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What's conserved

Page history last edited by Joe Redish 5 years, 4 months ago

6.3.P5

 

Prerequisites:

 

Although we know that the total energy in the entire universe is always conserved, the value of understanding energy conservation is figuring out where energy flows from one part of the universe to another and in what form. To do this, it is essential to clearly identify a subset of the universe -- a system -- that we are considering.

 

For convenience of discussion, we divide energy into a variety of types:

    • kinetic (coherent energy of motion of an object -- associated with an object's momentum)
    • potential (gravitational, spring, and electric -- associated with some of an object's interactions)
    • thermal (energy associated with the chaotic and random motion of an object's molecules)
    • chemical (energy that is internal to an object's molecules)

We refer to the combination of an object's coherent kinetic energy of motion and its potential energy arising from interactions with other objects as its mechanical energy.

 

In this problem, we will select a set of extremely simple (unrealistic) situations that allow us to see the basic mechanism of energy transformation most clearly. In realistic situations (in both physics and biology), things become more complicated, but being able to track the energy will be extremely valuable. 

 

A. Briefly state and describe the law of conservation of mechanical energy for a macroscopic object, being careful to define any terms or symbols you use and state the circumstances under which it holds. Describe how the law is related to Newton's laws.

 

B. For the macroscopic objects or set of objects described in the numbered list below, complete the following:

  • For each object in the system, draw a free-body diagram identifying the forces acting on the object.
  • For each force in your free-body diagram, identify whether the force is internal or external to the system. (A force is internal if both the objects causing the force and feeling the force are a member of the system.)
  • For each force in your free-body diagram, identify whether the force is conservative or non-conservative. (A force is non-conservative if the changes it causes in the energies of the objects it acts on are not reversible.)
  • Identify whether the objects in your system can be considered to conserve mechanical energy for the time interval described.
  • If mechanical energy of the system is NOT conserved, indicate where the energy has gone (into what objects and forms).

 

1. System = ball. The ball has been thrown straight upward. Consider the object after it has left the hand but may be rising or falling but has not yet been caught. Ignore the effect of air resistance.
 
2. System = block. The block is sliding on a smooth table after being pushed but before it comes to a stop. (Smooth ≠ frictionless!)
3. System = a car and a truck. Both are in neutral and can roll freely. The truck rolls into the car and smashes into it, doing damage to both vehicles. Friction with the ground can be neglected. Consider from just before the objects collide to just after they collide.
4. System = two cylinders marked A and B.  A heavy cylinder (A) with frictionless wheels rolling along on a horizontal table top and a lighter cylinder (B) that is lightly dropped onto the moving cylinder. Consider the time from just before B lands on A until a bit later when they are rolling together, both at the same speed. (Assume B is dropped from just above A so that the change in gravitational PE can be neglected.)  

 

For a system consisting of a small number of microscopic objects -- atoms and molecules -- we will talk about the mechanical energy of the atoms and molecules as being their kinetic energy and any potential energies they have while they retain their identities. When they react chemically and change the internal energies associated with their arrangements, we will refer to that as chemical energy

 

C. For the two systems below, ignore the effects of gravity.

  • Identify whether the objects in your system can be considered to conserve mechanical energy for the time interval described.
  • If mechanical energy of the system is NOT conserved, indicate whether the mechanical energy has increased or decreased and where (if it has increased) it came from, and where (if it decreased) it has gone (into what objects and forms).

 

1. System = Two atoms bound together in a molecule and a single atom. These collide with each other but the state of the molecule is not changed (AB + C → AB + C). Consider the time from a bit before the collision to a bit after.

2.  System = same. But this time when they collide, the two atoms previously bound are broken apart (AB + C → A + B + C). Consider the time from a bit before the collision (when it looks something like the picture in 1) to a bit after (when it looks something like the picture at the right).
 

 

 

 

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