What is the Speed of a Block After Traveling 0.9 m Up an Inclined Plane?

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SUMMARY

The problem involves a 1 kg block on a spring with a constant of 500 N/m, positioned on a frictionless inclined plane at a 30° angle. When the spring is released, the block travels 1.5 m up the incline, and the objective is to determine its speed after traveling 0.9 m. The relevant equations include the work-energy principle, specifically W=(1/2)kx² for spring potential energy and K=(1/2)mv² for kinetic energy. The angle of inclination is crucial for calculating the component of gravitational force acting on the block.

PREREQUISITES
  • Understanding of the work-energy principle
  • Knowledge of spring mechanics, specifically Hooke's Law
  • Familiarity with basic kinematics
  • Ability to apply trigonometric functions in physics problems
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  • Review the work-energy theorem in physics
  • Learn about Hooke's Law and its applications in mechanics
  • Study the effects of inclined planes on motion and forces
  • Explore the use of LaTeX for formatting equations in online discussions
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Students preparing for physics exams, particularly those focusing on mechanics and energy concepts, as well as educators looking for examples of problem-solving in inclined plane scenarios.

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Homework Statement


I have run across another problem while reviewing for finals that I am not able to really understand, and this one I have no clue how to approach. I am given that a block is of mass 1 kg, it is placed on a spring of constant 500 N/m at the bottom of a frictionless plane inclined at 30°. When the spring is released the block travels 1.5 m up the plane, losing contact with the spring. What is the speed of the block when it has traveled 0.9 m up the plane?

Homework Equations


Not really sure, I tried using:
W=(1/2)kx2
and:
K=(1/2)mv2

The Attempt at a Solution


So, I tried finding the work, and then using the work in place of K to find the velocity. This returned double digit numbers, which due to the question being multi-choiced with only single digit numbers, are obviously wrong. Also, where am I supposed to use the supplied angle?
 
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On a side note, how do you format your posts so the equations look nice as you see in a lot of other posts on these boards?
 
You'll have to show your attempt in detail so that we can see what you did right and where you went wrong.

As for equation formatting, you can use the icons and menus available in the edit panel header bar for things like subscripts and superscripts and special characters (such as Greek letters) if you use plain text equations, or you can use the built-in LaTeX syntax interpretation that the website implements. This requires learning some LaTeX syntax. For more information check out the LaTeX Primer.
 

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