Introduction
The present laboratory work studied the relationship patterns between the force applied to the cart and its mass. A smart cart moves vertically on a table by applying a pulling force; reinforcement is provided by hanging more weights. The work tests the relationship between the acceleration of the cart and the force applied to it, as well as the acceleration of the cart as a function of its mass.
Numerical data were collected in two experiments. First, the cart’s mass was changed (experiment I), and acceleration information was collected while holding the applied force constant. Second, the mass of the suspensions was changed (values of the applied force), but the cart’s mass remained unchanged, and information about acceleration was collected (experiment II).
Data
Table 1. Results of the experiment with a change in the cart mass while maintaining the applied force
Table 2. Results of the experiment with a change in the suspension mass with a change in the applied force
Results
Effect of Cart Mass on Acceleration
The regression straight-line equations for velocity dependence were plotted at the initial stage in Capstone, which was used to find the slopes that characterize the cart’s acceleration. The acceleration and varying cart mass values were plotted on the scatter plot shown in Figure 1. It can be seen that as the mass of the cart increases, there is a decrease in acceleration.
The slope was calculated for all points, but the logic of its calculation can be shown for the first two: see the equation. The relationship between the variables turns out to be linear, as follows from the equation 
. The model built is highly reliable and covers up to 94% of the data variance, and with each gram increase in cart weight, there is a 0.0019 m.s-2 drop in acceleration.
Influence of Applied Force on Acceleration
In the second part of the experiment, it was necessary to determine the dependence of acceleration on the applied force. As a measure of force, we used the values of hanger masses, which can be entered into the equation 
(equation [2]) to determine the value of the applied force (OpenStax, 2019). Figure 2 shows a visual representation of this dependence: it can be seen that the data form an almost linear upward trend, which means that when the applied force increases, the acceleration of the cart is observed to increase. In particular, the model built is highly robust and covers up to 93% of the variance of the data, and when the applied force is increased by every N, there is an increase in acceleration of 0.0995 m.s-2.
Answers to Questions
Factors Influencing Cart Motion
The cart’s motion is influenced by its total mass and the value of the force applied to it that motivates the motion. Additional factors are air resistance, friction against the road surface, and the slope of the horizontal surface.
Uncontrollable or Non-Quantifiable Factors
Gravity and air resistance are difficult to quantify and control, so experimenting with identical conditions makes these factors controllable variables.
Independent and Dependent Variables and Relationships Between Them
As the results showed, the mass of the cart, the applied force, the acceleration, and, therefore, the velocity were directly related. The first two factors can be called independent variables, and the second two are dependent variables.
Conclusion
The results of the present laboratory work confirmed the expected assumptions and showed that as the applied force increases and the cart’s mass decreases, its acceleration increases; the opposite is also true. Nevertheless, the shape of the dependencies was not perfectly linear, which could be the cause of measurement errors or random instrumental errors. However, the high values of the determination coefficients confirmed the regression equations’ overall reliability. It follows from this that if the goal is to increase the acceleration of an object moving horizontally, it is necessary to decrease its mass and increase the value of the resulting force.
Reference
OpenStax. (2019). Mass and weight. Libre Texts Physics. Web.