Ib Physics, Free Fall

Sagar Sood IB Physics Yr. 1 IB Lab Report Due: 9th October, 08

INTRODUCTION In this free fall lab, the investigation will relate to the one factor that affects a free falling drop of water. Here motion of a drop of water free fall will be analyzed which would further give us a calculated value of acceleration due to gravity. The water will be dropped at different heights using a burette which will be the independent variable. As the height would increase the velocity of the drop will vary, being the dependant variable as it directly depends on the height. Factors like the mass of drop of water, kind of water, the environment (the room) and the size of the burette would be the controlled variables. The main question will be to find out the one and only factor that affects the free falling drop of water. HYPOTHESIS As the height of the burette would increase, the velocity of the drop of water will increase. This would happen because as the height of the burette would increase, the water inside it would gain more potential energy which would further result in greater velocity. The height of the burette would be directly proportional to the velocity of the drop of water. By collecting the data, the acceleration would be calculated to be around 9.8 ms-2. DESIGN Materials Required o Ring Stand o Burette o Beakers with water o Stop Watch o Plastic Plate o Meter stick Procedure o When all the materials will be acquired, the burette is set on a ring stand with the help of clamps. o The water is poured into the top of a burette from the beaker. o The burette is opened so that drops of water can come out of it resulting in a free fall.

o A plastic plate is placed on the floor so that when the drop strikes it makes a sound making it easier for the timer. o The stop watch is started as soon as the water drops from the burette o The time of 10 drops are measured and then divided by 10 so as to find out the time for one drop of water. o Three trials are taken and the height is then increased after that. o The above steps are repeated again every time the height is increased (height is measured from the top of the plastic plate to the tip of the burette). DATA COLLECTION The table here shows the elapsed time for 10 drops. The time is then divided by 10 in order to find out the time for 1 drop. Time of 10 Drops

Time of 1 Drop (s)

Trial 1

Trial 1

Trail 2

Trail 3

Trail 2

Trail 3

(s) 2.50 2.71 3.21 3.62 3.65 5.03 5.51 5.62 6.21 6.04

2.60 2.82 3.25 3.65 4.01 5.12 5.91 5.98 6.18 6.59 ±0.01

2.52 2.84 3.39 3.74 4.21 5.34 5.63 5.76 6.54 7.16

0.25 0.27 0.32 0.36 0.36 0.50 0.55 0.56 0.62 0.60

0.26 0.28 0.32 0.36 0.40 0.51 0.60 0.60 0.62 0.66 ±0.01

0.25 0.28 0.34 0.37 0.42 0.53 0.56 0.58 0.64 0.72

When the time for one drop of water is calculated, the average time is calculated along with the uncertainty. After that the average velocity is calculated. Further the instantaneous velocity is calculated which would further give us the acceleration due to gravity.

Height (m) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 ±0.1

Time Elapsed (s) Trial 1

Trail 2

0.25 0.27 0.32 0.36 0.36 0.50 0.55 0.56 0.62 0.60

0.26 0.28 0.32 0.36 0.40 0.51 0.60 0.60 0.62 0.66 ±0.01

Trail 3

0.25 0.28 0.34 0.37 0.42 0.53 0.56 0.58 0.64 0.72

Average Time (s)

Average Velocity (ms-1)

0.25 0.28 0.33 0.36 0.41 0.52 0.58 0.59 0.63 0.68 ±0.01

1.2 1.5 1.5 1.7 1.8 1.6 1.6 1.8 1.8 1.9 ±0.9

Average acceleration = 7.93 ms-2

Acceleratio n (ms-2) 10 11 10 9 9 6 6 7 6 6 ±4 Average acceleration = 8 ms-2 ±4

Instantane ous Velocity (ms-1) 2.4 3.0 3.1 3.3 3.5 3.2 3.3 3.6 3.6 3.8 ±0.9

Accelerati on (ms-2) 9.62 10.97 9.77 9.26 8.75 6.40 5.95 6.78 5.72 6.05 ?

Data Processing DATA In this case the first height will be taken i.e. 0.3 m. The velocity of the drop will be calculated by dividing the height by the time taken. From there the instantaneous velocity will further give us the calculated acceleration. Time taken by one drop = Time taken by 10 drops / 10 = 2.50 s / 10 = 0.25 s Velocity = Distance / Time = 0.3 m / 0.25 s = 1.2 ms-1 ±0.9 Instantaneous Velocity = 2 x Velocity = 2 x 1.21 ms-1 = 2.4 ms-1 ±0.9 Acceleration = Final velocity – Initial Velocity / Time Elapsed =v–u/t = 2.42 ms-1 – 0 / 0.25 s = 9.62 ms-2 = 10 ms-2 ± 4

UNCERTAINTIES The height of the burette was calculated with the help of a meter stick having an uncertainty of ±0.1 m. The stop watch used had an uncertainty of ±0.01. By using above two, the uncertainty for the velocity was found: (Uncertainty/1st number) + (Uncertainty/2nd number) X 100 = (0.1/0.3) + (0.01/ 0.25) X 100 =0.869785 ≈ 0.9 (As to be rounded to one significant figure) =1.2 ± 0.9 The instantaneous velocity also has the same uncertainty as it is only multiplied by 2. Now to calculate the uncertainty of the calculated acceleration, the same method was used. (Uncertainty/1st number) + (Uncertainty/2nd number) X 100

= (0.9/2.42) + (0.01/ 0.25) X 100 =4.375 ≈4 significant figure) =9.68 ms-2 ± 4 =10 ms-2 ± 4

GRAPH

(As to be rounded to one

Here the slope of the above has been calculated as follows: Slope = Rise / Run = Distance / Time = 0.75/ 0.45 = 1.7 ms-1 ±0.9 velocity)

(which is the approximate value of the average

From here the instantaneous velocity is found by multiplying it by 2. Instantaneous Velocity = 2 X Average Velocity = 2 x 1.67 = 3.4 ms-1 ±0.9 Acceleration = Final velocity – Initial Velocity / Time Elapsed =v–u/t = 3.4 ms-1 – 0 / 0.45 s = 7.42 ms-2 = 7 ms-2 ±4 CONCLUSION My experiment related to the falling drop of water and the main purpose was to calculate the acceleration due to gravity which is the only factor affecting a free falling object. I hypothesized that as the height would increase the velocity would also increase but the acceleration would stay the same. By looking at the graph

and the data table it is clear that my hypothesis was correct. Although acceleration did not come exactly as 9.8 ms-2, the average comes out to be pretty close to it. This shows that there were errors in my experiment and/or investigation. EVALUATION As it can be seen from the points in the graph and the set of my data that there were some errors in my experiment. One of the main problem was that throughout the experiment the set up was not stable. This could have had a direct impact on the motion of the drop of water affecting the data collection. Another problem being a systematic error was the burette. As more water was added in the burette, it applied force on the drops of water. As the water kept finishing the force became less and as more water was added the force became more, hence not being a ‘free fall’ and having an effect on the time of 10 drops. Along with that the tap was not opened the same amount as other times, in other words the water was not coming out in the same amount and speed as it was the other times. As the time of 10 drops was first collected it had a direct impact on the collection of data.