Conservation of mechanical energy (help)

In summary, conservation of mechanical energy is a fundamental principle in physics that states the total amount of mechanical energy in a closed system remains constant over time. This allows us to predict the behavior of a system and understand energy transfer and transformation. Mechanical energy is conserved through the law of conservation of energy, but there are exceptions in real-world systems where external forces can cause energy loss.
  • #1
shorti2406
12
0
I just can't seem to derive the correct formula for this one.

A spring with k=40.0 N/m is at the base of a frictionless 30 degree inclined plane. A 0.50 kg object is pressed against the spring, compressing in 0.3m from its equilibrium position. The object is then released. If the object is not attached to the spring, how far up the incline does it travel before coming to res and then sliding back down?
 
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  • #2
I keep getting d=.43, and I am almost positive that is not correct!
 
  • #3
How are you solving this problem?
 

What is conservation of mechanical energy?

The conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy (potential energy + kinetic energy) in a closed system remains constant over time, regardless of any internal changes or external forces acting on the system.

Why is conservation of mechanical energy important?

Conservation of mechanical energy is important because it allows us to predict the behavior of a system and understand how energy is transferred and transformed within that system. It is a crucial concept in fields such as mechanics, thermodynamics, and astrophysics.

How is mechanical energy conserved?

Mechanical energy is conserved through the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, the potential energy and kinetic energy of the system will always remain constant.

What are some real-life examples of conservation of mechanical energy?

Some examples of conservation of mechanical energy in everyday life include a pendulum swinging back and forth, a roller coaster moving along its track, a bouncing ball, and a swinging child on a swing set. In each of these scenarios, the total mechanical energy of the system remains constant despite changes in potential and kinetic energy.

Are there any exceptions to the conservation of mechanical energy?

Yes, there are exceptions to the conservation of mechanical energy. In real-world systems, there are often external forces such as friction or air resistance that can cause energy to be lost from the system in the form of heat or sound. This is known as non-conservative forces, and in these cases, the total mechanical energy of the system is not conserved.

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