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AP Physics C: Mechanics
2.5 Newton’s Second Law
1.3 Representing Motion
Multi-Unit
AdvancedMCQGraphicalProportional Analysis24.6k
A horizontal surface is depicted as a horizontal line. Resting on this surface is a rectangular cart labeled \(M_c\), with two small circular wheels touching the horizontal line. A thin horizontal line representing an ideal string extends from the right vertical face of the cart toward the top edge of a circular pulley mounted at the right edge of the horizontal surface. The string passes over the pulley and hangs vertically downward. Attached to the lower end of the vertical portion of the string is a hanging rectangular block labeled \(m_h\). A vertical arrow pointing downward is placed to the right of the hanging block and is labeled \(g\). No other labels, lines, text, or axes appear.
A cart on a horizontal track connected to a hanging block via an ideal pulley.
A cart of mass \(M_c\) on a frictionless horizontal surface is connected by an ideal string passing over a massless, frictionless pulley to a hanging block of mass \(m_h\). A student measures the magnitude of the system acceleration \(a\) as a function of the parameter \(f = \dfrac{m_h}{M_0}\) under two different experimental procedures:

Procedure 1: The total mass of the system is held constant at \(M_0\) such that \(M_c + m_h = M_0\), and mass is transferred from the cart to the hanging block to increase \(f\) from \(0\) to \(1\).

Procedure 2: The mass of the cart is held constant at \(M_c = M_0\), and mass is added exclusively to the hanging block to increase \(f\) from \(0\) to \(1\).

Which of the following graphs best represents the acceleration \(a\) as a function of \(f\) for Procedure 1 (solid line) and Procedure 2 (dashed line)?

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