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AP Physics C: Mechanics
4.4 Elastic and Inelastic Collisions
4.3 Conservation of Linear Momentum
AdvancedMCQMathematicalProportional AnalysisConceptual24.4k
A horizontal schematic of the spacecraft system before separation. On the left is a larger rectangular block labeled Main Capsule. On the right is a smaller rectangular block labeled Canister. Between the adjacent vertical faces of the two blocks is a horizontal coiled spring shown in compression. A horizontal dashed centerline passes through the centers of both blocks. Above the spring, a centered label indicates U_0. No other labels, lines, text, or axes appear.
Spacecraft capsule and fuel canister with an internal compressed spring mechanism.
A spacecraft of total mass \(M\) is at rest in an inertial reference frame in deep space. The spacecraft consists of a main capsule and an attached fuel canister connected by an internal spring mechanism that stores elastic potential energy \(U_0\). When the mechanism is released, the spring expands and pushes the canister away along a straight line, converting all stored energy \(U_0\) into the kinetic energy of the separating capsule and canister.

Three different canister designs are evaluated, each using an identical spring mechanism with the same initial stored energy \(U_0\):

Design I: The canister has mass \(m_1 = \dfrac{1}{4}M\), leaving a capsule of mass \(\dfrac{3}{4}M\).

Design II: The canister has mass \(m_2 = \dfrac{1}{2}M\), leaving a capsule of mass \(\dfrac{1}{2}M\).

Design III: The canister has mass \(m_3 = \dfrac{3}{4}M\), leaving a capsule of mass \(\dfrac{1}{4}M\).

Which of the following correctly ranks the final kinetic energy of the main capsule, \(K_1\), \(K_2\), and \(K_3\), in the original reference frame after separation for the three designs?

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