Newton's 2nd Law Lab
10/13/2018
Research Question: How to Net Force and Mass effect Acceleration on a System?
10/13/2018
Research Question: How to Net Force and Mass effect Acceleration on a System?
This lab consisted of two experiments, one to test the effects of net force on acceleration and one to test the effects of mass on acceleration. For the net force experiment, The force exerted on the system was the independent variable and the system acceleration was the dependent variable, with the total mass of the system being kept constant. For the mass experiment, The the system mass was the independent variable and the system acceleration is the dependent variable, with the net force being kept constant.
To collect data, a near-frictionless rolling cart was placed on an elevated track, with a string with a hanging pass attached to the cart through a pulley. The string was attached so that as the weight would fall down, it would pull the cart horizontally across the track. Therefore, gravity would exert a constant force on the system. To change the total force on the system, masses are moved between the hanging mass and the cart. This converts some of the system's mass into force, while keeping the total mass constant. When changing the mass of the system, masses were only added to the cart and not the hanging weight as to not change the net force on the system.
For both experiments, the acceleration of the system was calculated using the time the cart took to roll 85 cm along the track starting from rest. To test the effect of net force, 6 different masses exerting 0 to 0.98 Newtons of force (0 to 100 grams) on the system were hung from the string. The total mass of the system each time was 400 grams. The cart was let go from rest for each different hanging mass and it's acceleration with each mass created a data point. To test the effect of total mass, 5 masses were placed on the cart, making the system mass between 400 and 800 grams. A constant 0.98 Newton force from the 100g mass on the hanging mass on each trial propelled the car down the track.
To collect data, a near-frictionless rolling cart was placed on an elevated track, with a string with a hanging pass attached to the cart through a pulley. The string was attached so that as the weight would fall down, it would pull the cart horizontally across the track. Therefore, gravity would exert a constant force on the system. To change the total force on the system, masses are moved between the hanging mass and the cart. This converts some of the system's mass into force, while keeping the total mass constant. When changing the mass of the system, masses were only added to the cart and not the hanging weight as to not change the net force on the system.
For both experiments, the acceleration of the system was calculated using the time the cart took to roll 85 cm along the track starting from rest. To test the effect of net force, 6 different masses exerting 0 to 0.98 Newtons of force (0 to 100 grams) on the system were hung from the string. The total mass of the system each time was 400 grams. The cart was let go from rest for each different hanging mass and it's acceleration with each mass created a data point. To test the effect of total mass, 5 masses were placed on the cart, making the system mass between 400 and 800 grams. A constant 0.98 Newton force from the 100g mass on the hanging mass on each trial propelled the car down the track.
Net Force vs. Acceleration
Force (N) |
Acceleration (cm/s/s) |
System Mass (g) |
400 |
||
0.196 |
42.5 |
400 |
0.392 |
66.4 |
400 |
0.588 |
141 |
400 |
0.785 |
197 |
400 |
0.980 |
215 |
400 |
Total Mass vs. Acceleration
Force (N) |
Acceleration (cm/s/s) |
System Mass (g) |
0.98 |
177 |
400 |
0.98 |
59.5 |
500 |
0.98 |
126 |
600 |
0.98 |
96.1 |
700 |
0.98 |
93.3 |
800 |
The relationship between net force and acceleration is linear, and for every newton of force the object will accelerate 235cm/s/s more. The Y-intercept of this model matches the recorded data point but not the best fit line as an object with no net force will remain at a constant velocity because of Newton's 1st Law.
Even with the one outlier data point of the acceleration at 500g, it is clear that as the mass of he system increases, the acceleration decreases. However, a simple linear fit would not be appropriate due to its intercepts. With a decreasing linear model, the the mass would increase until the line dipped below the x-axis, which would imply that above a certain mass, objects would accelerate in the opposite direction of net force. Also, all objects have mass, so a Y intercept would not be appropriate. An inverse model does not have intercepts, but asymptotes which more accurately describe the logical behavior of objects with extremely large and small masses. Note that even though this graph may appear to have a Y intercept, the graph excludes mass values less than 400 grams, as that was the least massive the cart could be when testing.
Because the Newton is a derived unit, both of these models can be combined into one elegant equation describing the relationship between force, mass, and acceleration which is Newton's 2nd Law:
Even with the one outlier data point of the acceleration at 500g, it is clear that as the mass of he system increases, the acceleration decreases. However, a simple linear fit would not be appropriate due to its intercepts. With a decreasing linear model, the the mass would increase until the line dipped below the x-axis, which would imply that above a certain mass, objects would accelerate in the opposite direction of net force. Also, all objects have mass, so a Y intercept would not be appropriate. An inverse model does not have intercepts, but asymptotes which more accurately describe the logical behavior of objects with extremely large and small masses. Note that even though this graph may appear to have a Y intercept, the graph excludes mass values less than 400 grams, as that was the least massive the cart could be when testing.
Because the Newton is a derived unit, both of these models can be combined into one elegant equation describing the relationship between force, mass, and acceleration which is Newton's 2nd Law:
F=ma or a=F/m
Where force is in Newtons, mass is in kilograms, and acceleration is in meters/second/second.
Where force is in Newtons, mass is in kilograms, and acceleration is in meters/second/second.
This online lab by Pivot Interactives, had advantages and disadvantages over a real life lab. Each trial was recorded as a video, with a properly calibrated ruler and timer onscreen. These features made analyzing the data very similar to analyzing data from a video analysis, which yielded more precise values than simply timing and measuring the cart by hand. However, each data point (EG 400g system mass with 0.98N net force) only had one video attributed to it. Consequently, it was impossible to conduct multiple trials, which created a large amount of uncertainty. This uncertainty clearly influenced the data of the Mass vs. Acceleration experiment, with the 500g cart accelerating much less than predicted. If multiple videos of each mass and force were posted with the lab, taking the average of these times would yield more accurate acceleration. Alternatively, Pivot could include only the video of each weight and mass which represented the median of multiple trials. Other sources of uncertainty include how the cart was released from its initial position. To release the cart, a string tying it to the track was cut by hand, which could influence the starting velocity when the cart is released. If the hand accidentally moves backward as it cuts the string, the cart could be pulled slightly back and travel a slightly longer distance down the track, increasing the measured time and acceleration. To solve this problem, a releasing pin could be used to release the cart, and this would not introduce any unwanted acceleration into the system.