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AS Required Practicals (1 - Stationary Waves (Method (Repeat for \(l=[0.5,…
AS Required Practicals
1 - Stationary Waves
Method
Attach a piece of string to a clamp stand and pass through the loop of a vibration, over a moveable bridge, and over a pulley clamped at the end of a bench
A mass of \(100g\) should be attached to the end of the string and a counter weight of \(2kg\) placed on the clamp stand's base, so that it does not topple over
Let \(l\) be the distance between the loop of the vibration generator and the tip of the bridge, measured using a ruler
Repeat for \(l=[0.5, 0.6, 0.7, 0.8, 0.9, 1.0]\,m\)
Tune the vibration generator until the first harmonic forms on the string
Record the frequency, \(f\), at which this occurs
Vary the mass, \(m\), on the end of the string and calculate the tension by \(T=mg\)
Observe how this affects the frequency at which the first harmonic forms on the string
Weight the string and divide by the length of the string to find the mass per unit length, \(\mu\), of the string
Repeat all twice and find average value for each value of \(f\)
Theory
The frequency of the first harmonic is given by:\[f_{0}=\frac{1}{2l}\sqrt{\frac{T}{\mu}}\]
The speed of the wave down the string is given by:\[c=\sqrt{\frac{T}{\mu}}\]
Notes
Vibration generator should be run for 20 minutes to ensure stable frequency has been reached
If frequencies too low are used then the vibration generator may produce irregular vibrations
The bridge should be at the same height as the hole in the vibration generator
Analysis
Plot \(\frac{1}{f}\) against \(l\)
Since \(f_{0}\,\propto\frac{1}{l}\) line of best fit should be a straight line through the origin with gradient equal to \(\frac{2}{c}\)
Can calculate a value of \(c\) from the gradient, and compare to a value calculated from \(T\) and \(\mu\)
Draw a line of best fit
2 - Diffraction and Interference
Diffraction Grating
Method
Illuminate a diffraction grating normally with laser light
Place a screen at a distance \(D=1m\), measured using a ruler, from the diffraction grating and observe a diffraction grating pattern form
Using a ruler, measure the distance from the central order to the first and second orders on either side of the zero order
Analysis
By calculating the tangents, calculate the angle of diffraction for the first and second orders on both sides of the slit, and then average to find the average angle of diffraction for a given order
Then, by using \(n\,\lambda=d\sin\theta\) find the wavelength of the light based on each order, and average these two values to find an average value for the wavelength of the laser light used
Theory
For a diffraction grating with slit separation, \(d\), illuminated with laser light of wavelength, \(\lambda\), the angle of diffraction, \(\theta\), of the \(n^{th}\) is given by:\[n\,\lambda=d\sin\theta\]
Notes
A large set square can be used ensure that the diffraction is being illuminated normally by the lasr
Double Slit
Method
Place a single slit in front of a pair of double slits
Illuminate the single slit with the laser light, such that both of the double slits act as a coherent source of slight
Place a screen at a distance, \(D\), from the slits, measured using a ruler
Measure the distance across \(n\) bright fringes in the interference pattern formed, and divide by \(n-1\) to find the fringe separation, \(w\), for a particular value of \(D\)
Measure the slit separation using a vernier calliper or a travelling microscope; take multiple measurements and average
Record \(w\) for different values of \(D\), from \(D=0.5m\rightarrow\,1.5m\) with \(0.1m\) intervals
Repeat all twice to find repeat values of \(w\) and find average value of \(w\)
Analysis
Plot \(w\) against \(D\)
Draw straight line of best fit
The gradient of the line will equal \(\frac{\lambda}{s}\)
Use the value of the gradient and the value of slit separation, \(s\), measured earlier to find a value for the wavelength of the laser light
Theory
For an interference pattern, formed from a double slit arrangement of slit separation, \(s\), wavelength of light \(\lambda\) and screen distance \(D\), the fringe separation in the interference pattern produced is given by:\[w=\frac{\lambda\,D}{s}\]
Notes
Cannot use travelling microscope to measure slit width
Laser Safety
Screens should be matt to avoid reflection of laser slight from screen
A partially darkened laboratory should be used
Goggles should be used (red for green laser and green for red laser)
A sign should be placed on door of lab to warn of laser
The laser should be switched off when not using it
Should stand behind the laser unless specifically needed in front (for measuring distances etc)
3 - g by Freefall
Method
Setup two light gates, at a distance \(h=0.5m\) away from one another, measured using a ruler, on a clamp stand
Setup an electromagnet (or clamp) at a fixed distance above the first light gate, attaching to the clamp stand
Setup the light gates to start the timer when the ball passes through the first light gate, and to stop when it passes through the second
Drop the ballbearing from the electromagnet, and record the time, \(t\), given by the timer. Repeat twice and obtain repeat values of \(t\)
Decrease \(h\) by \(0.05m\) and record three values of \(t\) for each value of \(h\) down to and including \(0.25m\)
Theory
For constant acceleration:\[s=ut+\frac{1}{2}at^{2}\]
For an object falling freely under gravity, through a distance, \(h\):\[h=ut+\frac{1}{2}gt^{2}\]\[\frac{2h}{t}=gt+2u\]
Plotting \(\frac{2h}{t}\) against \(t\) will give a straight line with gradient \(g\) and y-intercept \(2u\)
Analysis
Plot \(\frac{2h}{t}\) against \(t\)
Draw a straight line of best fit
Calculate the gradient of the line
This will equal the calculated value of \(g\)
Notes
A pad should be used to catch the ballbearing
The distance between the electromagnet and the top light gate should be kept constant so that the initial velocity with which the ball enters the light gates is kept constant
For values of \(h\) below \(0.25m\) it is difficult to obtain accurate readings
Using a clamp to release the ballbearing will not give as clean a drop as using an electromagnet
A plum line attached to the point of release can be used to be sure that the ballbearing will fall through both light gates
A counter weight should be used on the clamp stand to prevent toppling
4 - Young's Modulus
Method
Setup two wires of the same material, one test wire and one comparison wire. The main scale of a vernier scale is attached to the comparison wire while a vernier scale is attached to the test wire.
Add a 1kg mass the the bottom of each of the wires to ensure that both wires are taught. Record the initial extension, \(e_{i}\), of the test wire relative to the comparison wire
Measure the initial length of the test wire
Then, in 0.5kg intervals, add extra mass, \(m\), up to a maximum value of 7kg
Record the gross extension, \(e_{g}\) for each value of \(m\) added
Once all masses have been added, unload wire in same fashion as loading, and record gross extension values. Find average values
Find net extension by finding \(e_{g}-e_{i}\) for each value of \(m\)
Measure the diameter, \(d\) of the wire, in three different locations, at three different orientations using a micrometer, and find average. Calculate the cross sectional area of the wire by \(A=\pi\,(\frac{d}{2})^{2}\) - assuming the wire has a circular cross section
Analysis
Plot \(e\) against \(mg\) for each value of \(m\) added (not including the original \(1kg\) added
Gradient of this graph will be equal to \(\frac{l}{EA}\)
The Young's modulus of the wire can be found by:
\[\frac{l}{A\times grad}\]
Draw a line of best fit
Notes
When measuring diameter, if values are largely different, then flatten out wire and try again. If readings persist to be different then it is possible that the wire is not uniform, and so a different wire should be used
If unloading extensions are found the be generally greater than loading extensions then it is possible that in loading the wire one has exceeded the elastic limit of the wire. In such a case you would need to start again, using lower masses
Measure diameter in different locations and orientations to account for possible variation in diameter across wire, and with a non-circular cross section
The initial \(1kg\) mass is used to ensure that the wire is completely free from kinks one the extensions are recorded, or a false reading would be obtained from the kinks stretching out at the first few values of \(m\)
The comparison wire gives a good base to measure the extension from, as it normalises ones results to the effects of sagging and thermal expansion etc.
The wire could snap if too much mass is added. Therefore goggles should be used, and a sand tray placed underneath the masses to catch any falling weights
A horizontal arrangement can be used in which a marker is placed on a horizontal wire, and a ruler of traveling microscope is placed parallel to the wire
The initial length will be the distance between the fixed end of the string and the marker when the whole string is at it's natural length
Then record the initial position of the marker, and record the position of the marker once the string has extended by an amount.
Fix a string at a fixed surface and pass the other end over a pulley, hanging weights from the vertical end
Theory
The Young's modulus of a material is given by the ratio of the tensile stress and the tensile strain of a material, up to the LOP\[E=\frac{Stress}{Strain}=\frac{Fl}{eA}\]
If a weight of mass \(m\) is acting as the load, then:
\[E=\frac{mgl}{eA}\]
and so:
\[e=\frac{l}{EA}mg\]
5 - Resistivity
Theory
The resistance of a length, \(l\), of wire with cross sectional area, \(A\), and resistivity, \(\rho\) is given by:
\[R=\frac{\rho\,l}{A}\]
Method
Attach a variable voltage source to a pair of crocodile clips, with an ammeter in series and a voltmeter in parallel with the crocodile terminals
Attach the crocodile clips to a length of constantan wire.
Make the length of wire between the terminals \(l=0.100m\) measured using a ruler
Turn the voltage supply to \(0.5V\) and measure the current through and potential difference across the constantan wire
Increase \(l\) by \(0.100m\) and increase the voltage of the voltage source by \(0.5V\) to keep the current reasonably constant. Record \(\) and \(V\) again.
Repeat up to \(l=0.800m\)
Take another set of results and find the average resistance, \(R\) for each length by finding \(\frac{V}{I}\)
With the wire straight and using a micrometer, measure the diameter, \(d\), of the wire at three different locations and at three different orientations. Find average
Calculate the cross sectional area \(A=\pi\,(\frac{d}{2})^{2}\)
Analysis
Plot average \(R\) against \(l\)
Draw a straight line of best fit
Gradient of this line will equal \(\frac{\rho}{A}\)
Find resistivity of wire by \(\rho=grad\times A\)
Notes
The wire should be straightened out when measuring length
The voltage is increased so that the current through the wire (which could affect resistance) is kept reasonably constant throughout the experiment.
The current also needs to be kept reasonably high to be able to take accurate measurements of the current with the ammeter
The voltage source should only be switched on when readings are being taken to avoid heating up the wires which would cause the resistance of the wire to increase
6 - EMF and Internal Resistance
Method
Attach a battery in series with a variable resistor and an ammeter, and place a voltmeter across the terminals of the cell
Record the terminal p.d , \(V\), with the resistor disconnected (when the current through the cell is zero)
Attach the resistor and obtain pairs of values for \(V\) and the current in the circuit, \(I\) for as large a range as possible, with as many values as possible.
Vary the values of \(I\) and \(V\) by changing the resistance of the variable resistor
Analysis
Plot \(V\) against \(I\)
The gradient of the graph will equal the negative of the internal resistance of the battery
The y-intercept of the graph will equal the emf of the battery
Draw a straight line of best fit
Theory
The sum of the terminal pd and the lost volts will equal the EMF of the cell
\(\epsilon=V\,+\,v\)
\(\epsilon=V+Ir\)
\(V=-Ir+\epsilon\)
Notes
Disconnect the circuit in between measurements to avoid draining down the battery which could affect the internal resistance and the emf of the battery
New batteries should be used ideally, as old ones will have emfs that change throughout the experiment