Good Example Of Newton’s Second And Third Laws Report

INTRODUCTION

Newton’s second law postulates that acceleration of a body that results from a force being exerted on the body is inversely proportional to its mass and directly proportional to the force exerted. The assumption of newton's second law of motion is based on massless and frictionless bodies. The purpose of this report is to present the findings of an investigation to establish the force exerted on a spring. A spring can be considered to be an instrument that is used in the storage of elastic potential energy. The results will be tested to establish if they conform to Hooke’s law. The string does not stretch and as a result the acceleration of the string is equal to the acceleration of the system.
The investigation is called the Atwoods machine and the loggerpro software is used to measure the acceleration. Newton's third law is an expansion of the second law and it postulate that for every action there is an equal and opposite reaction. That is, when a force is exerted on an object, the object will exert an equal amount of force on something else.

DATA

PART ONE.
Trial one
Trial two
PART TWO. (Springs in series)
Uncertainty 0.5mm
Springs parallel
PART THREE (springs in parallel)
DATA ANALYSIS
The first part of the investigation has the objective of obtaining the theoretical value for acceleration through the use of loggerpro software which requires the mass and standard deviation of a falling object. The formula to be used is a= g (M-m)/M+m. The theoretical value of acceleration is obtained from the formula to be 0.8596m/s2.

The percentage error is obtained by diving the standard deviation with the mean and converting the result to percentage.

The value is obtained to be 10.1% error.
The percent difference between the experimental value and the theoretical value can then be computed. It is obtained by subtracting the experimental value from the theoretical value and then dividing by the theoretical value. The result is multiplied by 100 so as to be in percentage form. The difference is 63.65%
When considering spring in series, the uncertainty in the measurement of the length of the wire is approximated to be 0.5mm on both the negative and the positive sides.
Hooke's law postulates that the constant of a force on a spring is directly proportional to its length. Therefore, we will be using Hooke's law to calculate the spring constant.
We have been given the spring constant which is 41.8 N/M and the change in length is obtained to be 0.012M. Therefore, the force due to the first spring is obtained to be 0.5016N. The force due to the second spring is obtained similarly because we have the spring constant that is 13 N/M. The force due to the second spring is obtained to be 0.156N.
The total spring constant for the springs in series is obtained to be 9.916 N/M.

The spring in parallel.

For the springs in parallel, the total spring constant is obtained by summing the individual spring constants. The total spring constant is therefore obtained to be 41.8+13= 54.8 N/M.

DISCUSSION:

In part one the standard deviation indicate that there were differences between the recorded values and the average value of acceleration. It is important for the results to be consistently similar so as to reduce the amount of standard deviation which is a measure of the accuracy of the results. Replication of the experiment severally is one way of reducing the standard deviation. The guidelines of the experiment should be followed and precautions set out in the experiment procedure observed. Use of new springs is also recommended so as to reduce systematic errors.
The investigator should also ensure that he/she is using the most current apparatus so as to reduce the amount of errors.
Newton’s second law is used in the computation of the force exerted on a spring by use of the acceleration of the spring and the mass attached on the spring. The force obtained is assumed to be equal to the force on the spring according to Newton’s third law. The force is then used in the computation of the spring constant according to Hooke’s law.
Vertically, the unloaded spring did not stretch at all when under zero load. Thus the stretch is less than the length of the spring when it was flat on the table. The spring can therefore be assumed to be massless.
The investigation was successful in indicating the nature of the relationship of springs in series and also in parallel. However, the difference of over 63% was above the permitted level of difference which is in most cases 15%. The possible sources of these differences is systematic errors in the execution of the experiment and also experimental errors in the process of concluding the experiment.

CONCLUSION

The experiment was instrumental in displaying how the total spring constant can be computed from individual spring constants when the springs are connected in series and also when the springs are connected in parallel. The experiment made use of both newton's second law of motion and also Hooke's law on spring constant. The experiment, furthermore enhanced my understanding of the formulas for computing total spring constant when the springs are connected in series and parallel. The demonstration of the forces acting upon the springs in an Atwoods machine was also understood. The experiment could be improved upon if systematic errors due to faulty machines could be avoided.