Show how to calculate momentum from values of mass and velocity. Establish a sign convention e. Emphasise the need to draw diagrams showing the situation before and after an event collision or explosion when solving numerical problems. Emphasise the predictive power of the principle of conservation of momentum. Mention that it works in 3 dimensions, as well as in these simple 1-D situations. You could look at other examples of conservation they will have met, such as energy and electric charge.
They should be aware of the utility of such conservation laws in calculations and also that they are established experimentally. Students should now be able to do more questions of the type described above. Elastic collisions are not dealt with until Episode Try to prompt students to contribute to each stage in this argument. Think about two trolleys of different masses exploding apart. So the bigger trolley has a smaller acceleration than the smaller one. So the change in velocity of the bigger trolley is less than that of the smaller trolley, and in the opposite direction.
So total momentum is constant.
This episode extends the idea of conservation of momentum to elastic collisions, in which, because KE is conserved, useful information can also be found by calculating the changes in KE of the colliding objects. Demonstrate springy elastic collisions using trolleys, one of which has its spring-load released so its spring can soften the collisions Alternatively, use air-track gliders with repelling magnets attached.
Direct a single trolley at a second, stationary trolley. The first trolley stops, the second moves off at the speed of the first. Momentum is conserved. Now try a light trolley colliding with a heavy one, and vice versa. What pattern is seen? A light trolley bounces back from a heavier one its momentum is negative ; a heavier one moves on, but at a slower speed.
Students may accept that momentum is conserved; alternatively, with suitable light gates you should be able to measure the initial speed of the one trolley and the final speeds of both. Momentum conservation can be shown. Or try using a computer and motion sensor. Now ask: How do the trolleys know at what speed they must move? There are many combinations of velocity which conserve momentum; there must be something else going on here. Introduce the idea that kinetic energy KE is also involved, and that, in a springy collision, there is as much KE after as before; in other words, KE is conserved.
Ask whether KE is conserved in an explosion obviously not; it is created in the explosion in the change from chemical PE to KE and in an inelastic collision the total amount decreases, but you may need to work through a numerical example to show this. Discuss where KE comes from in an explosion from energy stored in a squashed spring, chemical explosive or whatever , and where it goes to in an inelastic collision work is done in deforming material leads to heating; some sound. Usually, elastic is taken to imply that KE is conserved.
In some texts, this is written as perfectly elastic.
Inelastic describes a collision in which some KE is lost. Students should learn to use these terms, rather than springy and sticky. Ask students to carry out an experiment to determine whether, in a springy collision between trolleys or gliders, momentum and KE are both truly conserved. They can use the same approach as the experiment in Episode , but they will have to calculate values of KE as well as momentum. Note that the second type requires solution of simultaneous equations, one of which is a quadratic; students may find this difficult, so check that it is required by the specification that you are following.
How a rocket ship works, as a controlled explosion in which reaction mass travels backwards. The rocket needs nothing to lift off except the expended fuel. There is a video of this with a man sitting on a cart firing a fire extinguisher on the Wake Forest University website. The same site shows another video of two people on roller-blades throwing a cushion back and forth. Discuss situations in which the Earth is involved, as it may appear that momentum is not conserved.
Where does momentum come from or go to in these situations? It helps to think about the forces involved. Emphasise that momentum is always conserved, but KE is not. One way to think of this is that KE is just one form of energy, so it can be transformed; there is only one form of momentum, so it cannot be transformed into anything else. The following is a brief summary of the Resourceful Physics activities given in the link in episode Momentum demonstrations. RP Pendulum on a trolley — to show conservation of momentum.
This could be filmed with a webcam and the film studied in slow motion to great effect. There is a link here between the motion of the trolley and the motion of a rowing boat, which shoots forwards when the rowers move back on their slides, rather than when they pull on their oars. RP Momentum in catching — compare to deforming barriers and elastic ones.
This contrasts the momentum change on catching something and the greater change on reflecting it back. RP If you have access to an air rifle demonstration, this is a lovely way to round off the topic. This episode focuses on the forces involved in changing momentum, and introduces the concept of impulse.
It is obvious that, the greater a force and the longer it acts for, the greater will be its effect. At this point, you might return to the discussion at the end of Episode , and extend it slightly to deduce the impulse equation. Episode Momentum demonstrations Word, 27 KB. Relate this to real world collisions such as car crashes, or jumping off a table important safety point: never try jumping, even small heights, with stiff legs and ankles — it is remarkably easy to break a bone.
No-one should climb onto a stool or table in the lab. If any experimental work is undertaken, it must be done in the gym under the supervision of a trained PE teacher.
Forces between objects are not usually constant. Ask students to think about, say, a bat striking a ball, or a collision between cars or a car hitting a wall.
What would the force-time graph look like? The force will rise to a peak and then fall, being approximately triangular. An alternative approach is to use sensors, but this is more demanding to set up and to interpret. Numerical questions involving impulse, including force-time graphs.
These will require the student to find the area under the graph, the total momentum change and possibly the average force. This latter is a particularly difficult concept, being the equivalent force which, if applied constantly over the entire contact time would produce the same impulse. This can be related to the idea of an average speed.
Descriptive questions which take these ideas and develop them in contexts such as seat belts and airbags. Are you a practising physics teacher? Want to become a Chartered Physicist? We're here to help.
With light gates, a cardboard mask will need to be attached to the vehicle to measure the time, t , for which the light is cut off. We're here to help. The fact that the electromagnetic field can possess momentum and energy makes that field very real, and so, for better understanding, the original idea that there are just the forces between particles has to be modified to the idea that a particle makes a field, and a field acts on another particle, and the field itself has such familiar properties as energy content and momentum, just as particles can have. The equation on the right shows the rule for the weight updates according to the SGD with momentum. Yet, acceleration depends on both force and mass. The second part of the equations, on the other hand, can be regarded as RMSProp, in which we are keeping the running sum of squared gradients.
Get in touch at teachercphys iop. Collection Momentum Episode Preparation for momentum topic Episode Momentum and its conservation Episode Elastic collisions Episode Impulse of a force. This assumption must be modified for objects travelling near the speed of light, without affecting the result that momentum is conserved. Because the changes in momentum add to zero, the total momentum of the two-car system is constant. That is,.