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(a) Mass, length and time are SI base quantities. State two other base quantities.
1. ........................
2. ........................
[2]
(b) A mass $m$ is placed on the end of a spring that is hanging vertically, as shown in Fig. 1.1.
The mass is made to oscillate vertically. The time period of the oscillations of the mass is $T$.
The period $T$ is given by
$$T = C \sqrt{\frac{m}{k}}$$
where $C$ is a constant and $k$ is the spring constant.
Show that $C$ has no units.
[3]
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(a) Define pressure. [1]
(b) A cylinder is placed on a horizontal surface, as shown in figure.
The following measurements were made on the cylinder:
- mass = 5.09 ± 0.01 kg
- diameter = 9.4 ± 0.1 cm.
(i) Calculate the pressure produced by the cylinder on the surface. [3]
(ii) Calculate the actual uncertainty in the pressure. [3]
(iii) State the pressure, with its actual uncertainty. [1]
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The resistance \( R \) of a uniform metal wire is measured for different lengths \( l \) of the wire. The variation with \( l \) of \( R \) is shown in Fig. 3.1.
(a) The points shown in Fig. 3.1 do not lie on the best-fit line. Suggest a reason for this. [1]
(b) Determine the gradient of the line shown in Fig. 3.1. [2]
(c) The cross-sectional area of the wire is 0.12 mm\(^2\).
Use your answer in (b) to determine the resistivity of the metal of the wire. [2]
(d) The resistance \( R \) of different wires is measured. The wires are of the same metal and same length but have different cross-sectional areas \( A \).
On Fig. 3.2, sketch a graph to show the variation with \( A \) of \( R \).
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A trolley moves down a slope, as shown in Fig. 4.1.
The slope makes an angle of $25^\circ$ with the horizontal. A constant resistive force $F_R$ acts up the slope on the trolley. At time $t = 0$, the trolley has velocity $v = 0.50\text{ms}^{-1}$ down the slope. At time $t = 4.0\text{s}$, $v = 12\text{ms}^{-1}$ down the slope.
(a) (i) Show that the acceleration of the trolley down the slope is approximately $3\text{ms}^{-2}$. [2]
(ii) Calculate the distance $x$ moved by the trolley down the slope from time $t = 0$ to $t = 4.0\text{s}$. [2]
(iii) On Fig. 4.2, sketch the variation with time $t$ of distance $x$ moved by the trolley.
(b) The mass of the trolley is $2.0\text{kg}$.
(i) Show that the component of the weight of the trolley down the slope is $8.3\text{N}$. [1]
(ii) Calculate the resistive force $F_R$. [2]
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A motor is used to move bricks vertically upwards, as shown in Fig. 5.1.
The bricks start from rest and accelerate for 2.0 s. The bricks then travel at a constant speed of 0.64 $ms^{-1}$ for 25 s. Finally the bricks are brought to rest in a further 3.0 s.
The total mass of the bricks is 25 kg.
(a) Determine the change in kinetic energy of the bricks
(i) in the first 2.0 s, [2]
(ii) in the next 25 s, [1]
(iii) in the final 3.0 s. [1]
(b) The bricks are in a container. The weight of the container and bricks is 350 N.
Calculate, for the lifting of the bricks and container when travelling at constant speed,
(i) the gain in potential energy, [3]
(ii) the power required. [2]
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Distinguish between $\textit{melting}$ and $\textit{evaporation}$.
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(a) A cell with internal resistance supplies a current. Explain why the terminal potential difference (p.d.) is less than the electromotive force (e.m.f.) of the cell.
..............................................................................................................................
..............................................................................................................................
.............................................................................................................................. [1]
(b) A battery of e.m.f. 12V and internal resistance 0.50Ω is connected to a variable resistor X and a resistor Y of constant resistance, as shown in Fig. 7.1.
The resistance \( R \) of \( X \) is increased from 2.0Ω to 16Ω. The variation with \( R \) of the current \( I \) in the circuit is shown in Fig. 7.2.
Calculate, for \( I = 1.2A \),
(i) the p.d. across X,
p.d. = ............................................................. V [2]
(ii) the resistance of Y,
resistance = .......................................................... Ω [3]
(iii) the power dissipated in the battery.
power = ................................................................. W [2]
(c) Use Fig. 7.2 to explain the variation in the terminal p.d. of the battery as the resistance \( R \) of \( X \) is increased.
..............................................................................................................................
.............................................................................................................................. [1]
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(a) Explain how stationary waves are formed. [2]
(b) The arrangement of apparatus used to determine the wavelength of a sound wave is shown in Fig. 8.1.
The loudspeaker emits sound of one frequency. The microphone is connected to a cathode-ray oscilloscope (c.r.o.).
The waveform obtained on the c.r.o. for one position of the microphone is shown in Fig. 8.2.
The time-base setting of the c.r.o. is 0.20 ms cm-1.
(i) Use Fig. 8.2 to show that the frequency of the sound is approximately 1300 Hz. [2]
(ii) Explain how the apparatus is used to determine the wavelength of the sound. [2]
(iii) The wavelength of the sound wave is 0.26 m. Calculate the speed of sound in this experiment. [2]
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