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In this experiment, you will investigate the angle through which a loaded beaker rolls as a turning force is applied.
(a) The apparatus has been assembled as shown in Fig. 1.1.
(b) Make sure that the beaker is positioned so that the masses do not touch the rails.
(c) Using the set square, measure and record the angle $x$, as shown in Fig. 1.2. [1]
(d) (i) Hook the mass hanger on the string loop. Record the mass $m$ that is suspended from the loop.
(ii) Wait for the beaker to stop moving, making sure that the beaker is positioned so that the masses do not touch the rails.
(iii) Using the set square, measure and record the angle $y$, as shown in Fig. 1.3. [1]
(iv) Calculate $\theta$, where $\theta = y - x$.
(e) Change $m$ by adding masses to the hanger and repeat (d)(ii), (d)(iii) and (d)(iv). Repeat this procedure until you have six sets of values for $m$ (the total suspended mass) and angle $y$.
Include in your table values for $\theta$ (using your answer from (c)) and $\sin \theta$. [9]
(f) (i) Plot a graph of $\sin \theta$ on the $y$-axis against $m$ 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) (i) Unhook the masses from the string loop and remove the beaker from the rails.
(ii) Take measurements to determine the radius $r$ of the beaker. [1]
(h) It is suggested that the relationship between $\theta$ and $m$ is
$$\sin \theta = \frac{rm}{a} + b$$
where $a$ and $b$ are constants.
Using your answers from (f)(iii) and (g)(ii), determine the value of $a$. Give an appropriate unit. [2]
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In this experiment you will investigate the motion of a mass suspended from a rubber band.
(a) (i) Suspend the rubber band from the retort stand and hang the 100g mass hanger from the rubber band, as shown in Fig. 2.1
(ii) Determine and record the radius $R$ of the suspended mass hanger at its widest point. [2]
(iii) Estimate the percentage uncertainty in $R$. [1]
(b) (i) Twist the mass hanger about half a turn and release it so that it turns between positions A and B, as shown in Fig. 2.2.
(ii) Take measurements to determine the time $T$ for the mass hanger to rotate from A to B and back to A.
(This may be determined accurately by using the time for several turns.) [2]
(c) For a mass hanger of mass $m$ and radius $R$, it is suggested that $T$ is related to a quantity $C$, where $C = mR^2$.
Calculate the value of $C$ for this mass hanger. Give an appropriate unit. [1]
(d) (i) Remove the 100g mass hanger and suspend the 50g mass hanger from the rubber band.
(ii) Repeat (a)(ii), (b) and (c) for this new suspended mass hanger. [4]
(e) (i) It is suggested that the relationship between $T$ and $C$ is
$$T^2 = kC$$
where $k$ is a constant.
Using your data, calculate two values of $k$. [1]
(ii) Explain whether your results support the suggested relationship in (e)(i). [1]
(f) (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]
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