Physics A Level
Chapter 6: Momentum 6.4 Explosions and crash-landings
Physics A Level
Chapter 6: Momentum 6.4 Explosions and crash-landings
There are situations where it may appear that momentum is being created out of nothing, or that it is disappearing without trace. Do these contradict the principle of conservation of momentum?
The rockets shown in Figure 6.12 rise high into the sky. As they start to fall, they send out showers of chemical packages, each of which explodes to produce a brilliant sphere of burning chemicals. Material flies out in all directions to create a spectacular effect.
Does an explosion create momentum out of nothing? The important point to note here is that the burning material spreads out equally in all directions. Each tiny spark has momentum, but for every spark, there is another moving in the opposite direction, i.e., with opposite momentum. Since momentum is a vector quantity, the total amount of momentum created is zero.
At the same time, kinetic energy is created in an explosion. Burning material flies outwards; its kinetic energy has come from the chemical potential energy stored in the chemical materials before they burn.
Roman candles are a type of firework that fire a jet of burning material into the sky. This is another type of explosion, but it doesn’t send material in all directions. The firework tube directs the material upwards.
Has momentum been created out of nothing here?
Again, the answer is no. The chemicals have momentum upwards, but at the same time, the roman candle pushes downwards on the Earth. An equal amount of downwards momentum is given to the Earth. Of course, the Earth is massive, and we don’t notice the tiny change in its velocity that results.
If you push a large rock over a cliff, its speed increases as it falls. Where does its momentum come from?
And when it lands, where does its momentum disappear to?
The rock falls because of the pull of the Earth’s gravity on it. This force is its weight and it makes the rock accelerate towards the Earth. Its weight does work and the rock gains kinetic energy. It gains momentum
downwards. Something must be gaining an equal amount of momentum in the opposite (upward) direction. It is the Earth, which starts to move upwards as the rock falls downwards. The mass of the Earth is so great that its change in velocity – far too small to be noticeable.
When the rock hits the ground, its momentum becomes zero. At the same instant, the Earth also stops moving upwards. The rock’s momentum cancels out the Earth’s momentum. At all times during the rock’s fall and crash-landing, momentum has been conserved.
If a rock of mass $60 kg$ is falling towards the Earth at a speed of $20\,m\,{s^{ - 1}}$, how fast is the Earth moving towards it? Figure 6.13 shows the situation. The mass of the Earth is $6.0 \times {10^{24}}\,kg$. We have:
$total\,momentum\,of\,Earth\,and\,rock\, = \,0$
Therefore:
$\begin{array}{l}
(60 \times 20) + (6.0 \times {10^{24}} \times v) = 0\\
v = - 2.0 \times {10^{ - 22}}m\,{s^{ - 1}}
\end{array}$
The minus sign shows that the Earth’s velocity is in the opposite direction to that of the rock. The Earth moves very slowly indeed. In the time of the rock’s fall, it will move much less than the diameter of the nucleus of an atom!
7) Discuss whether momentum is conserved in each of the following situations.
a: A star explodes in all directions – a supernova.
b: You jump up from a trampoline. As you go up, your speed decreases; as you come down again, your speed increases.
8) A ball of mass $0.40 kg$ is thrown at a wall. It strikes the wall with a speed of $1.5\,m\,{s^{ - 1}}$ perpendicular to the wall and bounces off the wall with a speed of $1.2\,m\,{s^{ - 1}}$. Explain the changes in momentum and energy that happen in the collision between the ball and the wall. Give numerical values where possible.