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In this experiment you will investigate the position of a wooden rod suspended in water as the load on it is varied.
Assemble the apparatus as shown in Fig. 1.1 and then fill the beaker to the brim with water.
Adjust the height of the clamp so that the rod is lowered into the water until the mass attached to the bottom of the rod is just covered, as shown in Fig.1.2.
(a) Record $h$, as shown in Fig.1.2.
(b) Add a mass $m$ to the mass hanger and repeat (a). Repeat this procedure until you have six sets of readings for $m$ and $h$. Include in your table values for $W$, where $W$ is the weight of the added mass $m$.
(Use $g = 9.81 \text{ ms}^{-2}$.)
(c) (i) Plot a graph of $W$ on the $y$-axis against $h$ on the $x$-axis, and draw the line of best fit.
(ii) Determine the gradient of the line.
(d) (i) Use the vernier calipers to determine the diameter $d$ of the wooden part of the rod.
(ii) Calculate the cross-sectional area $A$ of the wooden part of the rod, using the relationship
$$A = \frac{\pi d^2}{4}.$$
(e) The relationship between $W$ and $h$ is
$$W = c - h(k + \rho Ag)$$
where $c$ is a constant, $k$ is the spring constant, $\rho$ is the density of water (1000 kg m$^{-3}$), and $g$ is the acceleration of free fall (9.81 ms$^{-2}$).
Using your answers from (c)(ii) and (d)(ii), determine the value of $k$. Give an appropriate unit.
In this experiment you are provided with a ball suspended by a thread so that it is next to a solid vertical surface. You will investigate how the rebound distance is related to the release distance when it swings against the solid surface.
(a) Assemble the apparatus as shown in Fig. 2.1, with the thread clamped between the two wooden blocks so that $l$ is about 50 cm, and with the brick positioned so that it is just touching the stationary ball.
Measure $l$
(b) (i) Pull back the ball and measure the distance $a$ shown in Fig. 2.2. Do not exceed $a = 25$ cm.
(ii) Release the ball and make measurements to determine the rebound distance $b$ shown in Fig. 2.2.
(c) (i) Explain how you used the apparatus to ensure that the rebound distance $b$ was measured as accurately as possible.
(ii) Estimate the percentage uncertainty in $b$.
(d) For values of $a$ less than 25 cm, theory predicts that $$k = \frac{l - \sqrt{l^2 - b^2}}{l - \sqrt{l^2 - a^2}}$$ where $k$ is a constant.
Calculate a value for $k$.
(e) Repeat (b)(i), (b)(ii) and (d) using a different value of $a$.
(f) Explain whether your results indicate that $k$ is a constant.
(g) (i) State four sources of error or limitations of the procedure in this experiment.
(ii) Suggest four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.