Packages ride on a motorized conveyor belt that moves due east in a warehouse

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Packages ride on a motorized conveyor belt that moves due east in a warehouse. For a particular package the following measurements are made at the same instant: • An overhead camera fixed to the building records the package’s velocity as

1.85\,\text{m}\!\cdot\!\text{s}^{-1}

east with an uncertainty of

\pm0.05\,\text{m}\!\cdot\!\text{s}^{-1}

. • A sensor attached to the belt records the package’s velocity relative to the belt as

0.62\,\text{m}\!\cdot\!\text{s}^{-1}

east with an uncertainty of

\pm0.03\,\text{m}\!\cdot\!\text{s}^{-1}

. The belt is designed to operate at

1.20\,\text{m}\!\cdot\!\text{s}^{-1}

east with an allowable tolerance of

\pm0.05\,\text{m}\!\cdot\!\text{s}^{-1}

. (a) Determine the conveyor belt’s speed relative to the warehouse. Include units and clearly indicate the direction. (b) Propagate the given measurement uncertainties to find the uncertainty in the belt’s speed you calculated in part (a). State any assumptions you make in combining uncertainties. (c) Based on your result and its uncertainty, assess whether the belt is operating within the specified tolerance. Support your conclusion with quantitative reasoning.

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