How Fast Does a Paper Cone Fall?

Identifying key factors to vary, control and take into account,

There are many different factors which can be varied in this experiment, but if more than one factor is varied in this experiment, it would be unfair and our results would be inaccurate. The two main factors to vary would be the size or weight of the cones, however the height, direction or position the cone is dropped in could also be changed.  But because this experiment should be fair all factors excluding one should be controlled. In this experiment size is to be changed, so it is very important that the weight and other factors which could be changed stay the same. This must be done by not adding anything onto the cones and making sure each time the cone is dropped it is dropped from exactly the same height and in exactly the same fashion.  Some factors which should not be changed are impossible for us to control with the equipment provided.  Such as air currents changing, there being a split difference between the time the cone is dropped and the time the stopwatch is started and our cones being slightly off the required radius measurements. So these factors must be taken into account, and the results may not be 100% accurate and may have a few anomalous results.

Prediction,

I predict that as the surface area of the cones increases the time taken for them to reach the ground will increase. So I believe that the cone with a radius of 12cm will take longer to fall than the one with a radius of 2cm. This is because the bigger the surface area, the bigger the air resistance acting on it and because air resistance is greater, it will equal the cones weight sooner. This will mean the cone reaches its terminal velocity sooner and therefore the cone takes longer to fall.  I believe all cones will reach their terminal velocity before they hit the ground because there is a relatively large surface area compared to the weight; however the larger cones will reach their terminal velocity sooner, and will take longer to fall.

Suitable extent and range of evidence,

A suitable extent and range of evidence to be collected must be decided before the experiment, to ensure enough evidence is taken to give fair results, but not so much that it will not improve your results any further.  It is generally best to take as much evidence as possible but due to time restrictions it is not possible to do more than 3 results for each cone, so this is the amount we will settle for. This should give us a basic set of results which are sufficient to show a trend on a graph and be reasonably accurate.  Six cones are being used, so as to give us a fairly wide and comprehensive set of results.  It is important to do a reasonable number of results and take an average because if this is not done and one of the results is anomalous, it will completely throw your results. Without an average the experiment would not be very accurate and if not enough cones are used the spectrum will not be wide enough to see an obvious difference and trend between surface area and time taken.

Strategy for experiment,

Six paper cones are to be made, one cone with radius of 2cm, one cone with radius of 4cm, one with radius 6cm, one with radius 8cm, one with 10cm and a final cone with radius of 12cm. The radius (or size) will be the one factor we are to change, during the experiment all other factors will remain the same, other wise the experiment will be unfair.  The cones will be made by using a compass to draw an accurate circle on a piece of paper. These circles must be extremely accurate, because if they are not the surface area is likely to be affected, changing the speed the cones will fall, and making our experiment unfair.  According to the radius required, the compass point’s distance from the pencil will be measured and changed using a ruler, i.e.-if the radius required is 2cm the distance between the compass point and the pencil will be 2cm.  Once again these measurements must be accurate to avoid altering our cones surface area, having a direct affect on terminal velocity which  will in turn affect time taken.  Once the circles are drawn they will be carefully cut out, avoiding cutting into the circle or leaving any excess round the edges which would make the results less precise and reliable.  Once cut a line will be drawn from a point on the circumference of the circle to the centre point, this line will be carefully cut along and the cone will then be folded at the point of the cut.  It will be folded a quarter of its own circumference.  This must be exactly a quarter of its circumference to avoid affecting the surface area compared to the other cones.  This measurement must be accurate or the size of our cones will change out of proportion.  The cones will then be sellotaped in place, using the same amount of sellotape each time, so that no more than one factor is changed. If too much sellotape is used it would alter the weight of the cones. Once they are taped they are ready to be dropped.  A measuring tape will be attached to the wall and it will be ensured that   the bottom of the tape is against the floor to make sure distance measurements are accurate.  The cones will be dropped from the two meter mark of the measuring tape; the distance must be accurate to avoid changing more than one factor.  The cones will be dropped with the point facing downwards; this is done because if they dropped the other way, the air currents would catch under the cone, making it unstable and more likely to hit the wall.  The cones will be dropped with the rim level with the two meter mark, so the experiment is fair. The cones are held two centimetres from the wall when being dropped, to avoid them hitting the wall. When the cone is dropped a stopwatch will be started, the stopwatch will be started by the same person who drops the cone to achieve maximum accuracy, the stopwatch will be stopped the moment any part of the cone touches the ground. If the cone hits the wall or any other object on its way down, the measurement will be considered void, and that one will be re-measured.  This is done to prevent anomalous results, which would affect our averages.  Once one drop is complete the stopwatch will be reset ready for the next cone.  Each cone will be dropped 3 times, (we have chosen to drop each one 3 times because it should give us a reasonably accurate result if we take an average) assuming no measurements are void. Each time a cone is dropped the time will be taken and recorded.  When 3 measurements for each different sized cone have been taken, an average will be calculated, i.e.-the 3 times for the 2cm cone will be added together and divided by 3, giving an average, this is done to provide a more accurate and realistic result. Once all averages have been successfully made the experiment will be complete.  If the experiment is carried out correctly in this way our prediction should be correct.  Our prediction should be correct; because when the cone with the largest surface area, the 12cm cone, is dropped it should produce the most air resistance, and because terminal velocity is reached when weight equals air resistance and this cone has a large air resistance, terminal velocity should be reached quicker causing the cone to slow down quicker and reach the ground in a longer time than the smaller cones.  We can apply this experiment to Newton’s first law, as he stated that if balanced forces act on a moving object it will move with a constant velocity, and not accelerate. This is why when the two forces; weight and air resistance are equal the cone reaches terminal velocity, stopping it accelerating and increasing the time it takes to reach the ground.