能量守恒公式
能量可以定义为在物理学中进行工作的能力。能量守恒定律指出，能量在任何过程中都不能产生或破坏。但是，它可以从一种形式更改为另一种形式。当考虑各种能量时，孤立系统中包含的总能量保持不变。该定律适用于各种能源。把它们加起来：
一个单一的系统，从它的所有环境中关闭，保留它的全部能量。这通过下摆的摆锤图来说明：
公式
Ut = Ui + W + Q
where,
- Ui denotes the initial energy of a system
- W denotes the work done
- Q denotes the heat added or removed
推导
Assuming that the gravitational potential at the earth’s surface is zero. Consider the case of a fruit falling to the ground.
Assume A to be a point on the tree at a height of ‘h’ from the ground; the fruit’s velocity is zero, hence energy is highest there.
E = mass × gravitation constant × height …(1)
Along the path of its descent, its potential energy diminishes but its kinetic energy grows.
The fruit is falling freely under gravity towards the bottom of the tree at point B, and it is at a height ‘a’ from the ground, and it has speed as it reaches point B. As a result, it will have simultaneously kinetic and potential energy at this moment.
Potential energy = m × g × x …(2)
Third equation of motion states that: v2 = 2g × (h – a)
or, Kinetic energy of the fruit = mg × (h – a) …(3)
From the above equations, we have:
E = mg × (h – a) + m × g × x
= mgh
Similarly the result can be proved for different value of height of the falling fruit.
示例问题
问题 1. 一个 2 kg 的物体从 30 m 的建筑物中掉落。求它在地面以上 10 m 时的速度。
解决方案：
The object’s potential energy decreases as it falls, but its kinetic energy increases.
Change in potential energy = Final mgf – Initial mgf
= 2 kg x 10 m/s x 10 m – 2 kg x 10 m/s x 30 m
= −400 J
Now, mv2/2 = 400
or, v = 20 m/s
问题二、为什么永动机不能函数？
解决方案：
The perpetual motion machine is an idea for a machine that continues to move indefinitely without slowing down. Over the years, an endless variety of wondrous equipment have really been described. Pumps that are said to run themselves using their own top of water falling, wheels that are said to move themselves using unbalanced masses, and a variety of self-repelling magnets are among them.
问题 3. 在给定初始能量 600 J 和最终能量 4800 J 的情况下，求系统中守恒的能量。
解决方案：
ΔEsys = Ein−Eout
= 4800 – 600 J
= 4200 J
问题 3. 运动中的弹簧什么时候动能最高？解释。
解决方案：
When the spring is travelling at its quickest, the kinetic energy is at its maximum. When the spring is most squeezed and briefly immobile, however, potential energy is maximum. When the spring extends due to the force of compression, potential energy falls as velocity increases.
问题 4. 质量为 390 kg 的摆在 1.2 m 处达到其最大高度。求它在最低点的速度。
解决方案：
Potential energy of the pendulum at a height of 1.2 m = mgh
= 390 x 10 x 1.2
= 4680 J
Now, 4680 J = mv2/2
v = 4.88 m/s
问题 5. 一个 12 kg 的物体从 60 m 的建筑物中掉落。求它在地面以上 10 m 时的速度。
解决方案：
The object’s potential energy decreases as it falls, but its kinetic energy increases.
Change in potential energy = Final mgf – Initial mgf
= 12 kg x 10 m/s x 10 m – 12 kg x 10 m/s x 60 m
= 1200 – 7200
= −6000 J
Now, mv2/2 = 6000
or, v = 10 m/s