A particle of mass 2 kg is attached to a light inextensible string. Just before the string becomes taut, the particle has speed 10 m/s and its velocity makes an angle 60° with the string, with the component along the string directed outward. If the magnitude of the impulsive tension when the string suddenly becomes taut is N N·s, find N.
Physics · Center of maas , Momentum and Collision · impuse and question based on it
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Question

A particle of mass 2 kg is attached to a light inextensible string. Just before the string becomes taut, the particle has speed 10 m/s and its velocity makes an angle 60° with the string, with the component along the string directed outward. If the magnitude of the impulsive tension when the string suddenly becomes taut is N N·s, find N.

Physics · Center of maas , Momentum and Collision · impuse and question based on it

G1 Physics · Accepted Answer

Resolve the particle's velocity into components parallel and perpendicular to the string. The outward component along the string is u(radial) = 10cos60° = 5 m/s. When the inextensible string suddenly becomes taut, the outward radial component must instantaneously become zero, while the perpendicular component is unaffected by the impulsive tension. Therefore change in radial velocity is 0−5 = −5 m/s. The impulse magnitude is J = m|Δv(radial)| = 2×5 = 10 N·s. Hence N = 10.