Investigating cratering on the moon.

I am going to change the height from bearing and the surface of the sand. I will try and keep the other variables the same during the experiment (this is to keep it a fair test). I am going to use the same bearing so the size + mass will stay the same; I am going to drop the bearing from the same angle (horizontally) and will try to keep the surface of the sand as even as possible because if the bearing hit a small stone in the sand it would cause more friction and an upward force due to the larger surface area of the stone compared to a grain of sand.

To make this a fair test I will:

• Try to get the surface of the sand as smooth and same depth as posible
• Use a clamp to keep accurate heights.
• Use all of the same equipment each time I use it, including the same bearing so there will be no size or weight differences.

Method

• Tray (for the sand)
• Ruler (1 meter)
• Ball bearing (15mm diameter, 15.5g)
• Clamp (1 meter tall), boss + clamp
• Sand (fine sand)

• Magnet
• Vernier Calliper

How to do the test…

• Fill a the tray about half full with sand.
• Set up the apparatus like so:

• Drop the bearing from the clamp at a height of 200 – 1000mm (in 100mm steps)
• Use a magnet to lift the bearing out from the crater.
• Record the dimensions of the crater with the Vernier Calliper.

• Record the results
• Fill the hole and smooth the surface ready for the next test.
• Do the hole experiment two more times

Prediction

I predict that if the height (from which the bearing is dropped) is doubled, the depth of the crater will double. I chose the depth instead of width because the bearing can only go up to a certain width because the displacement will only work while the bearing is above the sand surface once below there will be no displacement above ground.

This equation proves my prediction:

Ep = Weight x height

As the bearing is dropped, potential energy transfers into kinetic energy. When the bearing hits the surface of the sand, an upward force (work) causes it to slow down and stop.

Work done = Force x Distance

Stopping distance = work done

                         force

work done = energy transfer

force = mass (10N)

e.g.

A bearing (0.5kg) and is held 5 meters above the surface of the sand. Its is:

Mass x Gravity x Height = potential energy

0.5 x 10 x 5 = 25J

So, before the bearing hits the sand it has 25J of kinetic energy.

Braking Distance = Work done

                           force

                       = 5J/2.5N

                       = 2

Results:

Analysis

My results did not provide evidence towards my prediction. So my prediction was not accurate. The Depth of the crater is not doubled if the height is doubled. The line of best fit shows 2mm of depth vs. 200 height. So the graph shows roughly that the depth is a 1:100 ratio against the height. The results on both graphs show a rise in a steady trend. My prediction could be wrong because I didn’t take into account that friction caused by the sand will affect the end result. The displacement of the sand as the ball strikes the surface would also have an effect on the stopping distance, because kinetic energy will transfer into heat and sound energy easier.

When the bearing is lifted higher above the sand surface, it potential is raised and more kinetic energy will be released when it strikes the surface. The higher the bearing hits the sand from, more sand is displaced and the ball bearings kinetic energy transfer to heat and sound, so the crater becomes wider because as the ball displaces more sand.

All of my results follow an upward trend, which I expected. I also expected that the results would level off at some point, because as the ball reaches terminal velocity, it gained  maximum kinetic energy and the crater cannot get any bigger in  diameter or depth as the kinetic energy does not change and will not me falling without anymore force when past Terminal velocity. At this point, the line will level and becomes horizontal.

This was not shown on my results but this does not mean it wouldn’t happen it may have happened much later at higher drop points, but I couldn’t drop the ball from much higher than I have already done.

Evaluation

If I was going to do this test again I would:

1. Do the experiment over at least 5 times.
2. Drop the ball from higher points (if possible)
3. Use finer sand which would make the test fairer because the bearing will not deflect off any stones or larger particles in the sand.
4. Somehow take the measurements better and more accurate, a vernier calliper is the best thing I could think of which is accurate but is easily wrong by a few millimetres.
5. Take my experiment further by using a table tennis ball with a small hole in the side to change the mass of the ball without changing the shape or air resistance of the ball.
6. Look at different velocity and see how that might affect the outcome. This could be achieved by either launching the ball from a catapult of some sort or dropping the ball from a much higher point.
7. Try different type of sands (or soil, fine gravel, etc) maybe a fine sand would have a different result than coarse sand. Because maybe the cosmic dust covering the moon isn’t of the same texture.

The experiment was a success in one way, that I learnt by my mistakes. But my results did not match up with my prediction so in that sense it was a failure. I don’t think I took enough results, more results could have been taken to make a wider and more reliable range but that would of need more time.