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In this experiment, you will investigate the forces acting on a wooden strip in equilibrium.
(a) The apparatus has been assembled for you as shown in Fig. 1.1.
(i) Adjust the positions of the stands so that the springs are vertical.
(ii) If necessary, adjust the height of the boss A so that the wooden strip is parallel to the bench.
(b)
(i) Increase the height of boss A by approximately 10 cm. Leave boss B at the same height throughout the experiment.
(ii) Hang the mass M from the string loop as shown in Fig. 1.2.
(c)
(i) Adjust the position of the string loop until the wooden strip is parallel to the bench again.
(ii) Measure and record the distance $h$ from the bench to the top of the spring at A, as shown in Fig. 1.2.
$h = \text{........................................... cm}$ [1]
(iii) Measure and record the distance $x$ from the string loop below A to the string loop supporting M, as shown in Fig. 1.2.
$x = \text{........................................... cm}$ [1]
(d) Lower boss A and repeat (c) until you have six sets of values of $h$ and $x$. Include values of $ \frac{1}{h} $ and $ \frac{x}{h} $ in your table.
The position of boss B should remain the same throughout the experiment.
(e)
(i) Plot a graph of $ \frac{1}{h} $ on the $y$-axis against $ \frac{x}{h} $ on the $x$-axis. [3]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and $y$-intercept of this line.
gradient = ..................................................
$y$-intercept = ................................................ [2]
(f)
The quantities $h$ and $x$ are related by the equation $$ \frac{1}{h} = \frac{ax}{h} + b $$ where $a$ and $b$ are constants.
Use your answers in (e)(iii) to determine the values of $a$ and $b$. Give appropriate units.
$a = \text{..................................................}$
$b = \text{..................................................}$ [2]
In this experiment, you will investigate the force from the surface of water acting on a wire loop.
(a) You are provided with two circular wire loops, each with a hook. Take the smaller loop.
(i) Make sure that the loop lies flat on the bench, and that the loop is horizontal if suspended by its hook.
(ii) Take measurements to find the diameter $D$ of the loop, as shown in Fig. 2.1.
$D = \text{.....................................} \text{cm}$ [2]
(iii) Estimate the percentage uncertainty in your value of $D$.
percentage uncertainty = \text{................................................} [1]
(iv) Calculate the circumference $C$ of the loop using the expression $C = \pi D$.
$C = \text{..................................................}$ [1]
(b) Justify the number of significant figures you have given for your value of $C$.
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(c) You are also provided with a stand holding a spring with a pointer.
Hold a ruler vertically behind the pointer, as shown in Fig. 2.2.
(d) (i) Place the hook of the wire loop onto the end coil of the spring, as shown in Fig. 2.3.
(ii) Record the pointer reading $r_1$.
$r_1 = \text{..................................................}$ [1]
(iii) Position the beaker of water underneath the wire loop and then lift the beaker up until the water is in contact with the loop, as shown in Fig. 2.4.
(iv) Slowly lower the beaker. The water surface will pull the loop down until it breaks away from the water surface.
(v) Repeat steps (iii) and (iv), this time recording the pointer reading $r_2$ just before the loop breaks away.
$r_2 = \text{..................................................}$ [1]
(vi) Remove the wire loop from the spring.
(e) Using the other wire loop, repeat (a)(i), (a)(ii), (a)(iv), (c) and (d).
$D = \text{..................................................}$
$C = \text{..................................................}$
$r_1 = \text{..................................................}$
$r_2 = \text{..................................................}$ [3]
(f) It is suggested that the relationship between $r_1$, $r_2$ and $C$ is
$$r_1 - r_2 = kC$$
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k = \text{..................................................}$
second value of $k = \text{..................................................}$ [1]
(ii) Explain whether your results support the suggested relationship.
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(g) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
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(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
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