# Lab Report

Experiment – Newton’s Second Law

OBJECTIVE
To investigate the validity of Newton’s 2nd law of motion
APPARATUS
· Vernier Logger Pro
· Motion Detector
· Vernier LabPro Interface
· Linear Air Track system
· Cart with a flag on top
· Pulley
· String
· Various masses
PROCEDURE
The set-up of the system will be shown in class and the data collection will be executed based upon the instructions below.
PART A
1) Using an electronic balance, find the mass of the cart and record it in Table I (given below)
2) Connect the USB link of the interface to your laptop first and then launch the Logger Pro
3) Check the motion detector to make sure that it is facing to the cart with a slight upward angle.
4) One student should hold the cart and the other should attach a small mass (record this mass in table I) to the string that is going over the pulley on the other end of the track
5) While still holding the cart, turn on the vacuum so that air starts flowing out of the air track
6) Click “Start” on Logger Pro and release the cart. Just before the cart hits the other end of the track, click “stop”.
7) Repeat steps 4) to 6) with 2 more different masses (hanging)
Table 1: Mass of the cart (including the flag) 0.1907 kg

ANALYSIS

1. Draw a schematic diagram of the system and label all the forces (ignore friction between cart and the air-track)

2. Draw a free body diagram of the cart

3. Draw a free-body diagram of the hanging mass

4. Write the equations for the net force for both masses separately. Eliminate the tension force to find the theoretical acceleration of the system

This is equation one.

This is equation two.

This is the result of setting the two equations equal to each other. The only unknown is the acceleration; therefore, we can find acceleration using this equation.

Theoretical Acceleration: Calculations

5.
Test the precision of your data by determining the percentage difference for acceleration:

What do the values mean?
The values of the percentage difference measure the precision of the results; how close the measurements are among themselves. The magnitude shows the percentage of the average measurement that is the difference between the highest and lowest values. Therefore, the higher the percentage, the lower the precision.

6. Test the accuracy of your results by determining the percentage error for acceleration:

Percent error = (estimate - actual)
--------------------------- * (100)
(actual)

1) Percent Error = (0.1802 - 0.1902)
------------------------ * 100
(0.1902)

= -0.05257 * 100
= -5.257 %

2) Percentage Error = (0.2926 - 0.2939)
------------------------ * 100
(0.2939)

= -0.004423 * 100
= -0.4423 %

DISCUSSION QU
ESTI ONS
1. Describe the relationship between the net force acting on an object and the acceleration of the object when the mass of the object is constant, with the support of your data.

2. Describe the relationship between the mass of an object and its acceleration when the net force is constant, with the support of your data.

3. Discuss the precision and accuracy of your experiment, based upon your calculation in step #4 of the data analysis.

The precision of the experiment is based on the calculations of percentage difference. Overall, moderate precision was achieved in this lab. The highest percentage difference, which would refer to the least precise result, was 16.42%. However, the difference between the largest and smallest value in this test was only 0.0414m/s/s. From this, one can conclude that this result seemed to be an outlier, in the way there was a large lack of precision in this result compared to the majority of the other results which had percentage differences of approximately 0.2048%. However, since all the tests were done in a uniform matter, the wide spread of percentage difference calculations shows room for possible systematic error. If one was to redo this test again, he or she would have to see what factors could have affected the differentiation in the results. Overall, the maximum difference per test was a span of 0.067m/s/s which shows for moderate precision.
The accuracy of the results is based on the calculations of percentage error. The most common percentage error was roughly -0.3000%. From this, one can conclude that moderate-to-high accuracy was also achieved in this lab. The majority of percentage error results were consistent with each other, with the exception of the first result that had a percentage error of 5.193%. This might have been due to the fact that it was our very first run through, and might not have been done with as much precision as the rest.

4. Provide some possible reasons for the difference between the theoretical value of acceleration and experimental value of acceleration of the cart
1. Friction Force- When calculating the theoretical acceleration, the friction force was not included. The mass of the pulley was also assumed to be negligible. However, this is not the real case with the lab- the pulley was not frictionless nor mass less. Therefore, the lack of these factors in our calculations might have affected the magnitudes of the theoretical accelerations.
2. The properties of the string- In order for there to be one acceleration, it was assumed that the string would not be able to stretch. However, it is quite possible that the string did stretch (especially since it had been used a number of times), no matter how small of an amount, thus meaning that the hanging mass might have accelerated at a fractionally slightly different rate than the cart. In the calculations of the theoretical acceleration, the string was also assumed to not have mass, when in reality this is not the case. However, these factors are very minute and may not have played a major role in skewing the data.
3. Air Resistance- In calculating the theoretical acceleration, air resistance was ignored (as well as all other possible forces aside from Normal Force, Force of Gravity and the tension Force). To reach the equation for theoretical acceleration, we had to assume that the net force acting on the hanging mass was the force of gravity- the tension force. However, with air resistance, this would have been the force of gravity-tension force-air resistance; creating a different numerical value.

5. Assume that there is a frictional force between the track and the cart and the coefficient of friction between the two is 0.015. If the mass of the cart (including the flag) is 95.2 g and the hanging mass is 12.5 g. Predict the rate of acceleration, based upon the given information. Make sure that free body diagrams are drawn and proper principles are applied and steps are provided.

6. Given an example of an application of Newton’s First Law and Third Law of Motion with sufficient explanation.
Newton's First Law states that "every body continues in its state of rest of or uniform motion in a straight unless it is acted upon by an unbalanced force". In simple words, this means that whether a body is moving or not, if it's forces are balanced (when there is no acceleration), the body will continue to move in a uniform pattern until a new force acts upon it, putting the body out of equilibrium and into a state of acceleration or deceleration. An example of this law is the seat belt system that equips all vehicles. During a car accident, the vehicle meets the oppositional force of another car, which radically decelerates the initial car in a split second. The occupants of the car still have the inertia from before the accident, so in correlation with Newton's First Law, their bodies want to keep moving forward. It is at this point that seat belt technology takes effect by safely holding back the occupant, preventing them from getting injured. Seat belts therefore successfully counter the effects of Newton's First Law by safely adjusting the occupant's inertia to that of the car.
Newton's Third Law states that, "for every action force, there exists a reaction force that is equal in magnitude bu opposite in direction, and acts upon the first body". The basic idea behind this law, is that forces in nature always exist in pairs.

Where, one is the force exerted on body 1 by body 2 and one is the reaction force exerted by body 2 onto body 1. A variety of action-reaction force pairs are evident in nature. An application of this law is the propulsion of a fish through the water. A fish uses its fins to push the water backwards. This push on the water, will cause the water to accelerate because it is being acted on by an unbalanced force (Newton's Second Law). Since the forces result from mutual interactions, the water must also be pushing forwards on the fish, thus causing the fish to accelerate in the opposite direction. The size of the force on the water equals the size of the force on the fish. The direction, however, of the force on the water (backwards) is opposite of the direction of the force on the fish (forwards). Action reaction force pairs make it possible for fish to swim.

Conclusion:
Write brief and concise statements to address the objective of this law.

Greg: Second part: #6 (newton's first law), #3 First Part: #6, Conclusion
Zeenia: Diagrams,Second Part: #1, #2, #5,#4, #6 (newton's third law) First Part:#5, #3,