What the Activity is for

Different graphs, same effect.

Both the force acting on an object and the time for which it is exerted contribute to the change in momentum: they are compensated quantities.

Here you can show that compensated relationship in a pair of physical artefacts.

What to Prepare

• two toy crossbows, one rigged with strong elastic, the other with much weaker elastic, both firing the same bolt
• a wooden block to be (just) knocked over when hit by the bolt
• images of compound bows and longbows (optional)

What Happens During this Activity

Compare the two crossbows, drawing attention to the force exerted by the elastic. Start with the crossbow with the stronger elastic and show just how much you need to stretch the elastic to fire a bolt that will just knock down the block. (A good everyday synonym for momentum is the punch that the object can deliver.) The longer the elastic is in contact with the bolt, the greater the duration of the action of the force. You could take this opportunity to reinforce the action of the force on the bolt, to further undermine any residual beliefs that the force is somehow transferred to the bolt.

Now the compensating focus:

Teacher: Now, who can tell me how far I'll have to pull back the weaker elastic on this bow to increase the momentum of the bolt by the same amount, to deliver the same punch to the block, just knocking it over again?

You'll have practised beforehand, so that you don't need to lose the flow by too much fiddling whilst experimenting to show what you want clearly. Nevertheless, a few trials are more persuasive that getting it right first time. It also allows more opportunity for discussion, to bring out the compensation between force and time. Students might be encouraged to sketch out force–time graphs to support their reasoning.

What the Activity is for

This is a quick puzzle, best done as a physical presentation, to compare the momentum of two very dissimilar balls after they have been subjected to the same impulse.

If both start at rest then of course they'll have the same momentum as a result of action of the same impulse, whatever the comparative masses, and so velocities.

What to Prepare

• a pair of balls of very different sizes
• a straw
• a smooth channel, to constrain the balls to the same line of motion
• access to this software assembly kit for constrained quantities, QWC (see below)

What Happens During this Activity

Put both balls side by side in their tracks. Blow on both so as to exert the same force for the same time.

Teacher: I exerted the same force for the same time, on both. What can you tell me about the impulse on each ball?

Teacher: Which has the greater momentum?

You might also use the downloaded interactive to build a model of the trade-off between velocity and mass that you've shown physically.

You might also show one or more of the interactives from the Physics Narrative to complement the physical contrast you've shown.

What the Activity is for

Changing direction of motion needs a change in momentum.

Things that are already moving require a force acting on them for a certain duration. You can't change the momentum without the accumulation of the action of force over time.

Here students change the motion of rolling balls of different masses and velocities by applying impulses.

What to Prepare

• a straw per student, to blow through
• three balls of varying masses, ideally all of the same size (For example, marble, ball bearing, plastic ball.)
• a marked ramp to ensure that the balls are launched at a repeatable velocity
• a series of routes marked out on paper, perhaps with momentum arrows

Safety note: Students should not swap straws.

What Happens During this Activity

The ball is launched so that it heads out along the desired inbound path. Students are to direct it to along the outbound route.

Discussions should focus around the momentum of the inbound ball and the impulse that has to be applied so that the momentum alters by the desired amount. Sets of three challenges work well, and students could profitably work so as to explore these systematically.

Note that the impulse is a compensated quantity, and students should be encouraged to explore varying both the force and the duration.

What the Activity is for

This experiment is to get a feeling for just how small a joule is – how little mechanical working needs to be done over just how short a duration.

The second part is to see that when gravity does this working, the energy shifted between the stores allows us to predict where an object will end up.

What to Prepare

• a 10 gram mass hanging over a pulley, so that it can be lifted by exactly one metre
• three or more 100 millilitre clear beakers
• a litre of orange liquid (use yellow food colouring)
• a ball on a flexible track
• some retort stands, bosses and clamps to hold the track
• some white-tack to hold the ball-bearing in place whilst you discuss this snapshot
• some cardboard velocity arrows of different lengths
• some labels for the kinetic and gravity stores (optional: add a thermal store) - see below

What Happens During this Activity

In the first part, introduce the hanging mass over the pulley, perhaps mounted semi-permanently in some kind of frame and left at the side of the laboratory, for students to try as and when they have time to do so. This allows students to get a feel for what's involved in shifting a joule of energy.

Now for a fresh start. As gravity is working, so energy is being shifted. We suggest allowing the ball-bearing to run from one side of a u-shaped track to another. Discuss the energy shifted by the mechanical working.

Then we suggest a change of focus by having the orange liquid model of the energy shifted in the foreground, and the u-shaped track in the background. After sharing the energy out, ask where the ball might be on the track, and what it's velocity might be, as a result of this particular sharing of the energy. Use the arrows and tack to position and label the ball. (Take care: as the track is u-shaped, there will usually be two positions, and also we can't tell which way the ball is travelling.)

You might add to the complexity by considering situations where the frictional forces are significant, but for many classes this may be a step too far.

You might also show the interactive from the Physics Narrative to complement the physical model and real-world that you've shown.

What the Activity is for

Adding and taking away momentum.

The model used to add or take away momentum explicitly accumulates the force over time and so allows you to see that it is this that alters the momentum.

As the model is explicit, so you can see the effect of varying the force as well as constant forces.

As it's a model, and not just a simulation, the inner workings are expressed in an intelligible way, and so might be shared with students.

What to Prepare

• a modelling program, displaying on a large screen (Modellus is free, and is suitable for the task)
• a prepared model of impulse

or

• access to the interactive, QWA (see below)

What Happens During this Activity

Open the model and draw attention to the representations of the force, the duration for which the force is applied and the momentum.

The core of the model will be statements like:

new value = old value + change

Δ →p = →F ×  Δ t

momentum_new = momentum_old +  Δ momentum

Choose a modelling system that you like, and can use with confidence.

Here are two simple models:

InsertCMR{FmAddingMometumSupportCMRS}

InsertCMR{FmAddingMometumImpulseSupportCMRS}

Run the model as it opens and talk through how the momentum is increased by the force. For this to be the case, the force (or at least a component of it – but we suggest you keep things simple by considering only collinear vectors) must be positive if the momentum is positive. Now is the time to look again at the representations and check that this is so. You might also look at the graphs of the momentum against time and the force against time, talking through why these have the form that they do.

Now try again, only this time setting the force anti-parallel to the momentum: if the momentum is positive, then the force will be negative and vice-versa.

A final variation is to allow the force to vary with time. The function to allow the force to vary with time is by far the most complicated part of this, so you might simply treat this part as something of a black box, just showing what it does (how it does so might interest mathematicians, but isn't central here).

You might also use one or more of the interactives from the Physics Narrative to open up this exploration.

What the Activity is for

Working reduces the energy in the kinetic store.

Here you can investigate the trade-off between the pair of compensated quantities: force and distance, the combined action of which alters the energy in the kinetic store.

You might also make the two-step connection between:

• The pair of compensated quantities, force and velocity, the combined action of which alters the power in the mechanical working pathway.
• The accumulation of energy in the kinetic store as a result of the power in this pathway acting for a duration.

As is often the case in physics, true understanding is achieved by making connections between many ways of looking at the same process: here the artefact from the lived-in world, an imagined-world model, and a physical-world laboratory experiment. It might be a good opportunity to explore how physics works by investigating the extent to which the different systems seem to exhibit the same behaviour. Clearly, cycle helmets are not designed just by trial and error, nor are the standards to which they have to comply arrived at by accident.

What to Prepare

• a collection of items which rely on crumple zones, for example, a cycle helmet
• a copy of a computer modelling program, displaying on a large screen
• a sensor-driven set-up to measure energy in the kinetic store, force and distance, during a collision.
• The interactive diagram, or one like it

What Happens During this Activity

We'd suggest starting with the physical artefacts (although in some cases you might justifiably choose to substitute images where these more clearly indicate the focus). You'll want to clearly identify their function as a sacrificial zone, what is being protected, the kinetic store which needs to be emptied, and the importance of the distance that can be crushed in determining the force that is acting on the object to be protected.

In your measurements you'll almost certainly find that the retarding force on the protected object is not constant, and so will want to refine the model. We hope your set-up will allow you to make some changes to the sacrificial material or structure and to control the initial energy in the kinetic store, so as to make these comparisons fruitful.

Finally, the model will allow you to explore many more situations, limited only by your technical skill and imagination in coding up how the retarding force varies. The core of the model will be statements like this:

new value = old value + change

Δ →p = →F ×  Δ t

momentum_new = momentum_old +  Δ momentum

change in energy = power × duration

energy_new = energy_old +  Δ energy

Do keep in mind that it'll be only too easy to code in variations of force that fire the object back off in the direction from which it came, or fail to bring it to a halt. Models need to be constrained by what they're designed to mimic, so there should be no surprise there.

You might also use one or more of the interactives from the SPT: Electricity and energy topic Physics Narrative or the SPT: Force and motion topic Physics Narrative to open up this exploration.