QUESTION
An object of mass $M$ moves in one dimension along the $x$-axis. A conservative force $F(x)$ is exerted on the object. The potential energy $U(x)$ associated with this force as a function of position $x$ is shown in graph 1. A student used the potential energy graph to construct the graph of $F(x)$ as a function of $x$ shown in graph 2 . Are these graphs consistent with one another, and if not, what is the error? Graph 1
Graph 2
A For $0<x<2 \mathrm{~m}$ and $3 \mathrm{~m}<x<4 \mathrm{~m}$, the graph of $F(x)$ should be curved, not constant. B For $0<x<2 \mathrm{~m}, F(x)$ should be negative, and for $3 \mathrm{~m}<x<4 \mathrm{~m}, F(x)$ should be positive. (C) For $0<x<2 \mathrm{~m}, F(x)$ should be negative because the slope of $U(x)$ is negative. (D) For $3 \mathrm{~m}<x<4 \mathrm{~m}, F(x)$ should be positive because $U(x)$ is positive. E The two graphs are consistent with each other.
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