Is Mechanical Energy Conserved: Why, When And Detailed Facts And FAQs


Mechanical energy is that type of energy that comes into action when the body is in motion or due to its position. Let’s know is mechanical energy conserved. 

Mechanical energy is conserved as long the resistance offered by surroundings is ignored. It is of two kinds: kinetic energy (due to motion) and potential energy (due to the position). Mechanical energy is basically the sum of these two kinds of forces. 

Suppose a car is in motion, then the energy it is possessing would be kinetic energy which would be equal to 1/2 mv2. Similarly, if the ball is kept on a table and we lift it to some extent, then the energy in it would be potential energy, mgh, due to its displacement.

Now we know that the mechanical energy of a system remains constant throughout the journey if we neglect other factors like air resistance, friction, etc. For example, if a boy is standing on a terrace and holding a ball in his hand. Now at the top position, the potential energy is maximum, and since the velocity is zero, the kinetic energy would be zero. If the boy drops the ball, it will come into motion; that is, its kinetic energy will increase, and potential energy will decrease. Thus through this example, we get to know if mechanical energy is conserved or not. 

is mechanical energy conserved
Image Credit: Wikipedia

When is mechanical energy conserved?

The mechanical energy remains conserved when only internal forces act on the body and no external forces are in action. It means that kinetic and potential may keep changing throughout the journey. But their sum is constant at every point. 

The forces are conservative, i.e., they do not depend on the path of the moving object and are only dependent on the starting and final position. For example, the gravitational force is conservative in nature, whereas the resistance offered by air is non-conservative in nature as it depends on the path. 

From the law of conservation of mechanical energy, we have: 

M.E = K.E + P.E 

M.E is the mechanical energy, K.E is the kinetic energy, and P.E is the potential energy.

We have;

M.E = 1/2 mv2+ mgh= constant 

Kf + Pf = Ki + Pi

That is, the sum of final kinetic energy and potential energy is equal to the sum of initial kinetic and potential energy.

We can understand it in detail with the help of an example. In roller coaster rides, the mechanical remains conserved in the complete journey. When the roller coaster starts, it attains kinetic energy due to motion. The kinetic energy then starts changing into potential energy, which becomes maximum at the top of the position. On moving further, the potential energy starts changing into kinetic energy. At the point just above the ground, the kinetic energy becomes maximum and the potential energy the minimum. 

Why is mechanical energy conserved?

“The law of conservation of energy states that energy can neither be created nor destroyed”. And thus, the different types of energy are possible due to its conversion from one form to other. As per this law, the mechanical energy remains conserved. 

If we take the forces to be conservative, then kinetic energy completely changes into potential energy. But if some external forces are acting on the object, then some of the energy is dissipated to overcome that. In this case, the energy would not be entirely conserved. 

Why is mechanical energy not always conserved?

It is not necessary that mechanical energy remains conserved. It only remains when the forces that act on objects are conserved, and no external force is in action. In case the external forces come into action, then the mechanical energy gets non-conservative  

The forces such as friction, air resistance, viscosity oppose the motion of any object. Thus to overcome them, some work is done, which leads to the conversion of some proportion of mechanical energy into thermal energy. For instance, if a ball is rolled on the ground, it stops after some time which is due to friction. 

In this case, the total mechanical energy becomes equal to kinetic + potential + thermal energy.  

Is mechanical energy conserved in free fall? 

Freefall means that objects fall freely under the influence of gravity. In free fall, the mechanical energy of an object remains conserved. The rate of velocity remains constant throughout the fall till it hits the ground. 

With an example, let us see how the energy is conserved. In the above figure, we have an object at a height h falling freely. Now let us see the mechanical energy at three different points A, B, and C. 

At point A, we have;

P.E = mgh 

K.E = 0 as v = 0

M.E = P.E + K.E

M.E = mgh + 0

M.E = mgh

After travelling through a distance ‘x’, the object comes at point B. 

P.E = mg(h-x) = mgh – mgx

Now, for kinetic energy, we have u = 0 and s = x and a = g

Therefore substituting in Newton’s third equation of motion, we have:

2as = v2 – u2

2gx = v2 – 02

2gx = v2

Therefore, K.E = 1/2 mv2

K.E =1/2 m 2 g x = mgx

Now, M.E = K.E + P.E

M.E = mgx + mgh – mgx

M.E = mgh 

Now at point C just only slightly above the ground, we have;

P.E = 0; since h = 0 

Again using the third equation of motion we have: 

2as = v2 – u2

2gh = v2 – 02

v2 = 2gh

Therefore the kinetic energy becomes:

K.E = 1/2 m v2

K.E = 1/2 m 2gh

K.E = mgh 

Therefore:

M.E = K.E + P.E 

M.E = mgh + 0 

M.E. = 0 

Looking at the above example, it has become clear that at all the three points A, B, and C, we have total mechanical energy equal to mgh. That is that it remains conserved throughout the journey. Now it is understandable how is mechanical energy conserved.

Is mechanical energy conserved in real situations?

The mechanical energy remains conserved to a great extent. However, there is always some kind of external force acting on the object. Therefore if they are present in very low magnitude, then the energy is conserved. 

Take the example of bow and arrow. When the arrow is stretched, it attains potential energy. When you release the arrow, stored potential energy gets converted into kinetic energy. Thus the total mechanical energy of the bow and arrow system comes out to be the sum of kinetic and potential energy. Now, if there are air resistances, then some kinetic energy of the arrow would be lost as thermal energy and therefore reducing the final mechanical energy. 

The Earth-Moon system has the mechanical energy always conserved. Due to the position of the moon concerning Earth, it acquires potential energy. And when the moon revolves around the Earth, it is in motion, and therefore the potential energy gets changed into kinetic energy. Thus energy is converted from one form to another. 

The car is moving on a road and experiences friction. Now friction changes some proportion of mechanical energy into friction. It is an example in which mechanical energy is not conserved. 

How is mechanical energy conserved based on the activity? 

Let us prove how is mechanical energy conserved using the pendulum. The above figure shows us the pendulum. It moves periodically from position O to A, then again to O and then to B, and finally to O again. 

Let us see the mechanical energy of the pendulum at three different positions such as A, B and O. In this case; we neglect the friction between air and the bob of the simple pendulum. The mass of the bob is ‘m’. 

Take the pendulum to the A position and then drop it. The pendulum starts oscillating. At position A the bob is at height ‘h’ and velocity becomes 0; therefore, we have: 

P.E = mgh

K.E = 0

Total mechanical energy = 0 + mgh = mgh

Now when the bob moves from position A to O, the height h starts decreasing and becomes 0 at point O. Since the bob has some into motion, its velocity starts to increase and therefore, its potential energy changes into kinetic energy. Now at point O, we have:

P.E = 0, as h=0

K.E = mgh 

Total mechanical energy = mgh + 0 = mgh

From the O position, the pendulum starts to move towards point B. On moving from B to O, the height starts to increase and becomes maximum at B, i.e., h. Now the velocity starts to decrease and becomes 0. Therefore at B position, we have:

P.E. = mgh

K.E = 0

Total mechanical energy = 0 + mgh = mgh

At every point, we have a total mechanical energy constant. Therefore from this, we get that mechanical energy remains conserved in the system of the pendulum. 

How can you prove that mechanical energy is conserved?

Let us prove that mechanical energy is conserved. Take a ball to say that it of 200 grams; now raise it to a height of 100 cm. Now the potential energy would: 

P.E = mgh 

P.E = 200/1000 kg*9.8 * (100/100)

P.E = 1.96 J

Since velocity is 0, therefore kinetic energy would also be 0. 

Therefore, 

Total mechanical energy = P.E + K.E

M.E = 1.96 + 0

M.E = 1.96 J

Now release the ball and using the third equation of motion calculate the velocity of the ball. 

2as = v2 – u2

2*9.8 = v2

v2 = 19.6

K.E = 1/2 m v2 + mgh

K.E = 1/2 *{200/1000}19.6

K.E = 1.96 J 

When the ball hits the ground, its potential will become 0. 

Mechanical Energy = P.E + K.E

Mechanical Energy = 0 + 1.96 

M. E = 1.96 J 

There can be little variations due to air resistance. In the above example, we have ignored the air resistance; that is why mechanical energy is found exactly equal. So, now we know how, when and why is mechanical energy conserved. 

Frequently Asked Questions (FAQs)

What is the law of conservation of energy?

As per the law of conservation energy, we know that energy can not be formed or destroyed on its own. It only changes the form. 

Does mechanical energy always remain conserved?

The form of energy that is either due to the position or motion of an object is said to be mechanical energy. 

The mechanical energy remains conserved throughout the journey only when the internal forces act on it. If any non-conservative force act on the object, the mechanical energy is not conserved. 

When is mechanical energy not conserved?

 Mechanical energy is not conserved when we take into consideration friction or air resistance. When the forces are non-conservative, then some of the mechanical energy dissipates as thermal energy. 

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: https://www.linkedin.com/mwlite/in/rabiya-khalid-bba02921a In my free time, I let out my creative side on a canvas. You can check my paintings at: https://www.instagram.com/chronicles_studio/

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