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AP Physics C: Mechanics
2.5 Newton’s Second Law
1.4 Reference Frames and Relative Motion
Multi-Unit
AdvancedMCQMathematicalConceptual21k
A large hollow rectangle represents an elevator cabin. In the upper right outside the cabin, a straight horizontal arrow points to the right labeled a_x, and a vertical arrow points upward labeled a_y. A small coordinate axis in the lower left corner shows an arrow pointing right labeled \hat{i} and an arrow pointing upward labeled \hat{j}. From the center of the top horizontal edge of the cabin, a straight thin line segment extends downward and slightly to the left, terminating at a solid shaded circle representing a pendulum bob. A vertical dashed line extends straight downward from the attachment point on the ceiling. An arc between the vertical dashed line and the thin line segment is labeled \theta. A downward vertical arrow next to the cabin is labeled g. No other labels, lines, text, or axes appear.
A pendulum hanging inside an elevator accelerating both horizontally and vertically.
An elevator cabin accelerates with a constant acceleration \(\vec{a} = a_x\hat{i} + a_y\hat{j}\) relative to the ground, where \(a_x > 0\), \(a_y > 0\), and the acceleration due to gravity is \(\vec{g} = -g\hat{j}\). Inside the cabin, a pendulum consisting of a small bob of mass \(m\) suspended by a light string hangs at rest relative to the cabin, deflected at a constant angle \(\theta\) from the downward vertical. Which row in the table correctly classifies the reference frame of the elevator cabin and provides the expression for \(\tan\theta\)?

Reference Frame of Cabin\(\tan\theta\)
(A)Inertial\(\dfrac{a_x}{g - a_y}\)
(B)Inertial\(\dfrac{a_x}{g + a_y}\)
(C)Non-inertial\(\dfrac{a_x}{g - a_y}\)
(D)Non-inertial\(\dfrac{a_x}{g + a_y}\)

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