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Physics Conundrums - Solutions and a discussion
1.)
We think it will bounce 98 cm. The ball's bounciness is due to the characteristics of its rubber, and the "bounce force" this produces is proportional to the amount the rubber is compressed when it hits the ground. And that is proportional to the ball's weight, which on impact is the compression force. The energy of the compression is stored by the rubber and then released as the ball slows on impact then returns towards its start point. 2% of the energy is lost as heat and sound, but the rest is put back into the ball as movement, as it climbs back towards its start point. It will eventually reach a height 98% of its initial start height, where it will come to rest for a moment before falling again, unless you catch it.
This remains true whatever planet you are on. Remember, the compression force on Mars is less because the weight is lower, due to the lower gravity. But because the weight is lower the compression energy release doesn't need as much to get the ball back towards its start point. In fact it all balances out, it is all in proportion. The bounce distance is the same.
However, something will be different: the rate at which the ball descends and returns will be slower.
2.)
The atmosphere is only 1% the density and pressure of Earth. All other things being equal, the plane will only fly 0.1 metres or 100 cm. However, the gravitational forces are lower on Mars: 38% of that on Earth, so we need to divide our answer by the gravitational pull: ie 0.38. We then get an answer of 263 cm.
3.)
Mars is further from the Sun than Earth, so does not receive as much sunlight (solar radiation). The solar panels therefore have to be bigger. But how much bigger? First let us understand how the Sun's light appears dimmer as we move away from the Sun. Lets try an experiment. Get a torch and turn it on. Have a friend hold it and shine it towards you, from a small distance away. Notice how bright it is. Now get the friend to move back, so the distance is doubled. Does it look as bright? No, it's dimmer. But how much dimmer? Half... or less? Less. In fact if you measure the light with accurate instruments you will discover that if you double the viewing distance, the apparent brightness reduces by four times. Now you will notice that 4 is the square of 2 (ie 2 x 2), so the relationship between distance and brightness is not linear (that is one for one) but a square; and also it is a reducing relationship. That is, as distance gets greater, apparent brightness decreases; and it decreases in proportion to the square of the distance. The mathematical law of physics that applies here is called an Inverse Square Relationship.
Now the apparent brightness is in fact the same as the amount of energy that the viewer's eyes (or solar panels) receive, so we can have a relationship:
Energy received is proportional to 1/(distance away)2
Now Earth is 150 M km from the Sun, on average. Mars is 228 M km from the Sun. Mars is therefore 1.52 times as far away from the Sun as the Earth. If our spacecraft at Earth receives 1 unit of solar energy over its panels, then at Mars it will only receive 1/(1.52)2 as much energy which works out as 43%.
Now, if we want to receive the same Energy at Mars as 10 square metres of panels gives us at Earth, we need to find out how many times 43% goes into 100%, and that will gives us the answer, which is just over 23 square metres.
So the Solar panels need to be nearly two and a half times as big!
But that is not the full story. While Earth's orbit is almost circular, Mar's orbit is quite eliptical and varies from 206 to 249 M km. The maximum distance is therefore what we should design for.
At a maximum, Mars is 1.66 times as far from the Sun as the Earth is. Therefore the energy received at Mars is then only 1/(1.66)2 or 36% that received at Earth. The result is that solar panels need to be just under 28 square metres.
4.)
The same. Mass remains constant wherever it is. However, the weight on different planets will change as this is dependent upon the gravitational pull of the planet the mass is on. Don't be confused by the units of mass and weight. We tend to use the same units for both on Earth as the gravitational force we experience in everyday life remains the same for all practical purposes. So we may express our weight in Kilograms, but really we should be talking of Newtons. But what would your market say if you asked for 5 Newtons of apples?
5.)
There are four main reasons: Radiation, Temperature control, Wind and dust blast and Micro-meteorite impact.
RADIATION: Solar and cosmic radiation on Mars is severe because the planet has almost no ionising ozone layer, unlike the Earth. On Earth this protects us and the animals and plants, as well as things we use like buildings and cars, from heavy bombardment by ultra-violet radiation. This will cause skin cancers in animals and people, damage plants and can make paintwork crack and peel and plastics disintegrate. On Earth, the ozone layer is being damaged particularly at the poles, by polluting gasses such as CFC, that mankind is releasing into our atmosphere. If you live in Australia, or New Zealand, Southern Latin America, Canada, Northern Europe or Russia, you will already be aware of the problem. Go to BRITISH ANTARCTIC SURVEY, NOAA for more information.
In addition, radiation that is beyond the ultraviolet, and more dangerous - microwaves, X rays and cosmic rays - reach the surface of Mars at higher levels. On Earth, luckily, we are protected from the worst of these by our magnetic field and the Van Allen radiation belts that surround Earth and deflect the radiation away.
Our thick, mainly nitrogen, oxygen and water vapour, atmosphere also acts as a filter to remove radiation. Mars' atmosphere, being so thin, does not have the same effect.
TEMPERATURE: Mars is much colder than Earth. Our base will need constant heating for us to be comfortable. By burying it in the ground it is easier to maintain a comfortable constant temperature. Less heat will escape from your habitation, because the ground provides cheap insulation. Caves on Earth usually remain at a constant temperature independent of outside conditions. This is why wine and cheese, for instance, are often matured in caves.
WIND AND DUST: Wind and dust storms are common and severe on Mars. The dust blast can erode and damage objects as well as get into things. Martian dust is particularly unpleasant, because it is corrosive when moisturised. Burying our base reduces such exposure to this effect.
MICRO-METEORITE IMPACT: Because Mars' atmosphere is so thin, the surface is vulnerable to meteor strike. On Earth, many small would-be meteorites burn up before hitting the ground. Ground impact on Earth is very rare. But this is not the case on Mars. Even small meteor particles can do a lot of damage as they travel so fast, and they do not burn up in Mars' thin atmosphere. Anything exposed on the surface of Mars is going to be hit many times a day. Over time, such impacts will erode the base structure if it is exposed.
6.) The compass is useless on Mars because the magnetic field is much lower than on Earth. It will not work properly. The star chart would be useful as it is night time. The stars will look almost the same as they do on Earth in the Northern Hemisphere. You can find the North Star (also called the Pole Star) in the same way that you do here. However, you can't see them! It is foggy. There are three clues to this. It is spring and you are near the base of Olympus Mons, which is often covered by fog. It is very dark - in other words you can't see the sky for clouds. It is still, there is no wind so the conditions are right for mist to form.
The torch is most use to you. Use it to retrace your tracks.
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EXPLORING MARS 