A-level Topics

26 December

3D Virtual Experiment on Torsional Pendulum

Seng Kwang Tan 10 Oscillations, GeoGebra, Simulations 0 Comments

In preparation for HBL in 2022, I designed a simple virtual experiment that will allow for students to collect data on oscillations using their own stopwatches and investigate the relationship between the period of oscillation and two separate variables. To access the simulation on GeoGebra, visit https://www.geogebra.org/m/jhc4xvpe.

Based on the given relationship $$T = cm^aL^b$$ where a, b and c are constants, students will be tasked to find the constants a, b and c. Students will then attempt to “linearise” the equation such that the independent variables m and L can be tested one by one.

Examples of data collected can be plotted using Excel to give the following graphs from which the gradients and vertical intercepts can be obtained instantly.

29 November

Multiple Representation of Vertical Throw

Seng Kwang Tan 02 Kinematics, GeoGebra, IP3 02 Kinematics 0 Comments

One common misconception among new learners of kinematics is that acceleration of an object being thrown upward is zero at the top of the path when it is momentarily at rest. I created this interactive, along with the 3 graphs in order to help students relate the vectors to the graphical representation of motion.

It is also worth noting that students often have conflicting ideas of the acceleration at the beginning of the throw, as they are aware that a resultant upward acceleration is necessary for the object to start moving upward in the first place. Hence, it must be stressed that the animation begins after the ball has left the throwing hand.

For a view that is optimized for your screen, visit https://www.geogebra.org/m/zvsydy9f.

05 November

Micrometer Screw Gauge – Self-Practice GeoGebra Applet

Seng Kwang Tan 01 Measurement, GeoGebra, IP3 01 Measurement 0 Comments

After completing the vernier calipers applet, I simply had to do a similar one for the micrometer. However, this was a lot more complex as the thimble’s numbers are supposed to be “rotating” rather than moving linearly. A lateral movement of the thimble had to be coupled with a vertical movement of the rotating scale, with the corresponding numbers on the scale constantly changing with each new problem.

Students will need to make readings when the spindle is closed and when open to measure an object before subtracting the zero error and keying in the answer for the actual measurement. The answer will be checked for accuracy, although not for the correct number of decimal places because I have not figured out a way to programme that check yet.

To access the applet in fullscreen, go to https://www.geogebra.org/m/qedrwymk. To embed into SLS, you may use this code:

<iframe scrolling="no" title="Micrometer with zero error" src="https://www.geogebra.org/material/iframe/id/qedrwymk/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>
18 October

Vernier Calipers – Self-Practice GeoGebra Applet

Seng Kwang Tan 01 Measurement, GeoGebra, IP3 01 Measurement 0 Comments

The aim of this applet is to help students who just learnt about zero errors in vernier calipers to get some practice of their own. Students just have to key in their answer into the textbox and they will know if they got it correct.

To modify later: an option to give the correct answer if the student asks for it.

I have not figured out how to ensure that the input is expressed in 2 decimal places, so if any expert is able to advise, I will be glad to try it out.

To access the applet in fullscreen, go to https://www.geogebra.org/m/jybrnwgp. Meanwhile, the applet is embeddable in SLS using the following iframe code.

<iframe scrolling="no" title="Vernier calipers with zero error" src="https://www.geogebra.org/material/iframe/id/jybrnwgp/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

Credits to Abdul Latiff for the original applet which I modified to add the zero error readings.

10 May

Calculating Energy Change in Nuclear Reactions

Seng Kwang Tan 20 Nuclear Physics 0 Comments

There are two methods of calculating the energy released in a nuclear reaction, which will be demonstrated using an example. Consider the nuclear reaction:

$$^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n$$

The table below shows the values of mass and binding energy per nucleon.

binding energy per nucleon / MeVmass / u
$^2_1H$ deuterium1.11228652.0141018
$^3_1H$ tritrium2.82727373.0160493
$^4_2He$ helium7.07391834.0026032
$^1_0n$ neutron 1.0086649

Method 1: Calculate difference in mass $\Delta m$ and take $E = \Delta m c^2$

$\Delta m$ = 2.0141018 + 3.0160493 – 4.0026032 – 1.0086649 = 0.0188830 u

$E = \Delta m c^2$
= 0.0188830 × 1.66054 × 10-27 kg × (2.99792 × 108 m s-1)2
= 2.8181 × 1012 J
= 17.589 MeV

Method 2: Calculate difference in binding energy

Changing in B.E. = B.E. of $^4_2He$ – (B.E. of $^2_1H$ + B.E. of $^3_1H$)
= 4(7.0739183) MeV – [2(1.1122865) + 3(2.8272737)] MeV
= 17.589 MeV