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(a) Define $\textit{density}.$ [1]
(b) Explain how the difference in the densities of solids, liquids and gases may be related to the spacing of their molecules. [2]
(c) A paving slab has a mass of 68 kg and dimensions 50$ mm \times$ 600 $ mm \times$ 900 mm.
(i) Calculate the density, in kg m$^{-3}$, of the material from which the paving slab is made. [2]
(ii) Calculate the maximum pressure a slab could exert on the ground when resting on one of its surfaces. [3]
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(a) Define the torque of a couple. [2]
(b) A uniform rod of length 1.5 m and weight 2.4 N is shown in figure 1.
The rod is supported on a pin passing through a hole in its centre. Ropes A and B provide equal and opposite forces of 8.0 N.
(i) Calculate the torque on the rod produced by ropes A and B. [1]
(ii) Discuss, briefly, whether the rod is in equilibrium. [2]
(c) The rod in (b) is removed from the pin and supported by ropes A and B, as shown in figure 2.
Rope A is now at point P 0.30 m from one end of the rod and rope B is at the other end.
(i) Calculate the tension in rope B. [2]
(ii) Calculate the tension in rope A. [1]
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A ball is thrown against a vertical wall. The path of the ball is shown in Fig. 3.1.
The ball is thrown from S with an initial velocity of 15.0 $\text{ms}^{-1}$ at 60.0° to the horizontal. Assume that air resistance is negligible.
(a) For the ball at S, calculate
(i) its horizontal component of velocity, [1]
(ii) its vertical component of velocity. [1]
(b) The horizontal distance from S to the wall is 9.95m. The ball hits the wall at P with a velocity that is at right angles to the wall. The ball rebounds to a point F that is 6.15m from the wall.
Using your answers in (a),
(i) calculate the vertical height gained by the ball when it travels from S to P, [1]
(ii) show that the time taken for the ball to travel from S to P is 1.33s, [1]
(iii) show that the velocity of the ball immediately after rebounding from the wall is about 4.6 $\text{ms}^{-1}$. [1]
(c) The mass of the ball is 60 × $10^{-3}$ kg.
(i) Calculate the change in momentum of the ball as it rebounds from the wall. [2]
(ii) State and explain whether the collision is elastic or inelastic. [1]
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(a) Distinguish between gravitational potential energy and electric potential energy. [2]
(b) A body of mass $m$ moves vertically through a distance $h$ near the Earth's surface. Use the defining equation for work done to derive an expression for the gravitational potential energy change of the body. [2]
(c) Water flows down a stream from a reservoir and then causes a water wheel to rotate, as shown in Fig. 4.1.
As the water falls through a vertical height of $120\, \text{m}$, gravitational potential energy is converted to different forms of energy, including kinetic energy of the water. At the water wheel, the kinetic energy of the water is only $10\%$ of its gravitational potential energy at the reservoir.
(i) Show that the speed of the water as it reaches the wheel is $15\, \text{ms}^{-1}$. [2]
(ii) The rotating water wheel is used to produce $110\, \text{kW}$ of electrical power. Calculate the mass of water flowing per second through the wheel, assuming that the production of electric energy from the kinetic energy of the water is $25\%$ efficient. [3]
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(a) Define the ohm.
................................................................. [1]
(b) Determine the SI base units of resistivity.
base units of resistivity = ......................................... [3]
(c) A cell of e.m.f. 2.0V and negligible internal resistance is connected to a variable resistor R and a metal wire, as shown in Fig. 5.1.
The wire is 900mm long and has an area of cross-section of $1.3 \times 10^{-7} \text{m}^2$. The resistance of the wire is 3.4Ω.
(i) Calculate the resistivity of the metal wire.
resistivity = ..................................................... [2]
(ii) The resistance of R may be varied between 0 and 1500Ω.
Calculate the maximum potential difference (p.d.) and minimum p.d. possible across the wire.
maximum p.d. = .......................................... V
minimum p.d. = ...........................................V [2]
(iii) Calculate the power transformed in the wire when the potential difference across the wire is 2.0V.
power = ........................................................ W [2]
(d) Resistance R in (c) is now replaced with a different variable resistor Q. State the power transformed in Q, for Q having
(i) zero resistance,
power = ........................................................ W [1]
(ii) infinite resistance.
power = ........................................................ W [1]
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(a) State Hooke's law. [1]
(b) The variation with extension $x$ of the force $F$ for a spring A is shown in Fig. 6.1.
The point L on the graph is the elastic limit of the spring.
(i) Describe the meaning of elastic limit. [1]
(ii) Calculate the spring constant $k_A$ for spring A. [1]
(iii) Calculate the work done in extending the spring with a force of 6.4 N. [2]
(c) A second spring B of spring constant $2k_A$ is now joined to spring A, as shown in Fig. 6.2.
A force of 6.4 N extends the combination of springs.
For the combination of springs, calculate
(i) the total extension, [1]
(ii) the spring constant. [1]
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(a) Two isotopes of the element uranium are $^{235}_{92} \text{U}$ and $^{238}_{92} \text{U}$.
Explain the term isotope.
..............................................................................................................................
..............................................................................................................................
.............................................................................................................................. [2]
(b) (i) In a nuclear reaction, proton number and neutron number are conserved. Other than proton number and neutron number, state a quantity that is conserved in a nuclear reaction.
.............................................................................................................................. [1]
(ii) When a nucleus of uranium-235 absorbs a neutron, the following reaction may take place.
$^{235}_{92}\text{U} + ^a_b\text{n} \rightarrow ^{141}_x\text{Ba} + ^y_{36}\text{Kr} + 3^a_b\text{n}$
State the values of $a$, $b$, $x$ and $y$.
a = ..................
b = ..................
x = ..................
y = .................. [3]
(c) When the nucleus of $^{238}_{92}\text{U}$ absorbs a neutron, the nucleus decays, emitting an $\alpha$-particle. State the proton number and nucleon number of the nucleus that is formed as a result of the emission of the $\alpha$-particle.
proton number = ........................................................
nucleon number = ........................................................ [2]
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