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In this experiment you will investigate how the depth to which a beaker is submerged in water depends on the mass added to the beaker.
(a) Measure and record the height $h$ of the beaker as shown in Fig. 1.1. [1]
(b) (i) Place the beaker from (a) inside the larger container, which contains water. The beaker will float in the water and may tilt to one side.
(ii) Measure and record the distance $d$ between the extbf{lowest} point of the bottom of the beaker and the water surface as shown in Fig. 1.2.
This measurement should be taken from outside the large container. [1]
(c) Carefully place the 50 g mass on top of the modelling clay in the beaker.
For this added mass $m$ of 50 g, measure and record the new distance $d$. [10]
(d) Change the added mass in the small beaker and measure $d$.
Repeat this until you have six sets of readings of $m$ and $d$.
Include values of $\frac{m}{d}$ and $\frac{1}{d}$ in your table.
(e) (i) Plot a graph of $\frac{m}{d}$ on the $y$-axis against $\frac{1}{d}$ on the $x$-axis. [3]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and $y$-intercept of this line. [2]
(f) It is suggested that the quantities $m$ and $d$ are related by the equation $\frac{m}{d} = \frac{-A}{d} + B$ where $A$ and $B$ are constants.
Use your answers in (a) and (e)(iii) to determine the least value of $m$ that would be needed to completely submerge the beaker.
Give an appropriate unit. [2]
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In this experiment you will investigate how the rate of heat energy transferred from a resistor depends on the voltage across it.
(a) (i) Pour water into the measuring cylinder to the 50 ml mark.
(ii) Pour the water from the measuring cylinder into the empty beaker. Determine and record the mass $m$ of water in the beaker. (1 ml of water has a mass of 1 g.) [1]
(iii) Estimate the percentage uncertainty in $m$. [1]
(b) (i) Set up the circuit shown in Fig. 2.1.
(ii) Adjust the output of the power supply to approximately 4V.
(iii) Close the switch. Measure and record the voltmeter reading $V$. Open the switch. [1]
(c) Measure and record the temperature $\theta_1$ of the water in the beaker. [1]
(d) (i) Close the switch and start the stopwatch.
(ii) After four minutes, measure and record the temperature $\theta_2$ of the water. [1]
(iii) Calculate and record the temperature rise ($\theta_2 - \theta_1$). [1]
(e) Repeat (b)(iii) for an output voltage in the range 7V–9V. [1]
(f) Repeat (c) and (d) for this new output voltage.
(g) It is suggested that the relationship between $V$, $\theta_1$ and $\theta_2$ is
$$V^2 = k (\theta_2 - \theta_1)$$ where $k$ is a constant.
(i) Using your data calculate two values of $k$. [1]
(ii) Justify the number of significant figures that you have given for your values of $k$. [1]
(iii) Explain whether your results support the suggested relationship. [1]
(h) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment. [4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures. [4]
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