Acceleration Due to Gravity Tushar Agarwal 17st November 2014
Aim-In this experiment I will be calculating the value of gravity by the drop of the ball. I will be measuring the distance and finding out the time . Distance will be changed however the size of the ball and the type of the ball will remain constant , The time will be then give me the value of gravity by the suvat equation ,where acceleration will be the subject . Background Knowledge.For an object to move, a force that is greater than its opposite force needs to act upon an object. Force =Mxa where in this case at least acceleration is due tp gravity . Every falling object accelerates at a constant rate and this happens simply due to the force of gravity ,so mathematically the distance “s” that the object is travelling is half the acceleration times of time squared additional to the initial speed and time .

Now , We are going to make a the subject of the equation .After making a the subject of the equation we find out that the acceleration due to gravity is twice the distance of Time Squared will equal to acceleration due to gravity . The answer should be somewhere close to 9.81m/s-2

Time (m/s)

Distance(m)

The graph above shows the relationship between the two variables .In this experiment distance is the independent variable and Dependent variable is time . As Distance increases time will increase as well resulting in a proportional relationship. Hypothesis-After getting the time the ball falls , by the equation gravity should equal to 9.81m/s -²

Variables
Controlled Variable • The size of the ball • Person recording time • Wind • Surface area of the ball • Type of the ball • Texture of the ball If the ball had a different surface area then the air resistance against the ball would be much larger and this would affect the time and therefore affect further calculations of gravity . If we keep changing the person recording the time his reaction time will make a huge difference because it will add on to the final time affecting the calculation of gravity .Wind is very essential If the experiment is being done directly under an air vent the ball would go much faster as there is extra downward force affecting time . Wind should be consistent throughout all the experiment trials . If the ball is heavy than it would fall much faster than a lighter ball so all experiment trials should have the same mass and this would mean to have the same type of ball. Suppose the ball was made out of rubber , it would have much more air resistance and will slow the time of the ball. Independent Variables-Distance at which the height is dropped Dependent Variables- The time of how long it takes for the ball to drop from Point A to B Diagram

Equipment • Stopwatch (±0.01s) • Ball(same mass and same type of ball) • 1 meter ruler (± 0.05cm) • 3 meter tape

Method
• • • • • First measure the distance ,Start with a height of 0.3m Accurately time the ball when released and time the ball when it hits the ground Then , Increase the height by 0.3m and repeat step 2 Take a minimum of three trials of each reading to improve accuracy Take an average of the readings and then using the formulae and the graph find the value of Gravity

Calculation(Raw Data) Distance 0.3m 0.6m 0.9m 1.2m 1.5m 1.8m 2.1m 2.4m Average Time1(s) Time2(s) Time3(s) Average Acceleration + 0.01 + 0.01 + 0.01 Time(s) m.s-­‐2 (2s/t2) + 0.01 0.22 0.23 0.22 0.22 12.39 0.34 0.33 0.35 0.34 10.38 0.46 0.47 0.43 0.45 8.89 0.52 0.53 0.53 0.53 8.6 0.57 0.57 0.58 0.57 9.23 0.64 0.63 0.65 0.64 8.78 0.66 0.67 0.68 0.67 9.4 0.72 0.72 0.74 0.73 9.24

9.67

(Acceleration been shown by the gradient of the curve, M being the slope gives the value of 9.6 , there are 3-4 points on the graph that do not follow the line of best fit . This could be due to the increase and decrease of acceleration due to gravity. This shows clearly that Distance is directionally proportional with the time given Conclusion: As the height increases of the drop the time increases , this should give a directionally proportional line , however there are 3 points of the line of best fit and as we know the literature value for gravity it’s a 9.81m/s-2 and this means the highest number should have been 9.81 however there are some results that exceed the limit of 9.81 for example at 0.3m the acceleration due to gravity is 12.39m/s2 .These lines signify systematic errors . Which are further explained in the evaluation part of this lab report. The Gradient of the curve gives a value of 9.6 which gave a percentage error of 1.42%(9.629.81/9.81*100).The value we found from our experiment was very close to the literature value however there are a number of improvements and correction that are required to be made . Evaluation: There are a number of errors in the experiment. From 0.3m to 0.6m the ruler was not completely parallel to the wall and because of this the distance measured might be a bit more from recorded value and thus the time is different . After 0.6 the ruler was switched to a measure tape and another error was reported then , the point was not touching the floor completely and again that would have added much more distance to the experiment thus affecting all the calculations and giving the points that are off the line of best fit . Even though a digital instrument was used in the recording of this experiment , human reaction would be a big problem in this experiment as the digitial instrument requires human interference to produce results, For example the reaction time to respond to the ball as soon as it touches the ground . If a time is late even by the slightest proportion all calculations would be wrong and the acceleration due to gravity would be much higher . There could be a big issue with parallax because while recording this I was not looking floor level and because of that I might think that the ball had bounced before it actually did and because of that acceleration due to gravity might be much more different form experimental Value . By the equation used to calculate this , It is vital that both distance and time are checked properly as they are directly affecting the final result. Some of the values might have been higher than 9.81 due to air resistance as distance increases . How would I do it Differently? Main errors were Random Errors and few Systematic Errors which could be eliminated if I used a more digital method . For example the light gates would not have any reaction issues as recording is instantaneous and also I would use the clamp rather than a human hand to drop the ball . The human hand might give pressure or force while dropping the ball thus reducing the time it takes to go through a certain distance . Or I would use the video frame method as I can get a very precise idea of when the ball falls and I can get the exact impact from between the ball and the ground , and since this is not looking from the top and is level with the ground I can avoid the parallax random error.

Reference: http://plato.stvincent.edu/physics/ph104/lab2.pdf -Background knowledge extracted from there .