Solve for Spring Compression: Physics 11 Momentum and Energy Problem

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Homework Help Overview

The problem involves two carts with different masses connected by a spring, focusing on the concepts of momentum and energy. The original poster seeks to determine the compression distance of the spring required for one cart to achieve a specific velocity after release.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the total kinetic energy of the carts and consider the momentum of the system. There are attempts to apply the conservation of energy principle, with some questioning the correctness of their calculations.

Discussion Status

Participants are actively engaging with the problem, sharing calculations and hints. There is a recognition of the need to equate kinetic energy to potential energy, and some guidance has been provided regarding the relationship between the two forms of energy.

Contextual Notes

There is an indication of confusion regarding the calculations, particularly in relation to the expected result for the spring compression. Participants are exploring various interpretations of the energy conservation principle and its application to the problem.

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Homework Statement



A 1.1 kg cart and a 2.2 kg cart are at rest with a compressed string between them. the force constant of the spring is 600 N/m. when the spring is released, the carts rapidly separate. how far must the spring have been compressed for the 2.2 kg cart to end up moving at 1.5 m/s?
(involves both momentum and energy)

Homework Equations



p = mv
Ek = 0.5mv2
Ep = 0.5kx2

The Attempt at a Solution



i don't even know where to start !
 
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Figure out the total KE of the carts. Hint: What's the momentum of the system?
 
Doc Al said:
Figure out the total KE of the carts. Hint: What's the momentum of the system?

ok so i got:
0.5(1.1)(3^2) = 4.95 J for Cart 1
0.5(2.2)(1.5^2) = 2.475 J for Cart 2
 
Using what you know about the system, apply the law of conservation of energy now.
 
jgens said:
Using what you know about the system, apply the law of conservation of energy now.

ok so
0.5mv2
= 0.5(7.425)(1.5)2
=8.35

but the answer should be 0.16 m.. did i do something wrong or is there another setp now?
 
Well, your total kinetic energy is the sum of the kinetic energy of each kart, so KE = 7.425. You know that the resultant KE must equal the initial potential energy so KE = .5(k)(x^2).
 
great thanks !
 
You're welcome.
 

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