# Is mechanical energy conserved ?

In summary, the conversation discusses the momentum, speed, kinetic energy, and conservation of mechanical energy in an explosion of an object with a mass of M into two pieces with masses of M/3 and 2M/3. It is concluded that the two pieces have equal and opposite momenta, smaller mass has larger speed and kinetic energy, and mechanical energy is not conserved due to the conversion of chemical energy into various forms of energy. The difference between tangential speed and tangential velocity is also explained.
Question:

An object has a mass of M ... it explodes up into two pieces.. one piece has a mass of M/3 and the other piece has a mass of 2M/3.

1. which object has larger l momentum l ? ... both have same
2. which object has larger speed ? ... smaller mass has larger speed
3. which object has larger kinetic energy ? ... smaller mass has larger KE
4. Is mechanical enrgy conserved ? ... No

I understood the part (ii) and (iii) ... but i am not getting that why they same momentum ? why is mechanical energy not conserved ?

Thanks

Question:

An object has a mass of M ... it explodes up into two pieces.. one piece has a mass of M/3 and the other piece has a mass of 2M/3.

1. which object has larger l momentum l ? ... both have same
2. which object has larger speed ? ... smaller mass has larger speed
3. which object has larger kinetic energy ? ... smaller mass has larger KE
4. Is mechanical enrgy conserved ? ... No

I understood the part (ii) and (iii) ... but i am not getting that why they same momentum ? why is mechanical energy not conserved ?

Thanks
They do not have the same momentum, but they do have the same magnitude of momentum. If the object is at rest before exploding, it has zero energy and zero momentum. Momentum is a vector. Equal and opposite momenta add to zero. Energy is a scalar; the separate energies of the two masses simply add and cannot cancel. Chemical energy is converted to mechanical energy (and heat and light and sound) in the explosion.

A bomb just sits there. 0 KE. Then it explodes... KE all over the place! Mechanical energy is clearly not conserved... Where did all this energy come from?

so you mean to say that the two objects must have the equal and opposite momentum so that they can add up to zero. In this way, we have to follow this rule

Intial momentum before explosion = Final momentum after explosion

the initial momentum of the bomb was zero, the final momentum must add up to zero too.
rite ?

and for the energy u mean, that it was saved in the form of chemical energy and after explosion, it is lost in the form of heat and sound and therefore it is NOT conserved.

am I thinking rite?

hi , I need to ask ... is that tangential speed and tangential velocity mean the same thing or there is a difference between two of them ?

so you mean to say that the two objects must have the equal and opposite momentum so that they can add up to zero. In this way, we have to follow this rule

Intial momentum before explosion = Final momentum after explosion

the initial momentum of the bomb was zero, the final momentum must add up to zero too.
rite ?

and for the energy u mean, that it was saved in the form of chemical energy and after explosion, it is lost in the form of heat and sound and therefore it is NOT conserved.

am I thinking rite?
Yes. You have the momentum part exactly right. The energy question was asking if mechanical energy is conserved. The answer is no because some of the chemical energy was converted into kinetic energy. If you examined all of the kinds of energy there are, you would conclude that total energy is conserved. The amount of chemical energy lost would equal the sum of all the forms of energy created.

hi , I need to ask ... is that tangential speed and tangential velocity mean the same thing or there is a difference between two of them ?
Speed is a scalar. An object in a circular orbit has constant speed; it moves the same distance in the same amount of time. Velocity is a vector that has both magnitude (speed) and direction. The direction of the tangential velocity of an object in a circular orbit is constantly changing, so the tangential velocity is constanly changing even though the speed remains constant.

OlderDan said:
Speed is a scalar. An object in a circular orbit has constant speed; it moves the same distance in the same amount of time. Velocity is a vector that has both magnitude (speed) and direction. The direction of the tangential velocity of an object in a circular orbit is constantly changing, so the tangential velocity is constanly changing even though the speed remains constant.

Thanks a lot

## 1. What is mechanical energy?

Mechanical energy is the energy that is possessed by an object due to its motion or position. It can be either kinetic energy, which is the energy of motion, or potential energy, which is the energy stored in an object's position or shape.

## 2. Is mechanical energy conserved?

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or transformed. Therefore, mechanical energy is conserved as long as there are no external forces acting on the system.

## 3. How is mechanical energy conserved?

Mechanical energy is conserved when there is no net change in the total amount of mechanical energy in a system. This means that the total amount of kinetic and potential energy remains constant. Any changes in one form of energy are offset by equal and opposite changes in the other form.

## 4. Can mechanical energy be converted into other forms of energy?

Yes, mechanical energy can be converted into other forms of energy, such as thermal energy, sound energy, or electromagnetic energy. This often happens due to friction or other external forces acting on the system.

## 5. What factors affect the conservation of mechanical energy?

The conservation of mechanical energy depends on the presence of external forces, such as friction or air resistance, and the system's initial and final positions. In addition, the type of mechanical energy (kinetic or potential) and the efficiency of energy transfers also play a role in the conservation of mechanical energy.

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