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AP Physics C: Mechanics
4.3 Conservation of Linear Momentum
4.2 Change in Momentum and Impulse
IntermediateMCQMathematicalConceptual15.2k
A graph of horizontal contact force \(F_x\) on the vertical axis versus time \(t\) on the horizontal axis on bare axes with no gridlines. The horizontal axis has tick marks at \(0\), \(t_0\), and \(T\). The vertical axis has a central origin at \(0\), a positive tick mark labeled \(+F_{\max}\), and a negative tick mark labeled \(-F_{\max}\). A horizontal axis line runs at \(F_x = 0\). From \(t = 0\) to \(t = T\), a solid curve starts at \((0, 0)\), curves upward to a smooth peak at \((t_0, +F_{\max})\), and returns to \((T, 0)\), labeled Cart 1. A dashed curve starts at \((0, 0)\), curves downward to a smooth trough at \((t_0, -F_{\max})\), and returns to \((T, 0)\), labeled Cart 2. The two curves are symmetric reflections of each other across the horizontal axis. No other labels, lines, text, or axes appear.
Force versus time for Cart 1 and Cart 2 during the collision.
Cart 1 of mass \(m\) and Cart 2 of mass \(2m\) travel along a horizontal, frictionless surface and collide. A sensor records the horizontal contact force \(F_x\) exerted on each cart as a function of time \(t\) during the collision interval from \(t = 0\) to \(t = T\). The graph displays two symmetric force curves: the force on Cart 1 reaches a maximum of \(+F_{\max}\), while the force on Cart 2 reaches a minimum of \(-F_{\max}\), with the two curves having identical shapes reflected across the time axis. Which of the following statements correctly interprets the collision data shown in the graph?

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