Experiments for Higher Physics - Eyemouth High … · CfE Higher Physics Experiments 4 Acceleration...

CfE Higher Physics Experiments

1


Contents 1

Introduction to Uncertainties 2

“g” – ball 3

Acceleration due to gravity using a single light gate 4

Acceleration and Angle of slope 5

F = ma 6

Explosions 7

2 coherent source loudspeaker interference 7

2 coherent source ripple tank 7

Determine λ using interference pattern 8

Snell’s Law 9

Critical Angle 10

Inverse Square Law 11

Determining Planck’s Constant 12

AC peak and rms 13

Internal Resistance 14

Charge/discharge graphs for a capacitor 15


2

Introduction to Uncertainties

When carrying out any of these experiments it will be worth practicing dealing

with uncertainties. Even as a small exercise, becoming more familiar with this

small section will be of benefit, since many pupils find them challenging (and

tend to ignore them, in the hopes that they will go away…)

Random uncertainties, which will arise in the taking of multiple readings and is

applied to an average is given by:

randomuncertainty =maximumvalue − minimumvalue

numberofvalues

This value can be reduced by repeating your experiment several times.

For the readings that you take, make a note of the reading uncertainty in the

reading.

• Analogue - take the reading uncertainty as a half of the smallest division,

i.e. on a 30cm ruler this is usually half a millimetre, 0.0005 m.

• Digital - take the reading uncertainty as one of the smallest division, i.e.

on a voltmeter displaying 1.27 V this would be ± 0.01 V.

Systematic uncertainties, which arise from repeating the same measurement but

with a consistent error, i.e. a “shrunken” ruler.

You will need to convert uncertainties into percentage uncertainties in order to

carry them through to your final value.

percentageuncertainty =absoluteuncertainty

value× 100

You will most likely apply the largest percentage uncertainty to your final

value, converting it back into an absolute uncertainty. At higher level this is

usually as complicated as it gets. Combining percentage uncertainties will play

a stronger role in Advanced Higher Physics.


3

“g” - ball

A “g” - ball is a specialised piece of Physics equipment which will time the duration of a fall. Combined with an accurate measurement of the distance travelled it can be used to determine g, the gravitational field strength. The theory here is that with initial velocity u = 0. We can use:

s = ut +�

�at� → s =

�

�at�

If we drop the ball from a range of heights we are able to measure a range of times. Repeats and averages help to increase the reliability of our results:

Initial Height (m)

Time taken to reach the ground (s)

1 2 3 average

0.2

0.4

0.6

0.8

1.0

1.2

By plotting the graph of falling distance against time taken squared, we should get a straight line through the origin and will find that the gradient can actually supply us with a, the acceleration due to gravity which is equal to g, the gravitational field strength. To do this, plot your results (s against time t2) and draw a straight line of best fit. Use this line (not just any 1 or 2 arbitrary points) to determine the gradient.

Theory

y = mx + c and s = ut +�

�at�

now y = s x = t2 c = ut = 0 so m =�

�a

Doubling the gradient should result in a value for g. You should expect this to be approximately 9.8 ms-2


4

Acceleration due to gravity using a single light gate Similar to the “g” - ball experiment. A streamlined object of known length should be dropped from a known height through a light gate (held horizontally). The theory here is that with initial velocity u = 0. We can use:

v� = u� + 2as → v� = 2as

If we drop the ball from a range of heights we are able to measure a range of final velocities. Repeats and averages help to increase the reliability of our results:

Distance dropped (m)

Final velocity (ms-1)

1 2 3 average

0.2

0.4

0.6

0.8

1.0

1.2

By plotting the graph of falling distance against final velocity squared, we find that the gradient can actually supply us with a, the acceleration due to gravity which is equal to g, the gravitational field strength.

Theory

y = mx + c and v� = u� + 2as

now y = v2 x = s c = u2 = 0 so m = 2a Halving the gradient should result in a value for g. You should expect this to be approximately 9.8 ms-2

Alternative This experiment can also be done by measuring the time taken to break the light gate beam. Using the length of the object the student can then calculate the velocity themselves.


5

Acceleration and Angle of slope

A straightforward investigation looking at the relationship between the angle of a slope and the acceleration of a vehicle allowed to roll down the slope. For instantaneous acceleration a single light gate and double mask will be best. The interface can be set to calculate acceleration for you as long as you provide a mask length and both masks are of that same length.

Some predictions here. If the slope is at an angle of 0˚ then the vehicle cannot roll “down” it, acceleration will be zero. If the slope is at an angle of 90˚ then the vehicle will fall vertically downwards due to gravity, acceleration will be 9.8ms-2. We cannot logically or practically expect values out with this range! Don’t be silly with the angles here, 45˚ is definitely too steep!

Angle of slope (˚)

Acceleration (ms-2)

1 2 3 average

2.5

5

7.5

10

12.5

15

Plot the relationship between angle (x-axis) and acceleration (y-axis).

There is an angle present here. Is it worthwhile trying to plot the sine or cosine of the angle?


6

F = ma We have been using F = ma almost as long as we have been studying Physics. Now you should be able to show that it makes sense.

An air track is used to minimise surface friction. The unbalanced driving force (F) is provided by the hanging mass and can be given by W = mg. The total mass being accelerated is in fact given by (M + m) so be careful here! There are 2 experiments here:

1. Constant mass (M + m), changing force (mg). Transfer mass from “M” to “m” and record both mg and acceleration.

2. Constant Force (mg), changing mass (M + m). Decrease mass of M but keep m constant to maintain constant mg.

Quite tricky conceptually but I’m sure you will get there. Carry out repeats and calculate averages. Record results as follows:

Driving force (W = mg) (N)

Acceleration (ms-2)

1 2 3 average

↓

Mass (M + m) (kg)

Acceleration (ms-2)

1 2 3 average

↓

Plot the two graphs, acceleration against driving force and acceleration against total mass (M + m). If you have made a hypothesis you should confirm that

1. acceleration is proportional to the driving force (in this case mg). 2. acceleration is inversely proportional to the total mass (M + m)

This leads to the observations that:

a ∝ F and a ∝ �!

When the Newton is defined this simplifies to F = ma!


7

Explosions This is a simple version of a collisions experiment. Begin with 2 stationary trolleys with a loaded spring between them, place these trolleys between 2 light gates. The initial velocity of both vehicles is zero and so total initial momentum is zero. When the spring is released the trolleys will move in opposite directions with speeds determined by their masses. Use the light gates to measure these speeds. Now use your knowledge of the conservation of momentum to determine whether or not the final velocities (after the explosion) are sensible.

2 coherent source loudspeaker interference Set up 2 loudspeakers connected to the same signal generator. Place them a small distance apart and walk past them both listening very carefully for any changes in the sound that you hear. Compare this to the signal from a single speaker Repeat this for different frequencies and possibly different spacing between the speakers. Comment on what you observe. Can you explain it using your knowledge and understanding of waves and interference?

2 coherent source ripple tank Set up 2 bobs connected to the same motor above and suspend them in a ripple tank. Projecting light through the tank will cast shadows showing the positions and movements of waves. Compare a single source to the twin source. Sketch what you see. Can you explain the observation using your knowledge and understanding of waves and interference?


8

Determine λ using interference pattern

In this experiment an equation is again used to determine an unknown value. To improve the quality, reliability and certainty of this we use a graphing method to analyse the result. Set up a fairly standard laser and grating experiment

Take note of the line spacing of the grating, you may need to convert from lines per millimetre. To find the angle θ it may be easier to determine the distance between the central maximum and the first, second, third order maximum etc. This can then be used along with the distance between the grating and the screen to find θ (see diagram below)

Record results in a table as shown:

Maximum m ∆x θ sin θ

-3

-2

-1

0 0 0 0

1

2

3

Equation: d sinθ � mλ Plot m as the x-axis, ranging from -3 to +3 Plot sin θ as the y-axis. Plot all 4 quadrants.

The resulting straight line through the origin should have a gradient = $% therefore the wavelength is

given by: gradient � d


9

Snell’s Law Using a ray box, rayzer kit or similar equipment, direct a single narrow beam towards the centre of the flat edge of a D shaped block. Vary the angle of incidence from 0˚ (at the normal) through to about 85˚, ensuring the light always enters the block at the centre of the straight edge. Using a protractor measure the angles of incidence (θ1) and refraction (θ2).

Results recording

θ1 (˚) sin θ1 θ2 (˚) sin θ2

0 0

5

10

15

↓ ↓

Data handling

You may try it but plotting θ1 and θ2 will not prove to be very fruitful as the result is not a straight line. Plotting sin θ1 and sin θ2 will give you straight line. Depending on which you choose to be the x and y axes then the gradient of the graph will either give the refractive

index, n or will give �& from which you can then calculate the refractive index.


10

Critical Angle Similar to the previous experiment. In this instance, direct the incident light at the curved surface, so that it is not deflected bwhen entering the block, see diagram. Vary the angle of incidence (this time inside the block) from 0˚ to 90˚, recording the angle of refraction as you go.

Does anything unusual happen during your experiment? Refine your experiment and find the angle at which this phenomenon happens. Record this angle of incidence.

From your notes you should know that this angle is the critical angle and that sin θ' � �&.

Use this equation and your value for the critical angle to determine the refractive index of the block and compare to your result from the Snell’s Law experiment. Which method is more rigorous?


11

Inverse Square Law In this experiment the irradiance should be measured at a range of distances from a light source.

This should be done in a dark room using as close to a point source as possible, avoid extended sources. A dedicated light sensor is not essential. A phototransistor connected to a voltmeter should suffice where the reading on the voltmeter is not equal to but is proportional to the irradiance. The irradiance can then be plotted against distance from the source. Students can attempt to

plot against �% before finally plotting

�%(. Further analysis of the graph is then also possible.

Results

Distance from source (m)

1d

1d�

Irradiance (or equivalent reading)


12

Determining Planck’s Constant This involves several steps to complete and the analysis of several graphs.

Wavelength of LED light (rgb)

To do this use the interference method covered earlier in the course to λ for a red, green and blue LED

Switch on voltage of LED’s (rgb)

Using a variable power supply, or variable resistor and fixed supply, monitor the current through an LED as the voltage across it is increased. You should be able to plot the following graph for a red, green and blue LED.

The switch on voltage should be taken as where the broken (traced back) line reaches the Voltage axis. You should have 3 curves, one for each colour of LED.

Finding Planck’s Constant

Energy of photon:

E � hf and E � +'$

Work done by electron:

W � QV

QV � hcλ

V � 1λ ∙ 0

hcQ 1

Plotting switch on Voltage, V, as the y-axis and �$ as the x-axis will give a gradient that is

equal to 234 , where h is Planck’s constant, c is the speed of light and Q is the charge on an

electron.


13

AC peak and rms Set up a signal generator connected to an oscilloscope. Set the frequency and amplitude to known values and try to create a trace on the screen where numerically the period (and frequency) and amplitude of the wave are accurately displayed and measureable. This will require you to think about using:

frequency � �6789:% and V;7<= � √2V8!?

Use the timebase and voltage per division dials to do this (some fine tuning may be required.)

Now have someone else set the frequency and the amplitude of the signal generator to unknown values. Then use only the oscilloscope to determine the new values of frequency and Vpeak.


14

Internal Resistance Set up the circuit as shown below.

Vary the resistance of the variable resistor and record a range of values for the voltage across the cell (terminal potential difference) and the current through it. It is not essential to record the value of the resistance in this case. Plot the graph shown with your results and obtain your significant values as shown:


15

Charge/discharge graphs for a capacitor

In this experiment you should be able to record the behaviour of the voltage across an inductor and the current passing through it, shortly after the circuit is switched “on” or “off”. Set up the circuit as shown.

Monitor both the current and voltage readings on the meters every few seconds (data logging equipment will make this easier, alternatively a large capacitance/resistance combination should increase the duration of the experiment to allow for more readings to be taken). Plot graphs of current and voltage against time.

Experiments for Higher Physics - Eyemouth High … · CfE Higher Physics Experiments 4 Acceleration...

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