Defining Problem

Independent variable: capacitance of capacitor $C$ Dependent variable: maximum extension of spring combination $e$ Quantities to be kept constant: potential difference $v$ , spring constant $k$ , initial length of spring combination, initial tightness of string, distance between spindle and spring combination

Method of analysis

a graph of $e^{2}$ against $C$ is plotted. a straight line passing through the origin is expected if the suggested relationship is valid.

β = gradient \times \frac{k}{2 V ^{2}}

Diagram

Diagram 1:

same diagram as in question

a metre rule placed on bench alongside the spring combination
The wooden block and motor are clamped to the bench using g clamps
a slow motion camera is attached to a retort stand and observes the experiment from above
the slow motion camera is connected to a monitor
on the monitor, a set square is used to line up the edge of the spring combination with the metre rule scale
a circuit is shown with a dc power supply and capacitor connected in parallel.
a voltmeter is connected parallel to capacitor
an spdt type switch is used to switch between charging and discharging to motor

Diagram 2:

same circuit as diagram 1 but a fixed resistor instead of motor

Constants

In a preliminary experiment, the spring combination is suspended from a retort stand and its initial length $L_{0}$ is measured using a metre rule. The mass $m$ of a mass hanger is measured using a top pan balance. The mass hanger is hung on the spring combination and the extended length $L$ is measured using a metre rule and recorded. the spring constant is determined by $k = \frac{m g}{L - L _{0}}$
The switch is closed and the Voltmeter reading $V$ is recorded. The switch is opened and closed again, a second value of $V_{2}$ is measured and recorded. The two values are averaged to get $V$
In a preliminary experiment a circuit as shown in Diagram 2 is setup to measure the capacitance $C$ of the capacitor.
The capacitor is connected to a D.C. power supply so that there is a potential difference of $V_{0}$ across it.
The position of the SPDT switch is changed so that the capacitor is now connected to the fixed resistor.
At the same time a stopwatch is started.
The voltmeter reading, $V$ at regular time intervals is measured and recorded.
A graph of $ln V$ against time is plotted.
the capacitance of the capacitor is calculated via $C = - \frac{1}{R \times gradient}$

Procedure

The capacitor is connected to the circuit. The switch is placed in position 1 to charge the capacitor.
Once the voltmeter reading shows $V$ , the switch is placed in position 2 to connect the capacitor to the motor.
At the same time the slow motion camera is turned on.
The recording is stopped once the voltmeter reading reaches zero
The footage is reviewed frame by frame to identify the largest extension reached
a set square is placed on the screen to measure the max stretched length with the metre rule as reference.
For the same capacitance, the experiment is repeated twice and an average value of e is calculated.

Safety precautions

Roll long sleeves and tie up long hair so they do not get caught in the spindle and injure the experimenter
Place a transparent shield between the experiment and experimenter to protect the experimenter in case that the string snaps and the springs snap back violently and fly off
Ensure proper polarity when connecting the capacitor to avoid explosions

Additional details

A newton metre is placed where the spring combination is suposed to be.
The spindle is rotated manually until the string is taught but while ensuring that the newton meter shows a reading of zero
a mark is made on the string and a pointer placed on the bench
Before the start of each experiment, the spindle is rotated manually until the mark lines up with the pointer

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