A1  ^0.80 Determine the cross section area $S$ of the tube.

Let fill a tube with a $V=2.0~\mathrm{ml}$ of water. The length of water segment is $l=29.8~\mathrm{cm}$.
\[S = \frac{V}{l}=0.068~\mathrm{cm}^2\]

A2  ^0.20 Choose the direction of the droplet's motion.

Towards open end

A3  ^2.50 For 5 different volumes $V$ perform the experiment and record the values of $x_0$ and $x$. Ensure the system reaches equilibrium before taking measurements!

For convenience, you may draw out and push in air between trials.

$V,~\mathrm{ml}$	$x_0,~\mathrm{cm}$	$x,~\mathrm{cm}$
10	9,8	16,0
5	9,8	12,5
8	4,6	9,8
6	7,3	10,4
4	5,2	7,6
2	10	10,8

A4  ^1.00 Plot the graph of $x-x_0$ vs. $V$.

A5  ^1.00 Determine the temperature $T_\mathrm{h}$ of your hand. Calculate the ratio $(T_\mathrm{h} - T_0)/(T_0 + 273^\circ\mathrm{C})$?

Using the graph:
\[\frac{1}{S}\frac{\frac{\Delta T}{T+273^\circ\text{C}}}{1+\frac{\Delta T}{T+273^\circ\text{C}}} = \mathrm{slope}= 0.6~\mathrm{cm}^{-2}\]\[\frac{\Delta T}{T + 273^\circ\text{C}}=0.0425, \quad \Rightarrow \quad T_\mathrm{h}=32^\circ\text{C}\]

B1  ^1.80 Assemble setup with $V=10~\mathrm{ml}$. Record the value of $x_0$. Heat the syringe to temperature $T_\mathrm{h}$.

Place the syringe on the table and start the stopwatch simultaneously. Record the dependence of $x$ on time $t$. Perform 12 measurements.

$x_0=10.0~\mathrm{cm}$

$t,~\mathrm{s}$	$x,~\mathrm{cm}$
0	16,0
20	15,6
30	15,3
42	14,8
56	14,2
70	13,7
85	13,4
100	13,1
125	12,7
165	12,0
210	11,9
240	11,4
265	11,2
300	11,0
377	10,5

B2  ^2.50 Choose the coordinates in which the dependence of $x$ on $t$ becomes linear and plot the corresponding graph.

B3  ^0.20 Determine the value of $\tau$.

\[\tau = 203~\mathrm{s}=3.4~\mathrm{min}\]