02Accumulating changes

Fm02TA of the Force and motion topic
• 01 Where to next?Fm02TAnugget01 Activity

Using accumulations and vectors to predict routes

What the activity is for

The whole apparatus of Newton's second law (dynamics – causes of changes in motion) and kinematics (describing the motion) is about being able to predict motion – for example, well enough to put men on the Moon, or to land a ship at the correct location.

So using calculated vectors to work out where something will be, when it'll be there, and what speed it'll be moving at focus on the core successes of this invented world in mimicking the lived-in world.

What to prepare

• an ordered set of vectors, able to be arranged tip to tail by translation, without being rotated
• a diagram of the whole schema of dynamics and kinematics

Support sheet – vectors

Support sheet – schema

QWA

What happens during this activity

Show the ordered collection of displacement vectors, reviewing what a displacement vector indicates in passing.

Then ask how they can tell where they'll be after each interval, if the vectors predict their route.

Assemble the vectors tip to tail, in order, to predict the path.

Teacher: Now, how are the displacement vectors found?

Review the whole process

• Velocity telling displacement how to change.
• Acceleration telling velocity how to change.
• Forcemass setting the acceleration.

You may choose to use the support sheet to help.

You might then use the interactive tool, QWA, to revise each of the separate stages of accumulation.

• 02 Relative motion and PoVFm02TAnugget02 Activity

Seeing from a second point of view

What the activity is for

Here students get to see a process from a second point of view, moving with respect to the first, and so get practice in putting themselves in another's shoes.

The ability to see the situation from several different points of view is essential to developing fluency in describing motion. It's also a very useful precursor to the approach developed in the Physics Narrative of episode 04, although we suggest that you avoid colliding the vehicles here, so avoiding an interaction.

What to prepare

• two small video cameras
• two freely running vehicles
• a screen to display clips, preferably side by side

What happens during this activity

We suggest restarting the relative motions to one line, rather than a plane, or higher dimensions: so run the vehicles either parallel or anti-parallel to one another. In either case there should be relative motion between the two. Mount one video camera on each vehicle pointing at right angles to the motion, so that it will see the other vehicle pass. Pay attention to the backgrounds of both cameras, so that there is something significant to be seen as they scan past. We suggest using a clap or other percussive noise to be captured by the running video cameras, as a means of synchronising the two recordings.

Before showing the clips it's worth asking the students to agree on what the clips will show, expecting them to translate from their point of view.

You might even exploit the Alice, Bob and Charlie routine in the Physics Narrative to discuss the three different points of view.

The experiment might be followed up by other clips from the moving object (there are many posted on the internet, or students may have some, as a result of the spread of sports-cams), and ask the students to describe the motion from a different point of view (note: a description does not have to be restricted to words).

• 03 Analysing motion by handFm02TAnugget03 Activity

Getting close to the data

What the activity is for

Although computer-mediated analysis may dominate your practical work, there is a case for a moderate amount of work close up with the data. For this purpose we recommend the use of offset tables and multiple-exposure photographs. These are simpler to deal with, away from the computer, where high-frame-rate digital cameras have more or less displaced this as a practical measurement technique. Nevertheless, we'd encourage you to demonstrate such an image being made in the laboratory, as perhaps the most direct and simple way to explain how such images come to be.

There is also a physical immediacy to the multiple-exposure photographs, as they present a trace of the motion, visible all at once, so making strong links with the graphical representation that is missing from the step-by-step presentation of the data when using video clips.

What to prepare

• a ruler
• a pencil
• a rubber
• some printed prepared grids

Support sheet

What happens during this activity

Introduce the multiple-exposure photographs, perhaps by putting an impressive one on a large screen. Talk through how these tell a story of the motion, and how students could tell the speed between any two (selected) points.

Show the image they are to work on, and bring to their attention the essential scaling factors that connect this representation to the original phenomenon (a measure of length on the image and the interval between the images).

Now introduce the offset sheets, making clear which columns are for the data, and which calculated. Finally set the challenge of producing good displacement–time and velocity–time graphs from the data.

This will be time-consuming, and you'll need to check with your mathematics-teaching colleagues, to see what their graph-plotting skills are like. It's probable that extracting and processing the data are the key activities here, so you may wish to use computational support for the plotting phase. However, we'd not recommend using a spreadsheet to process the data unless you can reproduce the offset cells of the support sheet. We think that these are important to keep track of the intervals.

• 04 GPS-enabled stories of motionFm02TAnugget04 Activity

Bringing GPS tracks into the laboratory

What the activity is for

Many students will probably be carrying a GPS with them embedded in a mobile phone or other electronic device. These can be exploited, together with freely available visualisation tools to bring some stores of everyday motion into their physics classroom. Depending on your class and personal style, you might offer a reward for the most interesting track.

What to prepare

• a set of GPX tracks downloaded from the students' mobile devices (You might provide a small library of GPX files for those who cannot make their own tracks – there are many such files on the internet, often placed there by runners, cyclists, or explorers.)
• one large screen or many small screens

What happens during this activity

You can, of course, use this either as a teacher-focused activity with a large screen, and a single computer, or a student-focused activity, where students use the visualisation tools for themselves. Since at least some of the tools are freely available on the internet, you might even ask students to process their tracks before class starts.

The range of things that students might consider will need to be adapted to the local environment. In a rural school located in undulating countryside, where some are known to cycle, a sample challenge might be:

Teacher: Can you show me some graphs that link the gradient of the hill to the speed you cycle at, on the way to school? Is your average speed higher on the way home?

But the emphasis ought to be on producing an illuminating trace, with some creative thinking going into the motions and into the displays. The best ones, suitably annotated, ought to be worthy of some wall space for a few weeks following the activity.

• 05 Graphical stories of motionFm02TAnugget05 Activity

A laboratory-based real-time version

What the activity is for

Students can walk-out target graphs, and so obtain a real understanding of what the story behind the graph is. The translation is between the graphical and the physical. The same technology also allows variations, as it's the act of translation that provides the key to understanding: you can phone a friend and have them reconstruct a graph just from a verbal description, walk out a graph just from the verbal description or walk out a graph from a set of vectors. Tune the translation to suit the class and what you want them to learn. In all cases the screen and display can provide a common reference point for the discussion. In this activity it's the graph that is the core representation.

What to prepare

• a motion sensor and display
• a series of graphs to mimic, or other instructions

What happens during this activity

Here is one variation. Set up the motion sensor, directed at a space where there will be few stray reflections (important for those sensors that emit and detect pulses of radiation), and load up a target graph. Invite a student forward to walk-out the graph, using their torso as the target for the sensor and therefore the object whose motion is graphed.

Teacher: I'd like you to see if you can walk as this graph shows, to make another graph exactly like this one.

We'd expect you to need to use several prepared graphs, each with several students, to establish the pattern that you're focusing on through your choice of graph.

There are alternatives, some of which might be used as follow up.

Teacher: Here's a graph. Get your friend to redraw the graph, without showing it to them. Imagine you're phoning the friend.

Teacher: Here are a set of vectors, showing how the velocity changes. Walk out the graph of the motion shown by these vectors.

• 06 Formative questionsFm02TAnugget06 Activity

A selection of questions to explore understanding

What the activity is for

These questions can be used to explore students' understandings of the connections between the quantities and the different representations of these quantities.

A good understanding is encouraged by the ability to move between representations, so we'd encourage you to spend time on practising these translations. The questions are selected to help learning, so for their formative value, rather than to make summative judgements.

What to prepare

• printed copies of the questions

What happens during this activity

There are many questions available on this topic, and in a variety of formats, from discussion about instances, through predict, observe, explain, to multiple choice in two- and three- step formats. Many have been developed from research projects, and extensively trialled. If exploring graphical representations, we think multiple-choice questions have significant value, because they offer the opportunity to present a range of answers for consideration.

One way of using the questions is to assign groups to work on the questions, so encouraging discussion of the translations. Students should be encouraged to see the different representations as telling stories about a motion in different ways, drawing the difference between reporting a motion and predicting a motion in helping to distinguish between instantaneous and average values.

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