Where does the crate permanently come to rest?

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Homework Help Overview

The problem involves a crate sliding down an inclined plane and interacting with a spring on a rough surface. It explores concepts of energy, friction, and motion in a physics context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the maximum height the crate reaches after sliding down and question the complexity of determining where the crate comes to rest. There is a focus on the energy-work principle and the effects of friction.

Discussion Status

Some participants have expressed understanding of the first part of the problem, while others are grappling with the second part's complexity. A question about the necessary compression of the spring to maintain the crate's motion has been raised, indicating a productive line of inquiry.

Contextual Notes

The problem includes specific values for weight, height, spring constant, and coefficients of friction, which may influence the discussion but are not fully resolved.

Doppler
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A small crate of weight 5.0N is released from rest at a height 2.0m up a smoyj inclined plane. The crate slides down the plane and across a smooth 1.50m floor to a rough plane where a spring is located.
The bottom of the spring is located at a height of 0.5m. The spring constant is 20N/m .
The coefficient of kinetic friction between the rough plane and crate is $\frac{1}{\sqrt{3}}$ and the coefficient of static friction is $\frac{1}{\sqrt{2}}$/

(a) What is the max height the crate reaaches on the right hand inclined plane?
(b) Where does the crate permanently come to rest? How many times does the crate travel up to the rough plane?
 

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Hint: Energy-work principle.
 
The first part is OK for me,
but the second part seems very complicated.
 
Well, how much must the spring compress in order to keep the crate going?
 

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