No questions found
(a) The drag force $F_D$ acting on a sphere moving through a fluid is given by the expression
$$F_D = K \rho v^2$$
where $K$ is a constant,
$\rho$ is the density of the fluid
and $v$ is the speed of the sphere.
Determine the SI base units of $K$. .[3]
(b) A ball of weight 1.5N falls vertically from rest in air. The drag force $F_D$ acting on the ball is given by the expression in (a). The ball reaches a constant
(terminal) speed of 33 ms$^{-1}$.
Assume that the upthrust acting on the ball is negligible and that the density of the air is uniform.
For the instant when the ball is travelling at a speed of 25 ms$^{-1}$, determine
(i) the drag force $F_D$ on the ball, [2]
(ii) the acceleration of the ball. [2]
(c) Describe the acceleration of the ball in (b) as its speed changes from zero to 33 ms$^{-1}$. [3]
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The variation with time \( t \) of the velocity \( v \) of two cars P and Q is shown in Fig. 2.1.
The cars travel in the same direction along a straight road.
Car P passes car Q at time \( t = 0 \).
(a) The speed limit for cars on the road is 100 km h\(^{-1}\). State and explain whether car Q exceeds the speed limit. [1]
(b) Calculate the acceleration of car P. [2]
(c) Determine the distance between the two cars at time \( t = 12 \) [3]
(d) From time \( t = 12 \)s, the velocity of each car remains constant at its value at 4\( t = 12 \)s.4
Determine the time \( t \) at which car Q passes car P.[2]
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539
(a) State the difference between a stationary wave and a progressive wave in terms of
(i) the energy transfer along the wave, [1]
(ii) the phase of two adjacent vibrating particles. [1]
(b) A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is placed
near one end of the tube, as shown in Fig. 3.1.
The speed of the sound in the tube is $340 \, \text{m s}^{-1}$. The length of the tube is $0.60 \, \text{m}$.
A stationary wave is formed with an antinode A at each end of the tube and two antinodes
inside the tube.
(i) State what is meant by an $antinode$ of the stationary wave. [1]
(ii) State the distance between a node and an adjacent antinode. [1]
(iii) Determine, for the sound in the tube,
- the wavelength, [1]
- the frequency. [2]
(iv) Determine the minimum frequency of the sound from the loudspeaker that produces a stationary wave in the tube. [2]
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570
(a) Define strain. [1]
(b) A wire is designed to ensure that its strain does not exceed $4.0 \times 10^{-4}$ when a force of 8.0 kN is applied. The Young modulus of the metal of the wire is $2.1 \times 10^{11}$ Pa. It may be assumed that the wire obeys Hooke’s law.
For a force of 8.0 kN, calculate, for the wire,
(i) the maximum stress, [2]
(ii) the minimum cross-sectional area. [2]
566
581
581
Three cells of electromotive forces (e.m.f.) $E_1$, $E_2$ and $E_3$ are connected into a circuit, as shown in Fig. 5.1.
Fig. 5.1
The circuit contains resistors of resistances $R_1$, $R_2$, $R_3$ and $R_4$.
The currents in the different parts of the circuit are $I_1$, $I_2$ and $I_3$.
The cells have negligible internal resistance.
Use Kirchhoff’s laws to state an equation relating
(a) $I_1$, $I_2$ and $I_3$, .....................................................................................................[1]
(b) $E_1$, $E_3$, $R_1$, $R_3$, $R_4$, $I_1$ and $I_3$ in loop WXYZW, .....................................................................................................
.................................................................................................................................[1]
(c) $E_1$, $E_2$, $R_1$, $R_2$, $I_1$ and $I_2$ in loop YZWY. ....................................................................................................[1]
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553
531
(a) Define electric field strength.
.................................................................................................................................
................................................................................................................................. [1]
(b) Two parallel metal plates in a vacuum are separated by a distance of 15 mm, as shown in Fig. 6.1.
A uniform electric field is produced between the plates by applying a potential difference between them.
A particle of mass $1.7 \times 10^{-27}$ kg and charge $+1.6 \times 10^{-19}$ C is initially at rest at point A on one plate. The particle is moved by the electric field to point B on the other plate. The particle reaches point B with kinetic energy $2.4 \times 10^{-16}$ J.
(i) Calculate the speed of the particle at point B.
speed = ................................................ m s$^{-1}$ [2]
(ii) State the work done by the electric field to move the particle from A to B.
work done = ................................................ J [1]
(iii) Use your answer in (ii) to determine the force on the particle.
force = ................................................ N [2]
(iv) Determine the potential difference between the plates.
potential difference = ................................................ V [3]
(v) On Fig. 6.2, sketch a graph to show the variation of the kinetic energy of the particle with the distance $x$ from point A along the line AB.
Numerical values for the kinetic energy are not required.
[1]
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569
(a) Define the ohm.
.................................................................................................................[1]
(b) Wires are used to connect a battery of negligible internal resistance to a lamp, as shown in Fig. 7.1.
The lamp is at its normal operating temperature. Some data for the filament wire of the lamp
and for the connecting wires of the circuit are shown in Fig. 7.2.
[Table_1]
(i) Show that $$\frac{\text{resistance of filament wire}}{\text{total resistance of connecting wires}} = 1000.$$
[2]
(ii) Use the information in (i) to explain qualitatively why the power dissipated in the filament
wire of the lamp is greater than the total power dissipated in the connecting wires.
............................................................................................................................
............................................................................................................................
............................................................................................................................[1]
(iii) The lamp is rated as 12 V, 6.0 W. Use the information in (i) to determine the total resistance
of the connecting wires.
total resistance of connecting wires = ....................................................... \Omega [3]
(iv) The diameter of the connecting wires is decreased. The total length of the connecting wires
and the resistivity of the metal of the connecting wires remain the same.
State and explain the change, if any, that occurs to the resistance of the filament wire of
the lamp.
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................[3]
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547
A neutron within a nucleus decays to produce a proton, a $\beta^-$ particle and an (electron) antineutrino.
n $\rightarrow$ p + $\beta^-$ + $\bar{\nu}$
(a) Use the quark composition of the neutron to show that the neutron has no charge.
[3]
(b) Complete Fig. 8.1 by giving appropriate values of the charge and the mass of the proton, the $\beta^-$ particle and the (electron) antineutrino.
[Image_1: Table]
Fig. 8.1
[2]
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