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(a) State what is meant by a $\text{scalar}$ quantity and by a $\text{vector}$ quantity. [2]
(b) Complete Fig. 1.1 to indicate whether each of the quantities is a vector or a scalar.[2]
(c) An aircraft is travelling in wind. Fig. 1.2 shows the velocities for the aircraft in still air and for the wind.
The velocity of the aircraft in still air is $95 \text{m s}^{-1}$ to the west.
The velocity of the wind is $28 \text{m s}^{-1}$ from $65^{\circ}$ south of east.
(i) On Fig. 1.2, draw an arrow, labelled R, in the direction of the resultant velocity of the aircraft. [1]
(ii) Determine the magnitude of the resultant velocity of the aircraft. [2]
500
575
518
(a) State what is meant by the mass of a body. [1]
(b) Two blocks travel directly towards each other along a horizontal, frictionless surface. The blocks collide, as illustrated in Fig. 3.1.
Block A has mass $3M$ and block B has mass $M$.
Before the collision, block A moves to the right with speed $0.40\,\text{m s}^{-1}$ and block B moves to the left with speed $0.25\,\text{m s}^{-1}$.
After the collision, block A moves to the right with speed $0.20\,\text{m s}^{-1}$ and block B moves to the right with speed $v$.
(i) Use Newton’s third law to explain why, during the collision, the change in momentum of block A is equal and opposite to the change in momentum of block B. [2]
(ii) Determine speed $v$. [3]
(iii) Calculate, for the blocks,
1. the relative speed of approach,
2. the relative speed of separation. [2]
(iv) Use your answers in (b)(iii) to state and explain whether the collision is elastic or inelastic. [1]
598
589
559
(a) For a progressive wave, state what is meant by
(i) the period, [1]
(ii) the wavelength. [1]
(b) Fig. 4.1 shows the variation with time $t$ of the displacement $x$ of two progressive waves P and Q passing the same point.
The speed of the waves is $20 \text{ cm s}^{-1}$.
(i) Calculate the wavelength of the waves. [2]
(ii) Determine the phase difference between the two waves. [1]
(iii) Calculate the ratio [2]
intensity of wave Q
intensity of wave P
(iv) The two waves superpose as they pass the same point. Use Fig. 4.1 to determine the resultant displacement at time $t = 0.45 s$. [1]
549
553
598
(a) When monochromatic light is incident normally on a diffraction grating, the emergent light waves have been diffracted and are coherent.
Explain what is meant by
(i) diffracted waves, [1]
(ii) coherent waves. [1]
(b) Light consisting of only two wavelengths $\lambda_1$ and $\lambda_2$ is incident normally on a diffraction grating.
The third order diffraction maximum of the light of wavelength $\lambda_1$ and the fourth order diffraction maximum of the light of wavelength $\lambda_2$ are at the same angle $\theta$ to the direction of the incident light.
(i) Show that the ratio
$\frac{\lambda_2}{\lambda_1}$ is 0.75.
Explain your working. [2]
(ii) The difference between the two wavelengths is 170 nm.
Determine wavelength $\lambda_1$. [1]
544
582
539
(a) Define the volt.
.............................................................................................................. [1]
(b) A battery of electromotive force (e.m.f.) 4.5 V and negligible internal resistance is connected to two filament lamps P and Q and a resistor R, as shown in Fig. 6.1.
[Image_1: Circuit Diagram]
The current in lamp P is 0.15 A. The $I-V$ characteristics of the filament lamps are shown in Fig. 6.2.
[Image_2: Graph of I-V Characteristics]
(i) Use Fig. 6.2 to determine the current in the battery. Explain your working.
current = ................................................... A [2]
(ii) Calculate the resistance of resistor R.
resistance = ................................................. Ω [2]
(iii) The filament wires of the two lamps are made from material with the same resistivity at their operating temperature in the circuit. The diameter of the wire of lamp P is twice the diameter of the wire of lamp Q.
Determine the ratio
$$ \text{length of filament wire of lamp P} \over \text{length of filament wire of lamp Q} $$
ratio = ..................................................... [3]
(iv) The filament wire of lamp Q breaks and stops conducting.
State and explain, qualitatively, the effect on the resistance of lamp P.
..............................................................................................................
..............................................................................................................
..............................................................................................................
.............................................................................................................. [2]
516
553
569
A $\beta^{-}$ particle from a radioactive source is travelling in a vacuum with kinetic energy 460 eV. The particle enters a uniform electric field at a right-angle and follows the path shown in Fig. 7.1.
(a) The direction of the electric field is in the plane of the paper. On Fig. 7.1, draw an arrow to show the direction of the electric field. [1]
(b) Calculate the speed of the $\beta^{-}$ particle before it enters the electric field.
speed = .................................................... m s$^{-1}$ [3]
(c) Other $\beta^{-}$ particles from the same radioactive source travel outside the electric field along the same incident path as that shown in Fig. 7.1.
State and briefly explain whether those $\beta^{-}$ particles will all follow the same path inside the electric field.
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.....................................................................................................................[2]
511
556
564
