Question

illustrate the law of conservation of mechanical energy with an example.

Answer 1

Hello Mate!

Let an object fall from point A to point C.

Since mechanical energy is sum of potential and kinetic energy.

So from point A,

U + K.E = mgh + ½ mv²

Since velocity at top is "0"

U + K.E = mgh + ½ m(0)²

U + K.E = mgh

At point B we get,

U + K.E = mg(h-x) + ½ mv²

Now, v² = u² + 2gx

Since u is 0.

v² = 2gx

U + K.E = mg( h - x ) + ½ m( 2gx )

U + K.E = mgh - mgx + mgx

U + K.E = mgh

Now at point C we get,

v² - u² = 2gh

Since we know that u is 0,

v² = 2gh

But potential energy is 0 at bottom.

U + K.E = 0 + ½ m( 2gh )

U + K.E = mgh

So in all the cases the total energy is mgh.

Hence the mechanical energy is conserved.

Have great future ahead!

Answer 2

• The capacity to do work is known as energy. We have heard of many types of energy like mechanical energy, potential energy, chemical energy, kinetic energy, thermal energy, solar energy, and many more. In this article, let us discuss in detail the conservation of mechanical energy.
• Let us consider the example of an ideal simple pendulum (friction-less). We can see that the mechanical energy of this system is a combination of its kinetic energy and gravitational potential energy.
• As the pendulum swings back and forth, a constant exchange between the kinetic energy and potential energy takes place. When the bob attains its maximum height, the potential energy of the system is the highest, whereas the kinetic energy is zero.
• At the mean position, the kinetic energy is the highest, and the potential energy is zero. Between these two extreme points, we see that the system possesses both kinetic and potential energy, the sum of which is constant. These observations tell us a lot about the conservation of mechanical energy.

According to the principle of conservation of mechanical energy:

• In order to understand this statement more clearly, let us consider an example of one-dimensional motion of a system.
• Here a body, under the action of a conservative force F, gets displaced by Δx, then from the work-energy theorem, we can say that the network done by all the forces acting on a system is equal to the change in the kinetic energy of the system.

Mathematically, ΔKE = F(x) Δx.

Where, ΔK is the change in kinetic energy of the system. Considering only conservative forces are acting on the system Wnet = Wc.

Thus, Wc = ΔKE.

Also, If conservative forces do the work in a system, the system loses potential energy equal to the work done. Hence, Wc = -PE.

Which implies that the total kinetic energy and potential energy of a system remains constant if the process involves only conservative forces.

KE + PE = constant.

KEi+ PEi = KEf+ PEf.

Where denotes the initial values and f denotes the final values of KE and PE.

• This law applies only to the extent that the forces are conservative in nature.
• The mechanical energy of the system is defined as the total kinetic energy plus the total potential energy.
• In a system that comprises only conservative forces, each force is associated with a form of potential energy and the energy only changes between the kinetic energy and different types of potential energy, such that, the total energy remains constant.

Learn more about law of conservation of mechanical energy here,

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