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This investigation will look at the effects of air resistance on falling objects, where the objects will have the same dimensions but different masses.

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This investigation will look at the effects of air resistance on falling objects, where the objects will have the same dimensions but different masses. I will firstly model these situations to make predictions. This can then be experimented to obtain a set of results which we can use to test the models. The objects that we used were paper cake cups. We can change the mass by stacking these cups together, where stacking has no significant change on the overall profile as it drops.

Modelling Assumptions

As I am modelling this, there are assumptions that need to be made in order for the models to be more practical:

  • The value of g (the acceleration due to gravity) is constant (9.81 m/s). This is probably not very significant as the actual mass of the paper cups is small, and so the value of g will be quite constant.
  • The centre of mass remains the same. The assumption will not be very significant as the centre of mass would be quite constant.
  • The paper cups reach terminal velocity. This is important as if the paper cups do not reach terminal velocity, we could get inaccurate values of k.
  • The cups used are uniform with equal masses. Not very significant as masses of cups are very small variations in mass with other paper cups is very small. Also, the paper cups do have virtually the same surface area when stacked.
  • There are only two forces which act on the paper cups, which are air resistance and weight, with no external forces (i.e. no downwards forces). This is quite significant as it could make readings inaccurate if there were any downward forces.
  • The motion of the paper cups is one dimensional meaning that the cups will fall straight down, with no horizontal motion. Quite significant as there would be some sideways motion. But we assume this as there would be more complicated equations if not assumed.
  • Model 1
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We then allocated people to each of the different heights to time how long the paper cups took to fall to that height, as well as a ‘dropper’ – the person who dropped the paper cups from the top floor. We started off with one paper cup and once the dropper was ready, he would shout ‘ready, steady, GO’, and at that point, all the timers would be started, and as soon as the paper cups passed each point, the timers would be stopped. The times were then recorded and this was repeated six times. We then repeated this for 3 cups and 5 cups.

Experimental Assumptions

We also have to make assumptions with the experiment, as we have to assume what occurs in the experiment is true:

  • The paper cups have only downwards (vertical) motion, with no sideways (horizontal) motion.
  • All timers start when the dropper signals ‘GO’ and are stop precisely once the paper cups have passed the interval
  • The cup always is dropped from the same point
  • There is no angular velocity of the cup, and hence no rotation
  • The surface area of the cups is unaffected when more cups are added
  • There are no external forces given to the cups, i.e. no downwards push
  • Cups used are uniform with equal mass
  • Initially the cups have no speed

Steps taken to reduce error

There were a few steps that we did to try and reduce the error in the results:

  • We repeated the experiment 6 times for 1,3 and 5 cups and took an average time for each distance
  • Closed all the doors in the building to try to minimise the drafts
  • Chose a dropper who was good at letting the paper cups go as quickly as possible when the timer is started, without giving it a downwards push
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Improvements in experiment

There are many improvements that could be made in the experiment to increase accuracy as well as to reduce any human/experimental errors. We could:

  • Use light gates to time the paper cake cups, where the timer is stopped as soon as the paper cups pass the light gate
  • Use an automated ‘dropper’ which is linked to the timers, where it starts all the timers simultaneously
  • Drop the paper cup in a tube, so drafts do not affect the motion of the paper cake cups
  • Conduct the experiment in a closed system, where air pressure, temperature will remain constant  
  • Take more readings to increase accuracy by taking an average

...read more.

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