No questions found
(a) The positive terminals of C and the d.c. supply are already connected. Complete the circuit shown in Fig. 1.1, making sure that the positive terminals are connected as indicated on the diagram.
(b) (i) Switch S should be open.
When the d.c. supply is switched on, the voltmeter reading will rise and become constant. Switch on the d.c. supply and record the voltmeter reading $V_S$ after approximately 60s.
$V_S = \text{.....................................................} \text{V}$
(ii) Calculate the value of $0.9V_S$.
$0.9V_S = \text{.................................................} \text{V}$ [1]
(c) (i) Close switch S. The voltmeter reading will fall to zero.
(ii) Open S and measure the time $t$ for the voltmeter reading to rise to a value $V_C$ of approximately 4.0 V.
Record $t$ and $V_C$.
$t = \text{........................................................} \text{s}$
$V_C = \text{.....................................................} \text{V}$ [1]
(d) (i) Write down your value of $0.9V_S$ from (b)(ii).
$0.9V_S = \text{................................................} \text{V}$
(ii) Repeat (c) for different values of $V_C$ in the range 0 to $0.9V_S$ until you have six sets of values of $t$ and $V_C$.
(e) (i) Plot a graph of $V_C$ on the $y$-axis against $t$ on the $x$-axis. [8]
(ii) Draw a smooth curve through your points. [2]
(f) (i) Calculate the value of $0.5V_S$.
$0.5V_S = \text{................................................} \text{V}$
(ii) Draw the tangent to your curve at $V_C = 0.5V_S$. [1]
(iii) Determine the gradient and $y$-intercept of this tangent.
gradient = \text{...........................................}
$y$-intercept = \text{.......................................} [2]
(g) The tangent has the equation
$$V_C = at + b$$
where $a$ and $b$ are constants.
Use your answers in (f)(iii) to determine the values of $a$ and $b$.
Give appropriate units.
$a = \text{..................................................}$
$b = \text{..................................................}$ [2]
(h) Calculate the value of $T$ using the relationship
$$T = \frac{V_S}{2a}.$$
$T = \text{.....................................................}$ [2]
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In this experiment, you will investigate the relationship between the dimensions of a spring
and its spring constant.
You are provided with two lengths of copper wire with the same diameter.
(a) Measure and record the diameter $d$ of the wire.
$d = \text{.........................................................}[1]$
(b) (i) Wind one of the lengths of wire around the rod labelled A so that it makes a spring,
as shown in Fig. 2.1.
(ii) Slide the spring off the rod and then twist the ends to give a loop at each end, as
shown in Fig. 2.2.
(iii) Count and record the number $n$ of coils in your spring, and measure and record the
outside diameter $x$ of your spring, as shown in Fig. 2.3.
$n = \text{..........................................................}$
$x = \text{..........................................................}[2]$
(c) Estimate the percentage uncertainty in your value of $x$.
percentage uncertainty = \text{.....................................................}[1]$
(d) Calculate the value of $D$ using the expression
$$D = x - d.$$
$D = \text{..........................................................}$
(e) (i) Set up the apparatus as shown in Fig. 2.4, with the boss approximately 25 cm
above the bench.
(ii) Measure and record the height $h_1$ of the bottom of the mass hanger above the
bench.
$h_1 = \text{..........................................................}[1]$
(iii) Add the 50 g mass to the mass hanger and measure the height $h_2$ of the bottom of
the mass hanger above the bench, as shown in Fig. 2.5.
$h_2 = \text{..........................................................}$
(iv) Calculate the spring constant $k$ using the expression
$$k = \frac{mg}{(h_1 - h_2)}$$
where $m = 0.050 \text{ kg}$ and $g = 9.81 \text{ Nkg}^{-1}$.
Give your answer to an appropriate number of significant figures.
$k = \text{.....................................................}[2]$
(f) Repeat (b), (d) and (e) using the rod labelled B and the other length of wire.
$n = \text{..........................................................}$
$x = \text{..........................................................}$
$D = \text{..........................................................}$
$h_1 = \text{..........................................................}$
$h_2 = \text{..........................................................}$
$k = \text{..........................................................}[3]$
(g) It is suggested that the relationship between $k, D$ and $n$ is
$$k = \frac{c}{D^3n}$$
where $c$ is a constant.
(i) Using your data, calculate two values of $c$.
first value of $c = \text{.....................................................}$
second value of $c = \text{.....................................................}[1]$
(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.
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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