattering. Fire a beam of alpha particles at a thin sheet of gold foil and observe the scattered alpha particles. The fact that some are deflected through more than 90^o is powerful evidence for the nuclear model of the atom.

7. Does a greater difference between the refractive index of the fibre and that of the surrounding air give a greater or smaller critical angle?
Smaller n₁sinq₁ = n₂sinq ₂ so if q₂ =90^o n1sinq₁ = n₂ sinq₁ = n₂/n₁ the bigger n₁ the smaller will be the critical angle

8. In view of your answer to number 3, why is the fibre surrounded by a layer of glass cladding? (at least three reasons are required here).
Protection.
Increases the critical angle and this gives: Reduced multipath dispersion. Short travel time.

9. An engine of mass 5000 kg pulls a train of ten trucks each of mass 2000 kg along a horizontal track. Assume that the frictional forces to be 5000 N and that the engine exerts a force of 50 000 N on the rails. If the trucks are numbered from 1 to 10 starting with the one next to the engine calculate:
(a) the net total accelerating force Force = 50 000 – 5000 = 45000N
(b) the acceleration of the train Acceleration = 45000/25000 = 1.8 ms^-2
(c) the force of truck 6 on truck 7
Net force = accelerated mass x a = 8000x1.8 = 14400 N
(d) the force of truck 9 on truck 8
Net force of truck 9 on truck 8 = force of truck 8 on truck 9 = accelerated mass x a = 4000x1.8 = 7200 N

10. What is a positron?
Positive electron b+ . Emitted in decay of proton to neutron.

11. Radiation of wavelength 120 nm falls on a zinc plate. The threshold wavelength for this surface is 200 nm.
(a) what is the energy of a quantum of the incident radiation
(b) what is the energy required to give photoelectric emission
(c) what is the energy of the emitted photoelectrons?
(a) E = hf = hc/l = [6.63x10^-34x3x10⁸]/120x10^-9 = 1.99x10^-25/120x10^-9 = 1.66x10^-18 J
(b) E = hf_o = hc/l _o = [6.63x10^{- 34}x3x10⁸]/200x10^-9 = 1.99x10^-25/200x10^-9 = 1.00x10^-18 J
(c) Kinetic energy = hf – hf_o = 1.66x10^-18 - 1.00x10^-18 = 0.66x10^-18 J

12. Two identical glass bulbs are joined with a thin glass tube and filled with air which is initially at 20 ^oC. What will the pressure in the apparatus become if one bulb is immersed in steam and the other in melting ice?
Let the original pressure in the bulbs be P_o.
P_oV_o = nRT n₁RT₁ = n₂RT₂
The total number of molecules in the two bulbs is equal to the sum of the number in each bulb n = n₁ + n₂
P_o = nRx293/V
n = 2VP_o/Rx293 = PV/RT₁ + PV/RT₂
Therefore: 2P_o/293 = P[(273+373)/(273x373)] = 0.00634P P = 1.08 P_o

13. (a) What is meant by the frequency of a wave?
(b) What is meant by the displacement of a wave?
(c) What is meant by the amplitude of a wave?
(d) What is meant by the wavelength of a wave?
(e) How are frequency, wavelength and velocity related to one another?
(f) How is the time period of a wave related to its frequency?
(a) the number of complete vibrations per second
(b) the distance of any pointy on the wave from the mean position
(c) the maximum distance of a point on the wave from the mean position
(d) the distance between two similar points on the wave
(e) velocity (speed) = frequency x wavelength
(f) Time period (T) = 1/frequency (f)

14. A beam of light is shone through two pieces of Polaroid arranged with their axes at right angles to each other. Describe what will be observed if a third piece of Polaroid is placed above the two fixed pieces and rotated through 360^o.
The third piece is now placed between the other two and rotated through 360^o. What is observed now?
(a) Nothing – there will be no transmission through the second polaroid
(b) The will be a variation in the output intensity as the plane of polarisation of the light meeting the third piece of Polaroid is changing

15. Explain how the distances from the Earth of stars within about 10000 light years may be determined.
Cepheid variables. If the period is known the luminosity can be found from the period-luminosity relationship. Hence the absolute magnitude can be found. If you know how bright a star really is and how bright it appears to be then its distance can be found.

16. (a) how is the law of force between two charges similar to that between two masses
(b) how is the law of force between two charges different to that between two masses?
(c) what is meant by the term e in the equation?
(a) depends on both charges, varies inversely as the square of the distance of separation
(b) electric fields can be repulsive, depends on the material between the charges
(c) Permittivity of the material between the charges