A 2-kg sphere A is connected to a fixed Point O by an inextensible cord of length 1.2 m. The sphere is resting on a frictionless horizontal surface at a distance of 1.5 ft from O when it is given a velocity \mathbf{v}_0 in a direction perpendicular to line OA. It moves freely until it reaches position A′, when the cord becomes taut. Determine the maximum allowable velocity \mathbf{v}_0 if the impulse of the force exerted on the cord is not to exceed 3 N⋅s.
Question 13.152: A 2-kg sphere A is connected to a fixed Point O by an inexte...
For the sphere at A^{\prime} immediately before and after the cord becomes taut
\begin{gathered}m \nu_{0}+F \Delta t=m \nu_{A^{\prime}} \\+⦨ m \nu_{0} \sin \theta-F \Delta t=0 \quad F \Delta t=3 \mathrm{~N} \cdot \mathrm{s} \\m=2 \mathrm{~kg} \\2\left(\sin 65.38^{\circ}\right) ν_{0}=3\end{gathered}
\nu_{0}=1.650 \mathrm{~m} / \mathrm{s}\blacktriangleleft
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