Maximum speed of a cylinder dropped on a spring

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SUMMARY

The discussion focuses on calculating the maximum speed of a 5kg cylinder dropped from a height of 100mm onto a spring with a stiffness of 1.8 kN/m. The participant confirmed the maximum compression of the spring as 0.106m and the spring deflection at maximum velocity as 27.2mm. The participant's calculation for maximum velocity using the energy conservation principle resulted in 1.4 m/s, while the correct answer is 1.49 m/s. The confusion lies in understanding when the cylinder's speed is at its maximum, which is before the spring fully compresses.

PREREQUISITES
  • Understanding of gravitational potential energy (Ep = mgh)
  • Familiarity with kinetic energy equations (Ek = (1/2)mv^2)
  • Knowledge of spring energy equations (Es = (1/2)kx^2)
  • Basic principles of force and acceleration (F = kx)
NEXT STEPS
  • Review energy conservation principles in mechanical systems
  • Study the dynamics of spring-mass systems
  • Learn about maximum velocity calculations in oscillatory motion
  • Explore the effects of damping on spring systems
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and energy conservation in spring-mass systems will benefit from this discussion.

Rajveer97
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Homework Statement


Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the cylinder

I just need to confirm part iii

Homework Equations


Ep=mgh
Ek=(1/2)mv^2
Es=(1/2)kx^2
F=kx

The Attempt at a Solution


For part (i) I got 0.106
(ii) 27.2mm
For (iii) I did Ep=Ek which gave me v=1.4. The correct answer is supposed to be 1.49, I feel my answer is similar is wrong but similar just by chance. I just don't fully understand the question, when will the speed be maximum, before or after deflection? I feel before but I'm unsure.

Thanks
 
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Hi,
You don't really specify what you did. Could there be a term missing in your 'doing'?
 
BvU said:
Hi,
You don't really specify what you did. Could there be a term missing in your 'doing'?
Well I meant I basically made gravitational potential energy equal kinetic energy and solved for v
 
Es ?
 
Rajveer97 said:
I did Ep=Ek
What, roughly, is the cylinder's acceleration very shortly after hitting the spring?
 

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