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Momentum and impulse - more interesting topics!

1. The recoil of a rifle

Why should holding a rifle against your shoulder rather than a short distance away reduce the risk of you breaking your collarbone when you pull the trigger?
This has also to do with momentum. When the bullet leaves the barrel the rifle recoils - the momentum of the rifle is equal and opposite to that of the bullet.
Now if there is a gap between the rifle and your shoulder you will get a nasty blow as the butt of the rifle hits your shoulder. However if the rifle is held firmly against your shoulder you will move back with the rifle when you fire it. Because the mass of the rifle is much less than the combined mass of you and the rifle you and the rifle together will recoil much more slowly.

2. The escalator

When I walked down an escalator that stopped suddenly it hurt a lot - why?
This is another effect of impulse and change of momentum. You expect the stairway to be moving away from you and if it stops suddenly your foot meets the stair before you expect it to. It hurts because it stops you suddenly, just like jumping onto the ground and not bending your knees.

3. The cracking glass beaker

Why does a glass beaker crack if I hit it sharply but one of the same type may bounce if dropped on a carpet?
Again this is to do with impulse. A certain impulse applied for a short time will give a large force but longer stopping distances and times reduce the force and so the glass does not break. For the same reason the glass in a window may bend in a very strong wind but will crack if a fixing nail is tapped against its edge.

4. How does the rainfall affect the design for the strength of a roof?

When rain falls and collects on the roof it obviously has to be supported. Imagine if 5 cm of rain fell in an hour onto a flat roof, hitting the roof at 6ms-1 and collecting on it. The pressure of the water would be 0.05rg where r is the density of water [1000 kgm-3] and g the acceleration due to gravity. This pressure would be 500 Nm-2 (500 Pa).

There is a further problem - when the rain hits the roof it must be stopped - this means a change of momentum and so the roof has to exert a force to do this. In our example the rate of change of momentum of the rain (the force on the roof) is mass x velocity change = 0.05Ar x 6. The pressure due to this would be [0.05Ar x 6]/A = 300 Pa and so the total pressure that the roof must withstand is 800 Pa. Of course the rain may not fall straight down and you can use your knowledge of the components of vectors to work out what difference that would make to the pressure.

5. The moderator in a nuclear reactor

Collisions and momentum are important in the choice of moderators for a nuclear fission reactor.
A moderator is designed to slow down neutrons as they collide with its atoms. If the atoms of the moderator are very heavy like lead the neutrons will loose very little kinetic energy during the collision, they will simply bounce off.
Imagine throwing a table tennis ball at a charging rhino and you will see what I mean!

If they are equal in mass the neutrons will stop dead and the moderator atoms will be shot forwards. (If the links to the solid as a whole are broken and the collisions are perfectly elastic). The ideal material is one with relatively light atoms so that the neutrons will lose some energy but still have enough to cause fission with uranium atoms in the fuel. It's partly for this reason that carbon is used in many British reactors and heavy water in reactors in France, the USA and Russia.

6. We talk about momentum being conserved so why does it hurt when I jump onto the ground?

The point is that it is the momentum of the whole system that must be conserved. So when you jump onto the ground we must consider the recoil of the Earth as well! As you collide with the Earth you loose momentum and the Earth gains it and moves off but not very fast. That's why it hurts.

The mass of the Earth is about 6x1024kg and the mass of the whole human population of the planet is roughly 3x1011 kg. So if all the population of the globe were to jump down a metre onto the Earth's surface at the same time and at the same place the Earth would recoil at a speed of roughly 2x10-10 mms-1 or a mm every thousand years! So one of us jumping up and down wont have much effect.


© Keith Gibbs 2020