GATE ME 2020 Set 2 — Question 50
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Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
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Question
A rigid block of mass having velocity strikes a stationary block of mass after traveling along a frictionless horizontal surface as shown in the figure.
The two masses stick together and jointly move by a distance of further along the same frictionless surface, before they touch the mass-less buffer that is connected to the rigid vertical wall by means of a linear spring having a spring constant . The maximum deflection of the spring is ______ cm (round off to 2 decimal places).
Correct answer
0.98 to 1.02
Solution
1.Velocity before collision: Since the surface is frictionless, the velocity of remains until it hits .
2.Collision: The collision is perfectly inelastic (they stick together). By conservation of linear momentum:
3.Post-collision movement: The combined mass moves at a constant velocity of (frictionless) before hitting the spring buffer.
4.Spring compression: At maximum deflection , all kinetic energy of the combined mass is converted into spring potential energy:
5.Conversion to cm: .
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