Month: February 2020

Two Body Problems in Dynamics

Problems involving two bodies moving together usually involve asking for the magnitude of the force between the two.

For example:

A 1.0 kg and a 2.0 kg box are touching each other. A 12 N horizontal force is applied to the 2.0 kg box in order to accelerate both boxes across the floor. Ignoring friction, determine:

(a) the acceleration of the boxes, and

(b) the force acting between the boxes.

To solve for (b) requires an understanding that the free-body diagram of the 1.0 kg box can be considered independently as only the force acting between the two boxes contributes to its acceleration since it is the only force acting on it in the horizontal direction.

This interactive app allows for students to visualise the forces acting on the boxes separately as well as a single system.

The codes for embedding into SLS:

<iframe scrolling="no" title="Two Mass Problem" src="https://www.geogebra.org/material/iframe/id/fh5pwc37/width/638/height/478/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="638px" height="478px" style="border:0px;"> </iframe>

Measuring Difference in Drop Time Using PhyPhox

In a recent class on Kinematics, I prepared a string of 4 pendulum balls, each separated about 20 cm apart and dropped them from a height. Before that, I got students to predict whether the intervals in time between drops will be constant, increasing or decreasing.

Most students are able to predict rightly that the intervals will be decreasing and explain their reasoning.

What challenged me was this: previously, we had to listen to the intervals of sound to verify the answer. I had tried using laptop software such as Audacity to record the sound before. However, I wanted students to be involved in this verification process. PhyPhox enabled that.

With each student being able to download the mobile app into their phones, all I needed to do was to ensure everyone uses the correct setting: the Audio Scope setting and to change their range to the maximum duration (500 ms). They then had to be familiar with the play and pause button so they can stop the measurement in time to see the waveform.

I then did a countdown before dropping the balls. This is an example of the graph obtained.

Through this graph, you can see that:

1. the time interval between drops decreases as the balls dropping over a larger height had gained more velocity by the time they reach the table.
2. the amplitude of sound increases as the balls drop with increasing velocity, therefore hitting the table with larger force.

Template for Creating GeoGebra Animations

In an introductory sharing for the use of GeoGebra to my colleagues, I have prepared a simple template for them to try their hands at animations of points and other elements.

You can try the same too. Create a moving point by typing into the Input field (5,5*sin(time)) so that you get a point at x = 5 that oscillates between 5 and -5 in the vertical direction.