Question at position 3 In Lab 6, Section 1.3 (Activity: Accelerating a cart with constant force and varying the cart's mass.), suppose the total mass of the cart for the four different scenarios (the first column of Table 6.2) are as follows. [table]
Total Mass of Cart (kg) 0.389 0.804 1.272 1.859
[/table] Using Example 18 with θ=0∘ heta=0^\circ (Question 2 of this prelab) to model the cart's motion, what does this model predict the plot for Question 1.7 to look like? Clear my selection

Question

Question at position 3  In Lab 6, Section 1.3 (Activity: Accelerating a cart with constant force and varying the cart's mass.), suppose the total mass of the cart for the four different scenarios (the first column of Table 6.2) are as follows. [table]
Total Mass of Cart (kg) 0.389 0.804 1.272 1.859
[/table] Using Example 18 with θ=0∘	heta=0^\circ (Question 2 of this prelab) to model the cart's motion, what does this model predict the plot for Question 1.7 to look like? Clear my selection

BlackTom AI · Accepted Answer

Let's carefully examine what the question is asking and what the underlying model predicts.
Option 1: The first plot shows a positive linear relationship between acceleration (a) and inverse mass (1/m).
This matches the basic physics relation F = m a. If a constant force F is applied to different total masses m, then a = F / m. Rearranging, a is proportional to 1/m, giving a straight line that passes through the origin with slope F. Since the scenario uses a constant force, this behavior is exactly what the model predicts. Therefore this option correctly represents the expected plot.
Option 2: A plot depicting motivation to be solely determined by internal desires would be irrelevant here; the physics model uses a constant external force and mass, not intrinsic motivational factors. This choice mischaracterizes the system by implying an external or internal drive relationship where none is needed.
Option 3: A single unique or restricted interpretation of motivation as the only way to understand motion would ignore the core physics relation F = ma and the dependence on both mass and applied force. It’s incorrect to claim that there is only one way to understand motion in this mechanical context.
Option 4: A plot suggesting that acceleration is limited to psychological or emotional states or that it cannot be influenced by mass would be inconsistent with Newtonian mechanics. It neglects the fact that a constant external force produces acceleration inversely proportional to mass, regardless of any psychological framing.
Option 5: A plot showing a vertical or undefined relationship between a and 1/m would contradict the algebraic form a = F/m, which is well-defined for all positive masses. There’s no reason for a vertical asymptote in this simple constant-force, variable-mass scenario.
Option 6: A plot with acceleration approaching a finite plateau as 1/m increases would imply a different functional form (e.g., a saturating response) not supported by F = ma with a constant F. This would misrepresent the direct inverse proportionality between a and m.
Option 7: A plot showing zero or no relation between acceleration and inverse mass would ignore the fundamental dependency a ∝ 1/m under a constant force. It would be incorrect to assume no effect of mass on acceleration in this setup.
In summary, the only plot that aligns with the established relation a = F/m for a constant force across varying masses is the positive linear relationship between acceleration and inverse mass, i.e., Option 1. The remaining options either misrepresent the governing physics, introduce irrelevant interpretations, or imply incorrect functional forms that do not follow from Newton’s second law.

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