GeoGebra

22 January

Standard Form and Prefixes

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

This little applet is designed to allow students to change the order of magnitude and to use any common prefix to observe how the physical quantities are being written. To view this applet in a new tab, click here.

Standard form (also known as scientific notation) is a way of writing very large or very small numbers that allows for easy comparison of their magnitude by using the powers of ten. Any number that can be expressed as a number, between 1 and 10, multiplied by a power of 10, is said to be in standard form.

For instance, the speed of light in vacuum can be written as 3.00 × 108 m s–1 in standard form.

When a prefix is added to a unit, the unit is multiplied by a numerical value represented by the prefix. e.g.     distance = 180 cm = 180 x 10-2 m = 1.80 m

The purpose of using prefixes is to reduce the number of digits used in the expression of values. Hence, students can use the prefix slider to find a user-friendly expression, such as 682 nm instead of 0.000000682 m.

The ten prefixes used are:

10-12pico
10-9nano
10-6micro
10-3milli
10-2centi
10-1deci
103kilo
106mega
109giga
1012tera
04 October

Appreciating the least square method of determining best-fit line

Seng Kwang Tan 21 Practical / Planning, GeoGebra, IP4 Practical 0 Comments

This interactive is designed to help students understand the statistical approach underpinning the drawing of a best-fit line for practical work. For context, our national exams have a practical component where students will need to plot their data, often following a linear trend, on graph paper and to draw a best-fit line to determine the gradient and y-intercept.

The instructions to students on how to draw the best-fit line is often procedural without helping students understand the principles behind it. For instance, students are often told to minimise and balance the separation of plots from the best-fit line. However, if there are one or two points that are further from the rest from the best-fit line (but not quite anomalous points that need to be disregarded), students would often neglect that point in an attempt to bring the best fit line as close to the remaining points as possible. This results in a drastic increase in the variance as the differences are squared in order to calculate the “the smallest sum of squares of errors”.

This applet allows students to visualise the changes in the squares, along with the numerical representation of the sum of squares in order to practise “drawing” the best-fit line using a pair of movable dots. A check on how well they have “drawn” the line can be through a comparison with the actual one.

Students can also rearrange the 6 data points to fit any distribution that they have seen before, or teachers can copy and modify the applet in order to provide multiple examples of distribution of points.

17 August

Docking with Tides

Seng Kwang Tan 10 Oscillations, GeoGebra 0 Comments

Did this simple interactive upon request by a colleague who is teaching the JC1 topic of Oscillations.

Based on the following question, this is used as a quick visual to demonstrate why there must be a minimum depth before the boat approaches harbour.

The rise and fall of water in a harbour is simple harmonic. The depth varies between 1.0 m at low tide and 3.0 m at high tide. The time between successive low tides is 12 hours. A boat, which requires a minimum depth of water of 1.5 m, approaches the harbour at low tide. How long will the boat have to wait before entering?

The equation of the depth of water H based on the amplitude of the tide a can be given by $H = H_o + a \cos \omega t$ where $H_o$ is the average depth of the water.

$H = H_o + a \cos \omega t$

When H = 1.5m,

$1.5 = 2.0 – 1.0 \cos (\dfrac{2 \pi}{12}t)$

$\cos (\dfrac{2 \pi}{12}t) = 0.5$

$t = 2.0 h$

02 April

Internal Resistance and Terminal Potential Difference

Seng Kwang Tan 15 DC Circuits, GeoGebra, IP4 12 DC Circuits 0 Comments

https://www.geogebra.org/m/puvfjxk5

This applet demonstrates how terminal potential difference (as measured by the voltmeter across the terminals of the battery) changes depending on :

  1. internal resistance r
  2. external resistance R
  3. emf E
  4. when a switch is turned on and off
<iframe scrolling="no" title="Internal Resistance and Terminal Potential Difference" src="https://www.geogebra.org/material/iframe/id/puvfjxk5/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>
30 March

Sky-Diving and Terminal Velocity

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

https://www.geogebra.org/m/wavar9bx

This is a wonderful applet created by Abdul Latiff, another Physics teacher from Singapore, on how air resistance varies during a sky-dive with a parachute. It clearly demonstrates how two different values of terminal velocity can be achieved during the dive.

Incidentally, there is a video on Youtube that complements the applet very well. I have changed the default values of the terminal velocities to match those of the video below for consistency.

Also relevant is the following javascript simulation that I made in 2016 which can show the changes in displacement, velocity and acceleration throughout the drop.