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In this experiment, you will investigate the equilibrium of a wooden rod.
(a) Set up the apparatus as shown in Fig. 1.1.
The mass $m$ should be 60g. The string should be approximately half-way along the wooden rod. The spring should be horizontal.
(b) (i) Measure and record the length $L$ of the coiled part of the spring.
$L = \text{................................................} \ [1]$
(ii) Measure and record the height $h$ of the loop of the spring above the bench.
$h = \text{................................................}$
(iii) Measure and record the angle $\theta$ between the wooden rod and the bench.
$\theta = \text{................................................}^{\circ}$
(c) Change mass $m$ to 80g.
Adjust the position of the spring and string so that the length $L$ is the same as in (b)(i) and the string is horizontal.
Repeat (b)(ii) and (b)(iii).
$h = \text{................................................}$
$\theta = \text{................................................}^{\circ} \ [1]$
(d) (i) Copy your value of $L$ from (b)(i).
$L = \text{................................................}$
(ii) Change $m$ and repeat (b)(ii) and (b)(iii) until you have six sets of values of $m$, $h$ and $\theta$.
For each value of $m$, adjust the position of the spring and string so that $L$ is the same as in (d)(i) and the spring is horizontal.
Include your values from (b) and (c).
Also include values of $\frac{h}{\cos \theta}$ in your table.
[10]
(e) (i) Plot a graph of $\frac{h}{\cos \theta}$ 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.
$\text{gradient} = \text{................................................}$
$\text{y-intercept} = \text{................................................} \ [2]$
(f) The quantities $h$, $\theta$ and $m$ are related by the equation $\frac{h}{\cos \theta} = Am + B$ where $A$ and $B$ are constants.
Using your answers in (e)(iii), determine the values of $A$ and $B$. Give appropriate units.
$A = \text{................................................}$
$B = \text{................................................} \ [2]$
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(a) (i) Set up the apparatus as shown in Fig. 2.1.
Support the wooden rod by passing it through the loop of the spring and the long string loop.
Mass $m_1$ should be 200 g and mass $m_2$ should be 100 g.
The bottom of mass $m_1$ should be approximately 6 cm above the bench.
(ii) Adjust the apparatus until the wooden rod is balanced and horizontal. The spring and long string loop should be vertical.
(iii) Measure and record the distances $x$, $y$ and $z$ as shown in Fig. 2.1, where
$x$ is the distance between the loop above $m_1$ and the spring loop,
$y$ is the distance between the spring loop and the long string loop,
$z$ is the distance between the long string loop and the loop above $m_2$.
$x = \text{..........................................................}$
$y = \text{..........................................................}$
$z = \text{..........................................................}$ [2]
(iv) Estimate the percentage uncertainty in your value of $y$.
percentage uncertainty = \text{..........................................................} [1]
(b) Calculate $C$ where
$$C = m_1(x + y)^2 + m_2z^2.$$
$C = \text{..........................................................}$ [1]
(c) (i) Pull the left side of the wooden rod down by 5 cm.
Release the wooden rod and watch the movement.
The wooden rod will move up and down again, completing a cycle as shown in Fig. 2.2.
(ii) The time taken for one complete cycle is $T$.
By timing several of these complete cycles, determine an accurate value for $T$.
$T = \text{..........................................................}$ [2]
(iii) Calculate $T^2$.
$T^2 = \text{..........................................................}$
(iv) Justify the number of significant figures that you have given for your value of $T^2$.
........................................................................................................................
........................................................................................................................
........................................................................................................................ [1]
(d) Keeping distance $y$ constant, change $m_2$ to 50 g and repeat (a)(ii), (a)(iii), (b), (c)(i), (c)(ii) and (c)(iii).
$x = \text{..........................................................}$
$y = \text{..........................................................}$
$z = \text{..........................................................}$
$C = \text{..........................................................}$
$T = \text{..........................................................}$
$T^2 = \text{..........................................................}$ [3]
(e) It is suggested that the relationship between $T$ and $C$ is
$$T^2 = kC$$
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 in (e)(i) support the suggested relationship.
........................................................................................................................
........................................................................................................................
........................................................................................................................ [1]
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ........................................................................................................................
........................................................................................................................
2. ........................................................................................................................
........................................................................................................................
3. ........................................................................................................................
........................................................................................................................
4. ........................................................................................................................
........................................................................................................................ [4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. ........................................................................................................................
........................................................................................................................
2. ........................................................................................................................
........................................................................................................................
3. ........................................................................................................................
........................................................................................................................
4. ........................................................................................................................
........................................................................................................................ [4]
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