Understanding Energy (kinetic and potential)

[Addem]

I have these two problems on energy where I just don't totally understand the explanations given. One goes:

(With a diagram showing a 14kg mass suspended 5m above the ground by a zero-mass rope, connected to a pulley, where on the other side of the rope is an 8kg mass resting on the ground. The rope is taut before the 14kg mass is released and the vector tension on each points straight up.)

"See the masses in Figure (1) which start out at rest. (i) Find the velocity of the 14kg mass just before it hits the ground. (ii) Find the maximum height reached by the 8kg (and don't worry about hitting the pulley). (iii) Find the fraction of mechanical energy left when the system finally comes to rest."

So with this one I can do the math, I just don't understand the conservation of energy principle here. Every force here is either a gravitational force or a tension force which is itself due to a gravitational force being transferred from one object to another. So I would think, here, that the energy would be conserved.

So like I said, I can do the math and see that the computations imply that the answer to part (iii) is less than 1 but I just don't get why, in light of conservation of energy. Can anyone explain to me why energy is not conserved here?

There is a second question,

"A rocket is launched at escape velocity from the surface of the Earth (radius R). What is its velocity when it is at a distance r from the center of the Earth in terms of G and M(of earth)?"

This one I very much don't understand, because when I read the solution it asserts that initial energy is 0. However, I would think that initial kinetic energy would be mv^2 / 2 and potential energy would be 0.

I've never totally understood energy and I'm not sure if that conceptual fogginess is responsible for why I'm not really getting these two problems. Any help is appreciated.

 

[DimReg]

Well, technically when the mass hits the floor, it's energy is transferred into the floor. Everything is made of atoms, and when two objects collide, those atoms are given more energy individually. In fact, waves would be created in the floor/air, which is responsible for the fact that you would be able to hear it fall.

But really, energy here isn't conserved because you are artificially imposing zero motion, without considering the physical process in which it would occur.

For the second question:

The initial energy is zero, at the surface of the earth.

 

[Andrew Mason]

I have these two problems on energy where I just don't totally understand the explanations given. One goes:

(With a diagram showing a 14kg mass suspended 5m above the ground by a zero-mass rope, connected to a pulley, where on the other side of the rope is an 8kg mass resting on the ground. The rope is taut before the 14kg mass is released and the vector tension on each points straight up.)

"See the masses in Figure (1) which start out at rest. (i) Find the velocity of the 14kg mass just before it hits the ground. (ii) Find the maximum height reached by the 8kg (and don't worry about hitting the pulley). (iii) Find the fraction of mechanical energy left when the system finally comes to rest."

So with this one I can do the math, I just don't understand the conservation of energy principle here. Every force here is either a gravitational force or a tension force which is itself due to a gravitational force being transferred from one object to another. So I would think, here, that the energy would be conserved.

So like I said, I can do the math and see that the computations imply that the answer to part (iii) is less than 1 but I just don't get why, in light of conservation of energy. Can anyone explain to me why energy is not conserved here?

Energy is conserved up to an instant before the 14 kg mass hits the floor. But it is the energy of the system that is conserved, not the energy of each mass individually. Energy is transferred from the 14 kg. to the 8 kg mass.

There is a second question,

"A rocket is launched at escape velocity from the surface of the Earth (radius R). What is its velocity when it is at a distance r from the center of the Earth in terms of G and M(of earth)?"

This one I very much don't understand, because when I read the solution it asserts that initial energy is 0. However, I would think that initial kinetic energy would be mv^2 / 2 and potential energy would be 0.

I've never totally understood energy and I'm not sure if that conceptual fogginess is responsible for why I'm not really getting these two problems. Any help is appreciated.

Potential energy is negative at the surface of the earth. At infinite r, its potential energy is 0. Escape velocity means it has enough kinetic energy at the Earth surface to reach infinite r at which point is speed is 0 (0 KE). Since total energy does not change, its total energy everywhere from R to ∞ is 0.

AM

 

[technician]

The 14kg mass falling through 5m 'gives up' 686J of PE.
This energy appears as PE of the 8kg mass rising by 5m + KE of 8kg mass + KE of the 14kg mass as it hits the ground
This last amount of KE is therefore not part of the total mechanical energy of the masses.