# Investigation Into How mass Affects the Rate of Fall of Cup Cakes

In this investigation we will observe and analyse the rate of fall of cup cakes when the mass is altered.In my preliminary work we conducted experiments where we dropped a large surface area parachute and small surface area parachute from the same height of 1 metre and 1.5 metres. The purpose of this preliminary experiment is to familiarise and understand the principles involved in the experiment.Diagram:Results of preliminary experiment:Parachute dropped at 1 metre -Time in seconds to fall 1 metreSmall surface area parachute1.

161.221.25Large surface area parachute2.002.031.84Average:Time in seconds to fall 1 metreSmall surface area parachute1. Large surface area parachute1.96From these results we can see that, the larger the surface of the parachute will fall at a slower speed compared to a smaller parachute with a smaller surface area, which will fall at a faster speed.

A larger surface area increases the air resistance, and slows the fall.Another experiment that was conducted is where cup cakes are dropped at the same level, the variable being the weight of the paper cup.

The weight was increased but adding paperclips to the paper cup.Diagram:Results of preliminary experiment Average time taken to fall in seconds5.165.91From these particular results we can tell that the more paper clips added the heavier the falling object is and the faster it will reach the ground.Because the weight and gravity are not balanced then paper cup accelerated in that direction. The rate of fall increased as the weight increased.Experiment: Investigation into how mass affects the rate of falling cup cakesAPPARATUS Paper cups.

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Metre sticks Clamp StopwatchDiagram of materials in useMETHODOnce the apparatus is set up correctly, at the height of 2 metres from the floor we will drop the paper cup and record the time it takes to finish the 2 metre drop.2 metres is chosen as the height as it allows time to release the paper cup and start and stop the clock sufficiently. As opposed to a shorter distance e.g. 1 metre where it allows errors to be made since it reaches the ground so fast, the person timing, their reflexes may not be fast enough to react accurately. 2 metres is also a practical height as it can be reached if we use a chair to aid us. If we increased the height to 3 metres the paper cup is more likely to be affected by disturbances towards the experiment e.g. Drafts.The paper cup will be dropped 3 times at each selected mass to insure accurate results and hopefully rule out any erroneous results.

I’ve chosen to drop the paper cup in an upright position because it is more streamline and so the particles in the air can travel at an equal velocity and low frictional drag. If the paper cup is dropped upside down  there will be an increased turbulent force as the streamline are more irregular and high frictional drag, these factors are more likely to affect the results.Table of selected Range:RANGE1 cup2 cups3 cups4 cups5 cupsI believe this is a good range as the mass is steadily increased. Also the differences between each cup, in ascending order are equal.To ensure that it will be a fair test there will only be one variable which is the mass of the paper cups, everything else will be kept the same.2 metres is chosen as it is an adequate time to release the cup as well as record the time sufficiently.

At a shorter distance our reflexes may not be quick enough to react to the touchdown of the paper cup and an increased distance will allow more outside factors to affect the drop of the paper cup e.g. drafts. I’ve came to the decision through the preliminary experiments where at dropping the parachutes from 1 metre we found it difficult to record an accurate time. The height of 2 metres will be kept through out the whole experiment.The paper cups itself will be of the same type and brand new so this minimizes and disturbments to the shape or creases of the cup, this will help maintain a streamline shape.So that the time can be recorded as accurately as possible, one specific person will be stopping the clock only, so all distractions are minimal, they will not have to concentrate on any other task e.g. dropping the cup. So hopefully the recorded times will be accurate. If we had to combine the jobs of dropping the paper cup as well as stopping the clock this could delay the reflexes and result in an inaccurate time being recorded.

Each experiment will be repeated three times on each mass to rule out any errors.From my preliminary work, I can use Newton’s Second Law to aid my prediction of the experiment;’If there is an UNBALANCED FORCE, then the object will accelerate in that direction. The size of the acceleration is decided by the formula F = ma A= F/M’Also, acceleration is proportional to force. The acceleration is inversely proportional to the mass -As the paper cups will have different masses this will affect the ‘terminal velocity’V = Initial velocity + (Acceleration ï¿½ Time)So from this formula I know that an increased mass will increase the fall of the paper cup.1) Initially the forces will be unbalanced so the paper cup will accelerate2) But then the two forces will balance out and move at a steady speed, this is because it has reached terminal velocity.

Due to a greater mass there will be a greater terminal velocity.The earth’s gravitational pull on the paper cup is proportional to its mass. The strength of the earth’s gravitational field is 10N/kg. The weight of an object is the force that gravity exerts on it, and is equal to the objects mass ï¿½ the pull of gravity on each kg.Weight = mgAnd the size of ‘g’ can show the gravitational acceleration – g = w/m.So, the paper cup which has the biggest, as will accelerate faster.Both balls have a spread of 40 m/s. At this speed the weight of the red ball is balanced be air resistance but the heavier green ball is still accelerating.

Surface area also affects the speed of fall; an object with a large surface area will be slowed down and shown in preliminary experiment with the parachutes.However in this particular experiment the surface are will stay the same, perhaps a minute increase of surface area where the added paper cups are places around the rim, but this would only make a minor difference.So, from these formulas I predict that as the mass increases, the time taken to fall a 2 metre distance will be less compared to the smaller mass paper cups. There will be a higher terminal velocity reached by the larger mass paper cups which will result in a quicker fallI’ve illustrated my results in a graph; I predict the graph to be inversely proportional.