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(a) The spacing between two atoms in a crystal is $3.8 \times 10^{-10}$ m. State this distance in pm. [1]
(b) Calculate the time of one day in Ms. [1]
(c) The distance from the Earth to the Sun is 0.15 Tm. Calculate the time in minutes for light to travel from the Sun to the Earth. [2]
(d) Underline all the vector quantities in the list below.
distance energy momentum weight work [1]
(e) The velocity vector diagram for an aircraft heading due north is shown to scale in Fig. 1.1. There is a wind blowing from the north-west.
The speed of the wind is $36 \text{ ms}^{-1}$ and the speed of the aircraft is $250 \text{ ms}^{-1}$.
(i) Draw an arrow on Fig. 1.1 to show the direction of the resultant velocity of the aircraft. [1]
(ii) Determine the magnitude of the resultant velocity of the aircraft. [2]
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Two planks of wood AB and BC are inclined at an angle of 15° to the horizontal. The two wooden planks are joined at point B, as shown in Fig. 2.1.
A small block of metal M is released from rest at point A. It slides down the slope to B and up the opposite side to C. Points A and C are 0.26 m above B. Assume frictional forces are negligible.
(a) (i) Describe and explain the acceleration of M as it travels from A to B and from B to C. [3]
(ii) Calculate the time taken for M to travel from A to B. [3]
(iii) Calculate the speed of M at B. [2]
(b) The plank BC is adjusted so that the angle it makes with the horizontal is 30°. M is released from rest at point A and slides down the slope to B. It then slides a distance along the plank from B towards C.
Use the law of conservation of energy to calculate this distance. Explain your working. [2]
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(a) Define power. [1]
(b) A cyclist travels along a horizontal road. The variation with time \(t\) of speed \(v\) is shown in Fig. 3.1.
The cyclist maintains a constant power and after some time reaches a constant speed of \(12 \, \text{ms}^{-1}\).
(i) Describe and explain the motion of the cyclist. [3]
(ii) When the cyclist is moving at a constant speed of \(12 \, \text{ms}^{-1}\) the resistive force is \(48 \,\text{N}\). Show that the power of the cyclist is about \(600 \, \text{W}\). Explain your working. [2]
(iii) Use Fig. 3.1 to show that the acceleration of the cyclist when his speed is \(8.0 \, \text{ms}^{-1}\) is about \(0.5 \, \text{ms}^{-2}\). [2]
(iv) The total mass of the cyclist and bicycle is \(80 \, \text{kg}\). Calculate the resistive force \(R\) acting on the cyclist when his speed is \(8.0 \, \text{ms}^{-1}\). Use the value for the acceleration given in (iii). [3]
(v) Use the information given in (ii) and your answer to (iv) to show that, in this situation, the resistive force \(R\) is proportional to the speed \(v\) of the cyclist. [1]
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A circuit used to measure the power transfer from a battery is shown in Fig. 4.1. The power is transferred to a variable resistor of resistance $R$.
The battery has an electromotive force (e.m.f.) $E$ and an internal resistance $r$. There is a potential difference (p.d.) $V$ across $R$. The current in the circuit is $I$.
(a) By reference to the circuit shown in Fig. 4.1, distinguish between the definitions of e.m.f. and p.d.
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............................................................................................................................................. [3]
(b) Using Kirchhoff's second law, determine an expression for the current $I$ in the circuit. [1]
(c) The variation with current $I$ of the p.d. $V$ across $R$ is shown in Fig. 4.2.
Use Fig. 4.2 to determine
(i) the e.m.f. $E$,
$E = ext{.....................}$ V [1]
(ii) the internal resistance $r$.
$r = ext{.....................}$ Ω [2]
(d) (i) Using data from Fig. 4.2, calculate the power transferred to $R$ for a current of 1.6 A.
power = ext{.....................} W [2]
(ii) Use your answers from (c)(i) and (d)(i) to calculate the efficiency of the battery for a current of 1.6 A.
efficiency = ................................. % [2]
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(a) State one property of electromagnetic waves that is not common to other transverse waves. [1]
(b) The seven regions of the electromagnetic spectrum are represented by blocks labelled A to G in Fig. 5.1.
A typical wavelength for the visible region D is 500 nm.
(i) Name the principal radiations and give a typical wavelength for each of the regions B, E and F. [3]
(ii) Calculate the frequency corresponding to a wavelength of 500 nm. [2]
(c) All the waves in the spectrum shown in Fig. 5.1 can be polarised. Explain the meaning of the term polarised. [2]
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(a) $\beta$-radiation is emitted during the spontaneous radioactive decay of an unstable nucleus.
(i) State the nature of a $\beta$-particle.
............................................................................................. [1]
(ii) State two properties of $\beta$-radiation.
1. .........................................................................................
2. ......................................................................................... [2]
(iii) Explain the meaning of spontaneous radioactive decay.
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(b) The following equation represents the decay of a nucleus of hydrogen-3 by the emission of a $\beta$-particle.
Complete the equation.
$$^3_1H \rightarrow \text{.......} \ _2\text{He} + \text{.......} \ \beta$$ [2]
(c) The $\beta$-particle is emitted with an energy of $5.7 \times 10^3$ eV.
Calculate the speed of the $\beta$-particle.
speed = ....................................... ms$^{-1}$ [3]
(d) A different isotope of hydrogen is hydrogen-2 (deuterium). Describe the similarities and differences between the atoms of hydrogen-2 and hydrogen-3.
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............................................................................................. [2]
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