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The cart is initially at rest on a horizontal surface and rolls without slipping when released. The inertia...

The cart is initially at rest on a horizontal surface and rolls without slipping when released. The inertia of the cart's wheels is negligible. Students have access to common laboratory equipment to make measurements of components of the system.

By collecting the appropriate data, the students can determine the relationship between the acceleration of the cart and the net force exerted on the cart.

Which of the following graphs should the students produce to show the correct relationship?
y-axis is (a)
x-axis is (F)

Select {responseValue}
Select {responseValue}

Answer

To determine the relationship between the acceleration (a) of the cart and the net force (F) exerted on it, we can utilize Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this scenario, the cart is initially at rest and rolls without slipping when released. Therefore, the following points are relevant for the analysis: 1. The net force (F) is proportional to the acceleration (a) of the cart. 2. As the force exerted on the cart increases, the acceleration of the cart also increases in a linear fashion. 3. The mass (m) of the cart is a constant value, so for a constant mass, the relationship between force and acceleration is linear. Given that the y-axis represents acceleration (a) and the x-axis represents net force (F), a graph illustrating this relationship would be a straight line through the origin. In summary, the graph that the students should produce would be a straight line with the following characteristics: - The y-axis (acceleration a) increases as the x-axis (net force F) increases. - The graph should start at the origin (0,0) since a net force of zero results in zero acceleration. - The slope of the line represents the inverse of the mass of the cart (1/m). A steeper slope indicates a lower mass, while a less steep slope indicates a higher mass. The correct representation of the graph will thus be linear, illustrating that as net force increases, acceleration also increases proportionally.

The students should produce a linear graph with:

  • y-axis: acceleration (a)
  • x-axis: net force (F)
  • The graph starts at the origin (0,0) and indicates that a greater net force results in greater acceleration.

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