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In this experiment, you will investigate an electrical circuit.
(a)
• Place the 15Ω resistor in component holder P.
• Place the 22Ω resistor in component holder Q.
• Set up the circuit shown in Fig. 1.1.
K and L are crocodile clips.
The resistors in the component holders have resistances P and Q.
Place L approximately half-way along the wire.
• The distance between K and L is y as shown in Fig. 1.1.
Record P, Q and y.
P = ext{..............................}
Q = ext{..............................}
y = ext{..............................}
• Close the switch.
• Record the ammeter reading I.
I = ext{..............................}
• Open the switch.
(b)
• Change one or both of the resistors in P and Q.
• Record the new values of P and Q.
P = ext{..............................}
Q = ext{..............................}
• Close the switch.
• Change the position of L on the wire so that the ammeter reading is as close as possible to the value for I in (a).
• Record y.
y = ext{..............................}
• Open the switch.
(c)
Repeat (b) until you have six sets of readings of P, Q and y. Include your readings from (a) and (b).
Record your results in a table. Include values of $\frac{PQ}{P+Q}$ in your table.
(d) (i) Plot a graph of y on the y-axis against $\frac{PQ}{P+Q}$ on the x-axis.
(ii) Draw the straight line of best fit.
(iii) Determine the gradient and y-intercept of this line.
gradient = ext{..............................}
y-intercept = ext{..............................}
(e) It is suggested that the quantities y, P and Q are related by the equation $y = -\frac{MPQ}{P+Q} + N$
where M and N are constants.
Using your answers in (d)(iii), determine values for M and N.
Give appropriate units.
M = ext{..............................}
N = ext{..............................}
(f) Theory suggests that $\frac{N}{M} = \frac{E}{I}$
where E is the electromotive force (e.m.f.) of the cell.
Calculate E. Give an appropriate unit.
E = ext{..............................}
530
510
543
In this experiment, you will investigate the equilibrium of a system of three identical springs.
(a) You have been provided with three springs attached to a ring.
Measure and record the unstretched length $S$ of the coiled section of one of the springs, as shown in Fig. 2.1.
$S = \text{.................................................................}$
(b) (i) Set up the apparatus as shown in Fig. 2.2.
• The total mass $m$ of the mass hanger and the slotted masses should be 0.300 kg.
• Adjust the position of the bosses so that the centres of the rods of the clamps are at the same height above the bench.
• Change the separation of the stands until the angle between the springs is 90$^{\circ}$.
• The lengths $S_1$ and $S_2$ of the coiled sections of the two springs attached to the ring are shown in Fig. 2.3.
The angle between the single spring and the vertical is $\theta$.
Measure and record $m$, $S_1$, $S_2$ and $\theta$.
$m = \text{....................................................}$ kg
$S_1 = \text{....................................................}$
$S_2 = \text{....................................................}$
$\theta = \text{....................................................} \degree$
(ii) Estimate the percentage uncertainty in your value of $\theta$.
percentage uncertainty = \text{..............................................}
(iii) Calculate $e_1 \cos \theta$ and $e_2 \sin \theta$ where $e_1 = S_1 - S$ and $e_2 = S_2 - S$.
$e_1 \cos \theta = \text{.......................................}$
$e_2 \sin \theta = \text{.......................................}$
(iv) Justify the number of significant figures that you have given for your value of $e_1 \cos \theta$.
(c) Change $m$ to 0.600 kg and repeat (b)(i) and (b)(iii).
$m = \text{....................................................}$ kg
$S_1 = \text{....................................................}$
$S_2 = \text{....................................................}$
$\theta = \text{....................................................} \degree$
$e_1 \cos \theta = \text{.......................................}$
$e_2 \sin \theta = \text{.......................................}$
(d) It is suggested that the relationship between $e_1$, $e_2$, $\theta$ and $m$ is $e_1 \cos \theta + e_2 \sin \theta \equiv \beta m$ where $\beta$ is a constant.
(i) Using your data, calculate two values of $\beta$.
first value of $\beta = \text{....................................................}$
second value of $\beta = \text{....................................................}$
(ii) Explain whether your results support the suggested relationship.
(e) Theory suggests that $\beta = \frac{g}{k}$ where the acceleration of free fall $g$ is 9.81 m/s² and $k$ is the spring constant of a spring.
Using your second value of $\beta$, calculate $k$. Give an appropriate unit.
$k = \text{....................................................}$
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. ..................................................................................................................
2. ..................................................................................................................
3. ..................................................................................................................
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. ..................................................................................................................
551
536
536
