Problem Statement - What are the accelerations produced by varying forces on a given mass?
Hypothesis - If the force on a cart with a constant mass is decreased, then the acceleration will be greater
In this experiment Newton’s second law of linear motion was being investigated. A cart was connected by a ticker tape and a ticker timer used to get the velocity and time. The hypothesis was that a decrease of the force on a cart with a constant mass results in greater acceleration. This is because removal of certain masses results in an equivalent resultant force, hence more resultant force causes more acceleration (Goswami 43).
Therefore, the hypothesis was proven by my data which showed that a resultant mass of 0.1kg produced less acceleration compared to 0.2Kg. However, from the data the 0.2kg mass produced more acceleration of 4.75 compared to 3.75 of the 0.3kg mass which did not support my hypothesis. This might be because of errors in the experiment such as human error. Furthermore in using Newton’s second equation which is F=ma where F is force, m is resultant mass, and a being acceleration, the expected acceleration in the three masses of 0.5, 0.4, and 0.3kg would be 2, 5, and 10 cm/ (tock)2 respectively. Therefore the percentage errors are:
(1) 500g mass is
(2) 400g mass is
(3) 300g mass is
Note, F=ma is applied as: a=F/m hence for acceleration for 500g is 1/0.5= 2; 400g is 2/0.4= 5; and 300g is 3/0.3= 10. The respective forces are 1, 2, and 3 N while masses are 0.5, 0.4, and 0.3 kg from table 2
The vast error in the 400g mass and 300g mass indicated that in the experiment for the 300g mass trolley, the acceleration was supposed to be more than that of the 400g mass trolley. Hence it was not consistent with the hypothesis of the practical. Hence it can be concluded that even though the second law was proven that resultant force was directly proportional to the acceleration, the hypothesis was not accurate for masses 400 and 300g where a decrease in mass caused greater acceleration. This was attributed to an error since the literature value stipulates that it should be more.
The findings were similar to other researches which indicate that force applied to an object is directly related to the acceleration the object moves in (Goswami 43). This was shown when object with different masses produced different accelerations signifying that the forces they exhibited were different. Higher masses removed signifying higher resultant forces produced higher accelerations hence a direct relationship. Furthermore, it was proved that there were unseen forces limiting movement of objects. This resulted in lower acceleration figures compared to ideal figures. This is in accordance to other researches which posit that the unseen forces are air resistance and kinetic frictional forces (Goswami 44).
Therefore, the findings are inaccurate due to errors such as human, gravity consideration, and kinetic frictional forces. The study could thus be improved by using of more masses, more trials per mass, and using oil or grease on the path of the cart to decrease kinetic friction. Even though the findings were inaccurate, they painted a rough picture that acceleration was directly proportional to the force applied. The limitations of the method are: that it is impossible to calculate larger distances, it is subject to human error since it depends on an experimenter taking readings and calculating them, and it is influenced by air resistance, gravity, and kinetic friction. The method can be enhanced through carrying it inside a vacuum to reduce air resistance and gravity. The possible applications of the experiment are that it can be used to calculate the effects of gravity, deceleration, and momentum apart from obtaining acceleration. This would be through using data for expected results and that for actual results obtained. Furthermore, the results in this experiment find real world application in designing of lifts and construction pulleys (Goswami 53). In lifts the engineer has to factor the maximum force of people who would make the machine move at the accepted acceleration. Without factoring the force and acceleration, there is a high probability that it would crash or people get injured due to higher accelerations. However, in this application, the gravity is also considered; which is a type of acceleration the earth experiences towards the center.
Table 2 (showing α verses F) shows that resultant force is directly proportional to the force applied. This is shown when the force increased with increase acceleration. However, mass of 400 and 300g did not prove the relationship which was attributed to human error. This result is consistent with Newton’s second law of motion where Force applied is directly proportional to acceleration when mass is constant.
Works Cited
Goswami, Amit. The Physicists' View of Nature: From Newton to Einstein. New York: Springer Publishers, 2000. Print. : 40-54
