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In this experiment, you will investigate how the equilibrium position of a pivoted wooden strip changes when a horizontal force is applied.
(a) Thread the string over the pulley and suspend the mass hanger from the end loop of the string, as shown in Fig. 1.1.
(b) Measure and record the height $H$ of the nail above the bench. [1]
(c) Record the mass $m$ that is suspended from the string.
(d) (i) Adjust the height of the pulley until the string is parallel to the bench. Measure and record the height $h$ of the string above the bench. [1]
(ii) Calculate the value of $(H-h)$.
(e) By adding masses to the hanger, change the total suspended mass $m$. Repeat (c) and (d) until you have six sets of values for $m$ and $h$.
In your table of results include columns for the values of $m^2$ and $\frac{1}{(H-h)^2}$. [10]
(f) (i) Plot a graph of $\frac{1}{(H-h)^2}$ on the $y$-axis against $m^2$ 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]
(g) It is suggested that the quantities $h$, $H$ and $m$ are related by the equation
\( \frac{1}{(H-h)^2} = abm^2 + b \)
where $a$ and $b$ are constants.
Using your answers from (f)(iii), determine the values of $a$ and $b$. Give appropriate units. [2]
563
512
569
In this experiment you will investigate the deflection of a metre rule when two loads are placed on it.
(a) (i) Position a metre rule on the two supports as shown in Fig. 2.1, with the supports 15.0 cm from each end of the rule.
(ii) Determine the distance $y$ between the two supports. [1]
(iii) Measure the height $h$ of the bottom edge of the mid-point of the rule above the bench. [1]
(b) (i) Position the two 500 g masses on top of the rule, with a mass 5.0 cm from each end of the rule, as shown in Fig. 2.2.
(ii) Determine the distance $x$ of a mass from its nearest support. [1]
(iii) Measure the height $h_1$ of the bottom edge of the mid-point of the rule above the bench. [1]
(c) (i) Calculate the deflection $d$ of the mid-point of the rule, where $d = h_1 - h$. [1]
(ii) Estimate the percentage uncertainty in your value of $d$. [1]
(d) (i) Remove the two 500 g masses and reposition the two supports 25.0 cm from each end of the rule.
(ii) Repeat (a)(ii) and (a)(iii).
(e) (i) Position the two 500 g masses on top of the rule, with a mass 15.0 cm from each end of the rule.
(ii) Repeat (b)(ii), (b)(iii) and (c)(i). [4]
(f) (i) It is suggested that the quantities $d$ and $y$ are related by the equation $d = k y^2$ where $k$ is a constant. Using your data, calculate two values of $k$. [1]
(ii) Explain whether your results support the suggested relationship. [1]
(g) (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]
585
597
578
