No questions found
(a) The frequency of an X-ray wave is $4.6 \times 10^{20} \text{Hz}$.
Calculate the wavelength in pm.
wavelength = .............................. pm [3]
(b) The distance from Earth to a star is $8.5 \times 10^{16} \text{m}$. Calculate the time for light to travel from the star to Earth in Gs.
time = ...................................... Gs [2]
(c) The following list contains scalar and vector quantities.
Underline all the scalar quantities.
acceleration, force, mass, power, temperature, weight [1]
(d) A boat is travelling in a flowing river. Fig. 1.1 shows the velocity vectors for the boat and the river water.
The velocity of the boat in still water is $14.0 \text{m s}^{-1}$ to the east. The velocity of the water is $8.0 \text{m s}^{-1}$ from $60°$ north of east.
(i) On Fig. 1.1, draw an arrow to show the direction of the resultant velocity of the boat. [1]
(ii) Determine the magnitude of the resultant velocity of the boat.
magnitude of velocity = ....................................... $\text{m s}^{-1}$ [2]
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Fig. 2.1 shows an object M on a slope.
M moves up the slope, comes to rest at point Q and then moves back down the slope to point R. M has a constant acceleration of $ 3.0 m s^{-2}$ down the slope at all times. At time t = 0, M is at point P and has a velocity of 3.6 $m s^{-1} $ up the slope. The total distance from P to Q and then to R is 6.0 m.
(a) Calculate, for the motion of M from P to Q,
(i) the time taken, [2]
(ii) the distance travelled. [1]
(b) Show that the speed of M at R is $4.8 m s^{-1}$. [2]
(c) On Fig. 2.2, draw the variation with time t of the velocity v of M for the motion P to Q to R. [3]
(d) The mass of M is 450 g.
Calculate the difference in the kinetic energy of M at P and at R. [2]
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A trolley T moves at speed 1.2 $m s^{-1}$ along a horizontal frictionless surface. The trolley collides with a stationary block on the end of a fixed spring, as shown in Fig. 3.1.
The mass of T is 250 g. T compresses the spring by 5.4 cm as it comes to rest. The relationship between the force F applied to the block and the compression x of the spring is shown in Fig. 3.2.
(a) Use Fig. 3.2 to determine
(i) the spring constant of the spring, [2]
(ii) the work done by T compressing the spring by 5.4 cm. [2]
(b) The spring then expands and causes T to move in a direction opposite to its initial direction. At the time that T loses contact with the block, it is moving at a speed of 0.75 $ms^{-1}$.
From the time that T is in contact with the block,
(i) describe the energy changes, [2]
(ii) determine the change in momentum of T. [2]
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(a) Define moment of a force. [1]
(b) An arrangement for lifting heavy loads is shown in figure 1.
A uniform metal beam AB is pivoted on a vertical wall at A. The beam is supported by a wire joining end B to the wall at C. The beam makes an angle of 30° with the wall and the wire makes an angle of 60° with the wall.
The beam has length 2.8 m and weight of 500 N. A load of 4000 N is supported from B. The tension in the wire is $T$. The beam is in equilibrium.
(i) By taking moments about A, show that $T$ is 2.1 kN. [2]
(ii) Calculate the vertical component $T_v$ of the tension $T$. [1]
(iii) State and explain why $T_v$ does not equal the sum of the load and the weight of the beam although the beam is in equilibrium. [2]
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559
A 240 V power supply S with negligible internal resistance is connected to four resistors, as shown in Fig. 5.1.
Two resistors of resistance 550 Ω and 950 Ω are connected in series across S. Two resistors of resistance 350 Ω and R are also connected in series across S.
The current supplied by S is 0.40 A.
Currents $I_1$ and $I_2$ in the circuit are shown in Fig. 5.1.
(a) Calculate
(i) current $I_1$,
$I_1 = \text{............................. A}$ [2]
(ii) resistance $R$,
$R = \text{............................. Ω}$ [2]
(iii) the ratio
$$\frac{\text{power transformed in resistor of resistance 350 Ω}}{\text{power transformed in resistor of resistance 550 Ω}}$$
ratio = .............................................. [2]
(b) Two points are labelled A and B, as shown in Fig. 5.1.
(i) Calculate the potential difference $V_{AB}$ between A and B.
$V_{AB} = \text{.............................................. V}$ [2]
(ii) The resistance $R$ is increased.
State and explain the effect on $V_{AB}$.
.....................................................................................................
.....................................................................................................
..................................................................................................... [1]
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518
531
A 12V battery with internal resistance 0.5Ω is connected to two identical filament lamps $L_1$ and $L_2$ as shown in Fig. 6.1.
The lamps are connected to the battery via switches $S_1$ and $S_2$. The power rating of each lamp is 48W for a potential difference of 12V.
(a) $S_1$ is closed and $S_2$ open.
State and explain whether the power transformed in $L_1$ is 48W.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................[2]
(b) $S_2$ is now also closed.
(i) State and explain the effect on the current in $L_1$.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................[1]
(ii) State and explain the effect on the resistance of $L_1$.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................[1]
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An arrangement that is used to demonstrate interference with waves on the surface of water is shown in Fig. 7.1.
(a) Two dippers $D_1$ and $D_2$ are connected to a motor and a d.c. power supply. Initially only $D_1$ vibrates on the water surface to produce waves. The variation with distance $x$ from $D_1$ of the displacement $y$ of the water at one instant of time is shown in Fig. 7.2.
Using Fig. 7.2, determine
(i) the amplitude of the wave, [1]
(ii) the wavelength of the wave. [1]
(b) The two dippers $D_1$ and $D_2$ are made to vibrate and waves are produced by both dippers on the water surface.
(i) State and explain whether these waves are stationary or progressive. [1]
(ii) Explain why $D_1$ and $D_2$ are connected to the same motor. [1]
(c) The points A and B on Fig. 7.1 are at the distances from $D_1$ and $D_2$ shown in Fig. 7.3.
State and explain the variation with time of the displacement of the water on the surface at
(i) A, [2]
(ii) B. [1]
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(a) The results of the \( \alpha \)-particle scattering experiment gave evidence for the structure of the atom.
State two results and the associated conclusions.
result 1: ................................................................................................................
...............................................................................................................................
conclusion 1: ...............................................................................................................
...............................................................................................................................
result 2: ................................................................................................................
...............................................................................................................................
conclusion 2: ...............................................................................................................
...............................................................................................................................
(b) In a model of a copper atom of the isotope \( ^{63}_{29}\text{Cu} \), the atom and its nucleus are assumed to be spherical.
The diameter of the nucleus is \( 2.8 \times 10^{-14} \text{ m} \). The diameter of the atom is \( 2.3 \times 10^{-10} \text{ m} \).
Calculate the ratio \( \frac{\text{density of the nucleus}}{\text{density of the atom}} \).
ratio = ........................................................
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