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In this experiment, you will investigate the equilibrium of a mass and pulley system.
(a) The apparatus has been set up in an arrangement similar to that shown in Fig. 1.1.
(b) Measure and record the height $H$ of the central knot above the bench. [1]
(c) (i) Suspend the mass hanger from the central loop as shown in Fig. 1.2.
(ii) Record the central suspended mass $m$. [1]
(iii) Measure and record the height $h$ of the central knot above the bench, as shown in Fig. 1.2.
(iv) Calculate the deflection $y$, where $y = (H - h)$.
(d) Change $m$ by adding masses to the hanger suspended from the central loop and repeat (c)(ii), (c)(iii) and (c)(iv) until you have six sets of values for $m$, $h$ and $y$.
Include in your table of results values for $\frac{1}{y^2}$ and $\frac{1}{m^2}$. [10]
(e) (i) Plot a graph of $\frac{1}{y^2}$ on the $y$-axis against $\frac{1}{m^2}$ 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) The relationship between $y$ and $m$ is
$$\frac{1}{y^2} = \frac{p}{m^2} - q$$
where $p$ and $q$ are constants.
Using your answers from (e)(iii), determine the values of $p$ and $q$. Give appropriate units. [2]
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575
In this experiment you will investigate the range of a steel ball projectile
(a) You are provided with a length of tube with a wooden block at each end. Mount the tube in clamps, with the tray of sand positioned below its lower end, as shown in Fig. 2.1.
(b) (i) Ensure that the lower end of the tube is horizontal and approximately 30 cm above the bench, and that the upper end of the tube is vertical and about 50 cm above the bench.
(ii) Measure and record the height $a$ above the bench of the lower end of the tube, as shown in Fig. 2.1.
(iii) Measure and record the height $b$ above the bench of the higher end of the tube.
(c) (i) Drop the steel ball into the top of the tube and note its landing position in the tray of sand. The range $R$ is the horizontal distance of the landing position from the end of the tube, as shown in Fig. 2.2.
(ii) Measure and record $R$.
(d) Estimate the percentage uncertainty in $R$.
(e) Calculate the horizontal velocity $v$ of the steel ball using the relationship $v = R \sqrt{\frac{g}{2a}}$, where $g = 9.81 \text{ ms}^{-2}$.
(f) (i) Adjust the height of the upper end of the tube to about 30 cm above the bench, and adjust the height of the lower end to about 20 cm above the bench. Ensure that the lower end of the tube is horizontal.
(ii) Repeat (b)(ii), (b)(iii), (c) and (e).
(g) (i) It is suggested that the relationship between $v$, $b$ and $a$ is $v^2 = k(b - a)$ where $k$ is a constant. Using your data, calculate two values of $k$.
(ii) Explain whether your results support the suggested relationship. [1]
(h) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
(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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