Conservation of Energy in a Spring-Powered Glider on an Incline

In summary, a 0.0900 kg glider is pushed up a 40.0° frictionless incline by a spring with a constant of 640 N/m. After losing contact with the spring, the glider travels 1.80 m along the inclined track before sliding back down. The distance of the spring's original compression cannot be determined with the given information. Additionally, at its highest point, the glider has a combination of potential and kinetic energy, which must have come from the energy stored in the compressed spring.
  • #1
student34
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Homework Statement



A 0.0900 kg glider is pushed up a 40.0° frictionless incline by a spring. The spring's constant is k = 640 N/m with negligible mass. The glider reaches a distance of 1.80 m along the inclined track after losing contact with the spring and then slides back down. What distance is the spring originally compressed?

Homework Equations



0.5kX2^2 - 0.5kX1^2 = 0.5mV2^2 - 0.5mV1^2

The Attempt at a Solution



I have absolutely no idea how we can possibly know the distance of the spring's comression. There does not seem to be enough information here.
 
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  • #2
What can you say about the potential and kinetic energy of the glider when it reaches its highest point? Where did that energy come from?
 
  • #3
tms said:
What can you say about the potential and kinetic energy of the glider when it reaches its highest point? Where did that energy come from?

Ahhhh, I see, thanks.
 

1. What is the definition of work-energy of a spring?

The work-energy of a spring refers to the potential energy stored in a spring when it is compressed or stretched from its equilibrium position. This potential energy is then converted into kinetic energy when the spring is released.

2. How is the work-energy of a spring calculated?

The work-energy of a spring can be calculated using the equation W = 1/2kx^2, where W is the work done on the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What is the relationship between the work-energy of a spring and its spring constant?

The work-energy of a spring is directly proportional to the square of the spring constant. This means that the higher the spring constant, the more potential energy the spring will store when compressed or stretched.

4. Can the work-energy of a spring ever be negative?

No, the work-energy of a spring can never be negative because it represents the potential energy stored in the spring. This potential energy can be converted into kinetic energy, but it cannot have a negative value.

5. How does the work-energy of a spring relate to Hooke's Law?

The work-energy of a spring is related to Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. This means that the work done on a spring is also directly proportional to its displacement, which is represented in the equation W = 1/2kx^2.

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