How Mass Affects Terminal Velocity.

How Mass Affects Terminal Velocity

Planning

Plan: In this investigation I am going to find out how the mass of an object affects its terminal velocity when it is falling. To do this I will drop a paper ‘parachute’ of given diameter from a given height each time changing its mass. I will measure the time taken for the parachute to fall a distance of 2 meters after allowing it to reach its terminal velocity over half a meter. I will start with a parachute of 10cm in diameter timing how long it takes to fall with no ballast then I shall increase the mass by 1 gram each time until I have added 5 grams of ballast. I decided to use these parameters after doing some preliminary testing.

To make this a fair test I shall have to keep all variables the same except the ballast. I will use the same parachute each time dropping it the same distance and timing it myself each time so that there will not be any difference in reaction times. I shall also repeat each parachute drop three times for each mass so to make my results more accurate and reliable.

To do this experiment I will need : paper parachute

Stop watch

Meter rule

Plasticine ballast

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Meter rule

Plasticine ballast

Weighing scales

Prediction: I think the greater the mass of the parachute the higher its terminal velocity will be. I think this as a constant speed, in this case the terminal velocity, is achieved when all opposite forces are equal there for when the downward force of a falling parachute is increased by increasing its mass the upward force will have to be increased also. The upward force is created when the downward falling parachute hits air molecules and the only way to increase the force is by hitting more air molecules a second i.e. by going faster.

Therefore if you double the mass I would expect the terminal velocity to doubled as the parachute will have to hit twice as many air molecules to match the upward and downward forces.

Preliminary tests: To find an appropriate height from which to drop the parachute and to find appropriate shape and size of the parachute as well as how much ballast to add I did some preliminary tests.

I had already decided to do the first drops of the parachute with no ballast at all so I needed to find what angle of paper cone to use to get a stable fall without it dropping too fast. I found the shallowest cone that could be dropt without any loss of stability was a cone of 40o. At this angle the Parachute would not fall too fast and it would be stable and would not flip over whilst falling.

I then needed to find an appropriate size of parachute to use. I found that a bigger parachute would fall more slowly than a smaller one so I decided to use a parachute of 10cm in diameter as this is the biggest parachute you can get from a single sheet of A4 paper. I wanted a parachute that would fall as slowly as possible so that any human error that could be made with the timing would be minimized.

I also needed to find appropriate amounts of ballast to add to the parachute. I had already decided to use 5 different masses plus the un-ballasted parachute for my results so I needed a number that would easily divide by 5. I tested the parachute with ballasts increasing in half grams (0.5, 1, 1.5, 2, 2.5), ballast increasing in single grams (1, 2, 3, 4, 5) and ballasts increasing in 2 grams (2, 4, 6, 8, 10). I found that the ballasts up to 10 grams fell too quickly to time efficiently and that the ballasts up to 2.5 grams showed too little a difference between each mass but the ballasts up to 5 grams showed a good compromise between the two and so this is what I decided to use.

Finally I needed to find an appropriate height from which to drop the parachutes. I found that the parachute I was to use with the maximum ballast I was to add that the parachute would accelerate to a constant speed within half a meter. Using the height of the ceiling to maximum effect I decided to measure the time it took the parachute to fall from the ceiling to the floor minus the half a meter used to accelerate the parachute, this distance conveniently turned out to be 2 meters.

Results

Analysis

In my prediction I thought the terminal velocity of the paper parachute would increase with the increase of mass. As you can see from my graph this has been proved correct. I also said in my prediction that the terminal velocity would be proportional to the mass i.e. if the mass is doubled the terminal velocity would also double, which is true of my experiment if you take into consideration that the un-ballasted parachute weighed 2.2 grams. Also my graph is not quite straight but is very close so I put this down to errors in the experiment. If the graph was straight it would show a direct proportion between mass and velocity. This direct proportion is due to a parachute of double the weight will have double the downward force and so will have to be travelling twice as fast to hit twice as many air particles to create an equal force upwards.

Evaluation

Although my experiment produced the results I expected it was not perfect and there were some anomalies. For instance there was some variation in the three different times for the same mass, this was probably due to different reaction times whilst timing. If I were to do the experiment again I might use a pair of sensors set at the top and bottom of the parachute fall which could time more accurately.

Other anomalies could have occurred due to due to fluctuations in air pressure and temperature which in a laboratory situation could be controlled slightly more accurately. Also using a larger parachute over a longer distance would help the accuracy of the experiment as well as repeating the experiment a greater number of times with a greater number of different masses.