动能

如果要加速物体，则需要向物体施加力，并且施加的力需要做功。然后，在完成工作之后，必须将能量传递到以新速度运动的物体。传递的这种能量称为动能，它取决于物体的质量和速度。

动能可以在物体之间传递，并转化为另一种形式的能量。例如，运动的对象可能会与静止的对象发生碰撞。碰撞后，移动物体的某些初始动能可能已转移到静止物体中或转化为某种其他形式的能量。

活力

The capability to perform work is defined as Energy. 

Its unit is similar to that of work, therefore, the SI unit of work or energy is equal to Joule (J).

能源类型

能源基本上分为两大类：

(i)  Kinetic Energy: The type of energy that is present in an object due to the property of its state. 

e.g. a downhill skier, falling asteroid, collected water in a lake etc.

(i)  Potential Energy: The type of energy that is present in an object due to the property of its motion. 

e.g. a yoyo before it is released, a parked car, flowing water through a river etc.

动能

物体的动能被定义为由于物体的运动而产生的能量。当物体加速运动时，就会产生动能，它需要在其上施加一些力才能完成工作。因此，在完成工作之后，能量被传递到物体上，从而导致物体以恒定速度运动。传递的能量称为动能，它完全取决于运动物体的速度和质量。

朝某个方向移动的对象可以工作。相对于相对较慢移动的相同对象，移动较快的对象可以完成更多的工作。一个移动物体由于其运动而拥有多少能量?顾名思义，可以说，以一定速度运动的物体的动能等于使物体获得该速度所进行的功。

e.g. A moving bullet, blowing wind, a speeding stone, a rotating wheel can do work. 

It is something to wonder, How does a bullet pierce the target? How does the wind move the blades of a windmill?

Examples of Kinetic Energy

Objects in motion possess energy. This energy is simply known to be kinetic energy. A falling coconut, a flying aircraft, a speeding car, flowing water, a rolling stone, blowing wind, a running athlete, etc. i.e. any moving object possesses kinetic energy.

In short, kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases when the speed of the object increase.

动能公式

由于物体的动能在数学上取决于其质量和速度，因此动能定义为：

$\textbf{K.E.}\bf{=\dfrac{1}{2}mv^2}$

Here, m is the mass of the object and 

v is the speed or velocity of the object.

这样得到的表达式称为动能方程。

动能单位

SI Unit:

The SI unit of kinetic energy is Joule (J) or kg.m².s^-2.

CGS Unit:

While in CGS system of units, the kinetic energy is defined in erg.

由于质量( m )是标量，速度( v )是矢量。但是从上式可以看出，速度是平方的，并且知道任何矢量量的平方都会给出标量。

因此，动能是一个标量。

动能方程的推导

考虑一个质量为m ，初始速度为u ，最终速度为v的物体。

假设当施加恒定的力F时，它的位移量为s。

Now, work is done by the object that is responsible to change in its velocity, the work done is:

W = F × s                                                                                                                                                                                               ……(1)

Let its velocity change from u to v and a is the acceleration produced.

Now, using the equation of motion that relates u, v, s and a as:

v² – u² = 2as

Solve above expression for s as:

$s=\dfrac{v^2-u^2}{2a}$

But it is known that, the net force acting on an object is defined as:

F = ma

Now, Substitute ma for F and \dfrac{v^2-u^2}{2a} for s in the equation (1) and solve to calculate W.

$\begin{aligned}W&=(ma)\left(\frac{v^2-u^2}{2a}\right)\\&=\dfrac{m(v^2-u^2)}{2}\end{aligned}$

Suppose the object is starting from its initial position, i.e. u = 0, then:

$\begin{aligned}W&=\dfrac{m(v^2-(0)^2)}{2}\\&=\dfrac{1}{2}mv^2\end{aligned}$

It is clear that the work done is always equal to the change in the kinetic energy of an object. So, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is

$\begin{aligned}\text{K.E.}=\dfrac{1}{2}mv^2\end{aligned}$

动能的类型

动能有五种类型：

辐射能

辐射能是动能的一种形式，它总是在运动中传播通过介质或空间。

e.g.:

• Ultraviolet light
• Gamma rays

热能

热能也可以称为热能。它是由于原子相互碰撞时的运动而产生的。

e.g.:

• Hot springs
• Heated swimming pool

声能

声能是物体振动产生的能量。它通过介质传播，但不能在真空或空间中传播，因为没有粒子可以充当介质。

e.g.:

• Tuning fork
• Beating drums

电能

可以从具有正电荷和负电荷的自由电子获得电能。

e.g.:

• Lightning
• Batteries when in use

机械能

动能和势能之和称为机械能。它既不能创建也不能销毁，但可以从一种形式转换为另一种形式。

e.g.:

• Orbiting of satellites around the earth
• A moving car

样本问题

Problem 1: A vehicle having mass of 150 kg, is moving with a uniform velocity of 4 m/s. What is the amount of kinetic energy possessed by the vehicle?

Solution:

Given that,

The mass of the vehicle, m = 150 kg,

The velocity of the vehicle, v = 4 m/s

The kinetic of the vehicle is, 

$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\&=\dfrac{1}{2}\times150\text{ kg}\times(4\text{ m/s})^2\\&=1200\text{ J}\end{aligned}$

Hence, the kinetic energy of the vehicle is equal to 1200 J.

Problem 2: A ball having a mass of 2 kg is thrown up with a speed of 10 m/s. What is the kinetic energy stored in the ball at the time of throwing?

Solution:

Given that,

The mass of the ball, m = 2 kg,

The velocity of the ball, v = 10 m/s.

The kinetic of the ball is, 

$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\&=\dfrac{1}{2}\times2\text{ kg}\times(10\text{ m/s})^2\\&=100\text{ J}\end{aligned}$

Hence, the kinetic energy of the ball is equal to 100 J.

Problem 3: An asteroid is coming towards the earth. Its velocity is 1000 km/s. Its estimated kinetic energy is almost 4 × 10¹⁵ J. Find out the mass of the asteroid.

Solution:

Given that,

The kinetic energy of the asteroid, K.E. = 4 × 10¹⁵ J,

The velocity of the asteroid, v = 1000 Km/s = 10⁶ m/s

Since, the kinetic of the asteroid is given as, 

$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\4\times10^{15}\text{ J}&=\dfrac{1}{2}\times m\times(10^6\text{ m/s})^2\\&m=8000\text{ kg}\end{aligned}$

Hence, the mass of the asteroid is equal to 8000 kg.