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(a) Define acceleration.[1]
(b) A small aircraft is flying horizontally at a speed of $42 \text{ ms}^{-1}$ at a height of $63 \text{ m}$ above horizontal ground, as shown in Fig. 1.1.
The aircraft drops a small parcel. The parcel is released from the aircraft at the instant shown in Fig. 1.1. Air resistance is negligible.
(i) On Fig. 1.1, draw a line to show the path of the parcel as it falls from the aircraft to the ground. [1]
(ii) Calculate the time taken from the instant of release to the instant the parcel reaches the ground. [2]
(iii) Calculate the vertical component of the velocity of the parcel immediately before it reaches the ground. [1]
(iv) Determine the speed at which the parcel reaches the ground. [2]
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(a) State the principle of conservation of momentum. [2]
(b) A ball X has mass 240 g and moves in a straight line on a horizontal frictionless surface with an initial speed of 16 m s-1. The ball collides with a stationary ball Y that has mass 480 g. After the collision, ball X is stationary, as shown in Fig. 2.1.
(i) Show that the speed v of ball Y after the collision is 8.0 m s-1. [1]
(ii) Calculate the change in the total kinetic energy ΔEK of the balls due to the collision. [3]
(c) The collision in (b) lasts for a time of 2.0 ms. Assume that the contact force between the balls is constant during this time.
(i) Determine the magnitude and direction of the force exerted on ball X by ball Y during the collision. [3]
(ii) Compare the magnitude and direction of the force exerted on ball Y by ball X during the collision with the answers in (c)(i). No further calculations are required. [2]
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(a) State the principle of moments. [1]
(b) A rigid uniform beam rests on a pivot at its centre, as shown in Figure 1.
A load of weight 2.6 N is suspended from the beam at distance x from the pivot.
A wooden cylinder of weight 4.0 N is suspended from the beam at a distance of 0.40 m from the pivot on the opposite side of the pivot to the load. The cylinder rests in a container of water. The lower part of the cylinder is immersed in the water to depth h.
Initially, h is equal to 0.10 m and x is equal to 0.40 m. The system is in equilibrium.
(i) Use the principle of moments to show that the upthrust U exerted by the water on the cylinder is 1.4 N. [2]
(ii) The density of the water is $1.0 \times 10^3\, \text{kg}\, \text{m}^{-3}$.
Calculate the area A of the circular cross-section of the cylinder. [3]
(c) More water is gradually added to the container in (b), so that depth h in Fig. 3.1 gradually increases. The length x is continuously adjusted so that the system remains in equilibrium.
On Figure 2, sketch the variation of x with h. Use the space below for any working. [3]
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(a) Define:
(i) stress [1]
(ii) strain [1]
(b) Two wires X and Y, with equal unstretched lengths of 0.84 m, are suspended from fixed points that are at the same horizontal level. The lower ends of the wires are attached to a beam of negligible mass. The beam is horizontal and in equilibrium, as shown in Fig. 4.1.
Wire X is made from a metal that has a Young modulus of $1.9 \times 10^9$ Pa.
Wire Y is made from a different metal.
A load of weight 18 N is suspended from the beam at a point that is equidistant from the two wires. This load causes both wires to extend by 0.47 mm.
(i) Determine the cross-sectional area of wire X. [3]
(ii) Wire Y has a greater diameter than wire X.
Explain, without calculation, whether the Young modulus of the metal from which wire Y is made is less than, the same as or greater than $1.9 \times 10^9$ Pa. [2]
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(a) A stationary wave is formed on a string XY that has a length of 0.48 m. Fig. 5.1 shows the string at one instant in time.
The speed of the wave on the string is 1400 m s^{-1}.
(i) On Fig. 5.1, draw a cross (×) at one position that is a node and another cross at one position that is an antinode. Label the node N and the antinode A. [1]
(ii) Show that the wavelength of the wave produced is 0.32 m. Explain your reasoning. [1]
(iii) Calculate the frequency of the wave. [2]
(b) A source of sound waves of frequency 780 Hz is on a rotating platform. The speed of the source is 39 m s^{-1}.
The sound is detected by an observer that is a large distance from the rotating platform, as shown in Fig. 5.2.
(i) The speed of sound in air is 320 m s^{-1}.
Calculate the maximum frequency of the sound detected by the observer. [2]
(ii) At time t = 0, the observer detects the sound emitted by the source when it was in the position shown in Fig. 5.2.
On Fig. 5.3, sketch the variation with t of the frequency f of the sound detected by the observer for one complete rotation of the platform. Calculations are not required. [2]
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(a) Define resistance.
................................................................................................................................. [1]
(b) A cylindrical metal wire of length 2.4 m and cross-sectional area $8.0 \times 10^{-6} \text{ m}^2$ has a resistance of $0.33 \Omega$. There is a current in the wire of 4.7A.
(i) Determine the resistivity of the metal from which the wire is made.
resistivity = ................................. $\Omega$ m [2]
(ii) Calculate the charge that passes through the wire in a time of 5.0 minutes.
charge = ..................................... C [2]
(iii) The free electrons (charge carriers) in the wire have an average drift speed of $0.16 \text{ mm s}^{-1}$.
Determine the number density of charge carriers in the metal.
number density = .................................. $\text{ m}^{-3}$ [2]
(c) The wire in (b) may be considered to be a fixed resistor. It is connected in series with a thermistor to a battery that has negligible internal resistance.
(i) Use circuit symbols to complete Fig. 6.1 to show the circuit diagram of this arrangement.
!(Fig. 6.1) [1]
(ii) Explain, without calculation, how the power dissipated in the wire changes as the temperature of the thermistor is increased.
................................................................................................................................. [2]
[Total: 10]
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(a) Complete Table 7.1 to show the charges, in terms of the elementary charge $e$, on each of the flavours of quark and antiquark shown.
Table 7.1
[Table_1]
(b)
(i) State the name of the class (group) of fundamental particles to which baryons and mesons belong.
......................................................................................................................................................... [1]
(ii) Compare baryons and mesons in terms of their constituent particles.
......................................................................................................................................................... [2]
(c) Describe $\beta^+$ decay in terms of the fundamental particles involved.
......................................................................................................................................................... [2]
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