Law of conservation, and efficiency problem?

In summary, the problem involves calculating the maximum speed of a 2.0x10^2 g pendulum bob that is released from a height of 22cm above its rest position, using the law of conservation of energy and assuming 100% efficiency. The equations used are eg=mgh and ek=(mv^2)/2, and the attempt at solving involves finding the value of ek. However, since the energy is converted between PE and KE, the value of ek cannot be determined without knowing the value of PE at the maximum speed point.
  • #1
raininggently
2
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Homework Statement


A 2.0x10^2 g pendulum bob is raised 22cm above its rest position.The bob is released, and it reaches its maximum speed as it passes the rest position.

Calculate its maximum speed at that point by applying the law of conservation of energy and assuming that the efficiency is 100%.


Homework Equations


-eg=mgh
-ek=(mv^2)/2
-et=eg+ek
-eff=eoutput/einput x 100%


The Attempt at a Solution


-m=2.0 x 10^2 = 0.200 kg
-h=22cm=0.22 m
I know the law of conservation states when energy is changed from one form to another no energy is lost.

I tried using ek=(mv^2)/2 but I didn't know what ek so I coulden't solve for V.

eg=mgh
eg=(0.200kg)(9.8)(0.22)
eg=0.4312 j

I don't know what to do from here :eek:
eg=(
 
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  • #2
raininggently said:

Homework Statement


A 2.0x10^2 g pendulum bob is raised 22cm above its rest position.The bob is released, and it reaches its maximum speed as it passes the rest position.

Calculate its maximum speed at that point by applying the law of conservation of energy and assuming that the efficiency is 100%.


Homework Equations


-eg=mgh
-ek=(mv^2)/2
-et=eg+ek
-eff=eoutput/einput x 100%


The Attempt at a Solution


-m=2.0 x 10^2 = 0.200 kg
-h=22cm=0.22 m
I know the law of conservation states when energy is changed from one form to another no energy is lost.

I tried using ek=(mv^2)/2 but I didn't know what ek so I coulden't solve for V.

eg=mgh
eg=(0.200kg)(9.8)(0.22)
eg=0.4312 j

I don't know what to do from here :eek:
eg=(

When a pendulum swings there is a repeated interchange of Kinetic Energy and Gravitaional Potential Energy.
When it was to the side - 22 cm higher than rest position, it was all PE.
When it swings past the middle position, all that energy has been transformed into KE.
 

FAQ: Law of conservation, and efficiency problem?

What is the Law of Conservation?

The Law of Conservation states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system will remain constant over time.

What does the Law of Conservation apply to?

The Law of Conservation applies to all forms of energy, including mechanical, thermal, chemical, and nuclear energy. It also applies to the total mass of a closed system, as mass and energy are interchangeable through the famous equation E=mc².

How does the Law of Conservation relate to the efficiency problem?

The efficiency problem refers to the fact that no energy transformation is 100% efficient, meaning that some energy is always lost in the form of heat or other waste. The Law of Conservation helps us understand that these losses result in a decrease in the total usable energy in a system.

Can the Law of Conservation be violated?

No, the Law of Conservation is a fundamental principle of physics and has been extensively tested and proven to hold true in all physical systems. It is considered a universal law and is one of the foundations of modern science.

How is the Law of Conservation important in everyday life?

The Law of Conservation is important in everyday life because it helps us understand and predict how energy will behave in different systems. It also reminds us of the finite nature of energy and the need to use it efficiently and responsibly to sustain our planet and its resources.

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