Impulse changes momentum

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.