Conservation of Energy with Spring and Incline (Diagram Included)

In summary, the conservation of energy with spring and incline is the principle that states energy cannot be created or destroyed, but can only be transformed from one form to another. When a spring is compressed on an incline, its potential energy increases, and this is affected by the angle of the incline and the stiffness of the spring. This principle can be applied to real-world situations, such as in the operation of a catapult. It is also related to the broader law of conservation of energy, which states that the total energy of a system remains constant.
  • #1
Wara
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Elastic Potential Energy with Spring and Incline (Diagram Included)

Homework Statement


04.21.2012-17.21.10.png



Homework Equations


ET = 1/2(m)(V2) + mgh + 1/2k*x2


The Attempt at a Solution


ET1 - Wf = ET2
1/2k*x2 - Wf = mgh + 1/2mV2

where, Wf = [(0.53)(2kg)(9.8m/s2)(cos67)](1.3m+0.4m)

^ I used this formula and went through by subbing in all numbers but I get error since you can't square root a negative value. Plus we can assume Height off ground is negligible since it cancels out on both sides of equation.
 
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  • #2
does anyone know why I'm getting that negative error? Is my formula correct?
 

Related to Conservation of Energy with Spring and Incline (Diagram Included)

1. What is the conservation of energy with spring and incline?

The conservation of energy with spring and incline refers to the principle that energy cannot be created or destroyed, only transformed from one form to another. In this case, the potential energy stored in a compressed spring is converted into kinetic energy as the spring is released and the object moves along an inclined plane.

2. How does the spring's potential energy change as it is compressed on the incline?

As the spring is compressed on the incline, its potential energy increases. This is because the spring stores potential energy in the form of elastic potential energy, which is directly proportional to the amount the spring is compressed. The more the spring is compressed, the more potential energy it has.

3. What factors affect the conservation of energy with spring and incline?

The two main factors that affect the conservation of energy with spring and incline are the angle of the incline and the stiffness of the spring. As the angle of the incline increases, the amount of potential energy stored in the spring also increases. Similarly, a stiffer spring will have a greater potential energy when compressed compared to a less stiff spring.

4. Can the conservation of energy principle be applied to real-world situations with spring and incline?

Yes, the conservation of energy principle can be applied to real-world situations with spring and incline. For example, it can be seen in the operation of a catapult, where the potential energy stored in the tension of the catapult's arm is converted into kinetic energy as the arm is released and the object is launched along an inclined plane.

5. How is the conservation of energy with spring and incline related to the law of conservation of energy?

The conservation of energy with spring and incline is a specific application of the law of conservation of energy, which states that energy cannot be created or destroyed. In this case, the total energy (potential and kinetic) of the system remains constant, demonstrating the law of conservation of energy.

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