Mechanical Engineering - Engineering Mechanics - Discussion

Energy conservation should not be confused with linear momentum. Whilst one concerns itself with the fact that energy cannot be created or lost, the other is focused on changes that can happen within a system of masses moving in a particular direction when external forces are applied. Is there a change in system energy when momentum changes? Possibly.

Kinetic energy of a moving system of masses is 0.5 x (m1 x v1^2 + m2 x v2^2 x ......mn x vn^2). The mass of objects will not change unless some molecular distortion occurs which is not treated herein. However, the velocity can reduce or increase.

Hence, the system energy can go up or go down. However, if this is happening in a closed system, the kinetic energy lost becomes gained as heat energy. Hence, total energy remains unchanged. But if this is not a closed system, then energy is exchanged across our artificial boundary which contains the system of masses, and therefore system energy changes.

So, the key word here for the statement to be true is whether the system is CLOSED or OPEN. And, since we were not informed on this, the assumption is that it is an OPEN system in which case the correct answer is FALSE because the energy conservation principle will NOT hold in an OPEN system.

I think option (a) is correct as -> Unless force external from the system is applied the system will continue to maintain its condition of constant motion or of stationary position.

Conservation of ENERGY.

It's true that motion is a change in displacement, but that doesn't need the continuous addition of energy to maintain as the conditions are always IDEAL in such questions.

Moreover, it's changed in motion which points toward change in energy not a change of position (Displacement). So motion in any direction is possible for a system that has a constant level of energy. (Imagine a ball in space which not in the influence of gravity from a body > if you give it a push it will start to travel with a constant velocity, NOW for this ball the total momentum of the system of masses (ball itself) in any direction remains constant unless acted upon by an external force in that direction. MEANING unless a force (or a force field) interferes with this system (WHICH (Force or force field) will be labelled EXTERNAL) the ball will go on its way beyond infinity (Literally).

False.

The principle you mentioned seems to be a mix-up of two different concepts: the conservation of energy and the conservation of momentum.

The principle of conservation of momentum states that the total momentum of an isolated system of objects remains constant if no external forces act on it. This means that in the absence of external forces, the total momentum of the system in any direction remains the same.

The conservation of energy, on the other hand, states that the total energy of an isolated system remains constant over time, and energy can be transferred or transformed but not created or destroyed.

So, the correct statement would be: According to the principle of conservation of momentum, the total momentum of a system of masses in any direction remains constant unless acted upon by an external force in that direction.

The law of conservation of energy, first formulated in the nineteenth century, is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time. For an isolated system, this law means that energy can change its location within the system, and that it can change form within the system, for instance chemical energy can become kinetic energy, but that energy can be neither created nor destroyed.

From: http://en.wikipedia.org/wiki/Conservation_of_energy

Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.

In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

False is the correct answer.

The principle described in your statement is the principle of conservation of momentum**, not energy. According to the principle of conservation of momentum, the total momentum of a system of masses in any direction remains constant unless acted upon by an external force in that direction.

The principle of conservation of energy states that the total energy of an isolated system remains constant over time.

No, the statement is False. The principle of conservation of energy states that the total energy of a closed system is constant, it does not say anything about the momentum of a system of masses. The law of conservation of momentum states that the total momentum of a closed system of masses remains constant unless acted upon by an external force in that direction. So, momentum is conserved, not energy.

It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time. For an isolated system, this law means that energy can change its location within the system, and that it can change form within the system, for instance chemical energy can become kinetic energy, but that energy can be neither created nor destroyed.

According to principle of conservation of energy "energy cannot be created nor be destroyed but it can be transformed from one form to another". The given statement follows the Newton's 2nd law of motion which states "Rate of change of momentum(m x a) is directly proportional to the force(F) which applied in that direction".

If a body has some constant momentum in one direction, it means that a constant external force is acting on it. But if the momentum has to change in magnitude in that direction then an external unbalanced force has to act.

Here only external force is given and not external unbalanced force hence answer is false.