Finding the Speeds of Objects in a Spring System

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SUMMARY

The discussion focuses on calculating the speeds of two objects, A (1 kg) and B (3 kg), after a spring (k=1250 N/m) between them expands to its unstretched position. Using the work-energy principle, the initial potential energy stored in the spring is converted into kinetic energy of the objects. The user attempted to apply the equation W=1/2kx^2 but encountered difficulties in solving for the velocities of both objects. Additionally, the discussion addresses the impact of friction on the speed of object A when object B is moving at 0.2 m/s after 0.5 seconds.

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  • Understanding of the work-energy principle in physics
  • Familiarity with Hooke's Law (F=k.x)
  • Knowledge of kinetic energy equations (K=1/2mV^2)
  • Concept of center of mass in a system
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  • Review the work-energy principle and its applications in spring systems
  • Study the implications of friction on motion and speed calculations
  • Learn how to calculate the center of mass for systems with multiple objects
  • Practice solving problems involving springs and kinetic energy using real-world examples
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking for problem-solving strategies in spring dynamics and energy conservation.

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Homework Statement


Object A (1 kg) and B (3 kg) are forced together,
initially compressing a spring S between them by 6 cm;
then the system is released from rest. The spring with
k=1250 N/m is not fastened to either block and drops to
the surface after it has expanded to its unstretched position.
a) By assuming frictionless surface, what are the speeds of objects after the spring has expanded
to its unstretched position?
b) Assume that the surface is frictional with s=k=0.1. If object B has speed of 0.2 m/s at 0.5 s
after the system is released from rest, what should the speed of object A be at this time instant?
(Hint: Consider “center of mass of a system” concep


Homework Equations



W=1/2kx^2
F=k.x
K=1/2mV^2

The Attempt at a Solution



i'm having trouble with this energy thing. i tried 1/2kx^2=1/2mv1^2+1/2mv2^2
i found 37,5=1/2v1^2 + 1/2v2^2
and i tried F=k.x=75 .
then used f=m.a formula both objects and found V1=3V2. so i solved equation but it seems all wrong.
can you help?
 
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and i have no idea what to do in part b :)
 
can anyone help ? :(
 

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