Asst 14 Query

#$&*

course phy 201

Aug 1 4:15pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

 

   http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution. 

014.  `query 14

*********************************************

Question:  `qset 3 intro prob sets

If you calculate the acceleration on a mass m which starts from rest under the influence of a constant net force Fnet and multiply by a time interval `dt what do you get? 

• How far does the object travel during this time and what velocity does it attain? 

• What do you get when you multiply the net force by the displacement of the mass? 

• What kinetic energy does the object attain? 

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 

 

The final velocity of a mass can be calculated by its acceleration multiplied by the `dt if it starts at rest. Its acceleration is derived from the Fnet acting on the specific mass. Since it started at rest, half of its final veolcity is the average velocity. The average velocity * `dt will give the total distance traveled. The Fnet * `ds gives the KE gain of the mass. Since its initial velocity was 0, then the KE gain is equal to the final KE attained.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: 

`a The acceleration of the mass is a = F_net / m, so the velocity of the object changes by amount

• `dv = a * `dt = F_net / m * `dt.

Since the initial velocity is zero, this will also be the final velocity:

• vf = F_net / m * `dt.

From this and the fact that acceleration is constant (const. net force on const. mass implies const. acceleration), we conclude that

• vAve = (v0 + vf) / 2 = (0 + (F_net / m) * `dt) / 2 = F_net * `dt / (2 m).

Multiplying this by the time interval `dt we have

• `ds = vAve `dt = (F_net * `dt) / (2 m) * `dt = F_net `dt^2 / (2 m).

If we multiply this by F_net we obtain

• F_net * `ds = F_net * F_net * `dt^2 / (2 m) = F_net^2 * `dt^2 / (2 m).

From our earlier result vf = F_net / m * `dt we see that

• KE_f = 1/2 m vf^2 = 1/2 m ( F_net / m * `dt)^2 = F_net^2 * `dt^2 / (2 m).

• Our final KE, when starting from rest, is therefore equal to the product F_net * `ds.

Since we started from rest, the final KE of the mass on this interval is equal to the change in KE on the interval.

We call F_net * `ds the work done by the net force.  Our result therefore confirms the work-kinetic energy theorem:

• `dW_net = `dKE.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 ok

 

 

------------------------------------------------

Self-critique rating:

*********************************************

Question:  `q Define the relationship between the work done by a system against nonconservative forces, the work done against conservative forces and the change in the KE of the system.  How does PE come into this relationship?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 

 

 The work done by a system against nonconservative or conservative forces = KE lost by the system. Only in the case where the

system does work against a conservative force does the PE of the system increase.

Only in the case where the system does work against a nonconservative force is PE lost by the system.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: 

`a** The system does positive work at the expense of its kinetic and/or potential energy.

The work done by the system against all forces is `dW_net_BY.

`dW_net_BY is equal and opposite to `dW_net_ON, which is in turn equal to `dKE, the change in the kinetic energy of the system.

We conclude that `dW_net_BY = - `dKE.    The change in KE is equal and opposite to the work done by the system against the net force acting on it.

To consider the role of PE, we first review our formulation in terms of the work done ON the system:

`dW_net_ON = `dKE.

The work `dW_net_ON is the sum of the work done on the system by conservative and nonconservative forces:

• `dW_net_ON = `dW_cons_ON + `dW_NC_ON

and `dW_cons_ON is equal and opposite to `dPE, the change in the system's PE.

Thus `dW_net_ON = `dW_NC_ON - `dPE so that `dW_net_ON = `dW_cons_ON + `dW_NC_ON becomes

• `dW_NC ON - `dPE = `dKE so that

• `dW_NC_ON = `dPE + `dKE. 

Since `dW_NC_BY = - `dW_NC_ON, we see that

• -`dW_NC_BY = `dPE + `dKE so that

• `dW_NC_BY + `dPE + `dKE = 0.

Intuitively, if the system does positive work against nonconservative forces, `dPE + `dKE must be negative, so the total mechanical energy PE + KE of the system decreases.  (Similarly, if the system does negative work against nonconservative forces that means nonconservative forces are doing positive work on it, and its total mechanical will increase).

As usual, you should think back to the most basic examples in order to understand all these confusing symbols and subscripts (e.g., if I lift a mass, which you know intuitively increases its gravitational potential energy, I do positive work ON the system consisting of the mass, the conservative force of gravity acts in the direction opposite motion thereby doing negative work ON the system, and the work done BY the system against gravity (being equal and opposite to the work done ON the system by gravity) is therefore positive).

The equation -`dW_NC_BY = `dPE + `dKE isolates the work done by the system against nonconservative forces from the work it does against conservative forces, the latter giving rise to the term `dPE.

If the system does positive work against conservative forces (e.g., gravity), then its PE increases.

If the system does positive work against nonconservative forces (e.g., friction) then `dPE + `dKE is negative:  PE might increase or decrease, KE might increase or decrease, but in any even the total PE + KE must decrease.  The work done against a nonconservative force is done at the expense of at least one, and maybe both, the PE and KE of the system.  (In terms of gravitational forces, the system gets lower or slows down, and maybe both, in order to do the work).

If nonconservative forces do positive work on the system, then the system does negative work against those forces, and `dW_NC_ON is negative.  Thus -`dW_NC_ON is positive, and  `dPE + `dKE is positive.  Positive work done on the system increases one or both the PE and the KE, with a net increase in the total of the two.  (In terms of gravitational forces, the work done on system causes it to get higher or speed up, and maybe both.)

STUDENT RESPONSE WITH INSTRUCTOR COMMENTARY:  The work done by a system against nonconservative forces is the work done to overcome friction in a system- which means energy is dissipated in the form of thermal energy into the 'atmosphere.'

 

Good.  Friction is a nonconservative force. 

 

However there are other nonconservative forces--e.g., you could be exerting a force on the system using your muscles, and that force could be helping or hindering the system.  A rocket engine would also be exerting a nonconservative force, as would just about any engine.  These forces would be nonconservative since once the work is done it can't be recovered.

 

STUDENT RESPONSE WITH INSTRUCTOR COMMENTS:  The work done by a system against conservative forces is like the work to overcome the mass being pulled by gravity.

 

INSTRUCTOR COMMENT:  that is one example; another might be work to compress a spring 

STUDENT QUESTION

ok, alot to absorb but I think I am getting there. So KE is equal to work done ON the system not BY the system...this is a little confusing. I was thinking that when we calculate the dw= fnet * 'ds we were caculated the work done BY the system not on the system.?
INSTRUCTOR RESPONSE

To be very specific

• `dW_net_ON = F_net_ON * `ds

is the work done by the net force acting ON the system, where F_net_ON is the net force acting on the system.
The work-kinetic energy theorem states that

• `dW_net_ON = `dKE

If positive work is done on a system, it speeds up. If negative work is done on the system, it slows down.
From the point of view of the system, if positive work is done by the system then the system has to 'use up' some of its kinetic energy to do the work, so it slows. 
Positive work done BY the system constitutes negative work being done ON the system.
If part of the net force is conservative, then `dW_net_ON can be split into `dW_net_ON_cons and `dW_net_ON_noncons.

The quantity `dPE, the change in PE, is defined to be equal and opposite to `dW_net_ON_cons. That is,

• `dPE = - `dW_net_ON_cons.

It follows that `dW_net_ON = `dW_net_ON_noncons - `dPE, so that the work-kinetic energy theorem can be rewritten as

• `dW_net_ON_noncons - `dPE = `dKE.

This is commonly rearranged to the form

• `dW_net_ON_NC = `dKE + `dPE.

STUDENT COMMENT (confused by too many symbols)

Once again this makes no since to me. All the symbols lost me


We can say this first in words, then translate the words into symbols:

remember that

• work done by all forces acting on a system is equal to the change in the kinetic energy of the system, and

• change in potential energy is equal and opposite to work done by conservative forces.

Now, some forces are conservative and some are nonconservative, so

• work on system by all forces = work on system by nonconservative force + work on system by conservative forces

• work on system by conservative forces = - change in potential energy so

• work on system by all forces = work on system by nonconservative force - change in potential energy

Since work on system by all forces = change in kinetic energy

• work on system by nonconservative force - change in potential energy = change in kinetic energy and thus

• work on system by nonconservative force = change in potential energy + change in kinetic energy

Saying exactly the same thing in symbols:

• `dW_net = `dKE

• `dPE = -`dW_cons_ON

Some forces are conservative and some are nonconservative, so

• `dW_net_on = `dW_nc_on + `dW_cons_on

• `dW_net_on = `dW_nc_on + (-`dPE)

• `dW_net_on = `dW_nc_on - `dPE

Since `dW_net_on = `dKE

• `dW_nc_on - `dPE = `dKE and thus

• `dW_nc_on = `dKE + `dPE

STUDENT QUESTION

I do not understand conservative and nonconservative forces at all. Could you explain this to me in simpler terms?

INSTRUCTOR RESPONSE

The official definition is that conservative forces are path-independent. However that in itself is a tough concept to understand and I don't find it very useful when students first encounter the idea.
The basic idea itself is simple enough. A conservative force 'stores up' the work you do against it. So for example when you lift something you do work against gravity. If you then release it, gravity does equal work on it as it falls back to its original position.
As another example suppose you hang an object from a rubber band and allow it to come to rest at an equilibrium position. If you then pull it further downward you do work against the increasing tension in the rubber band. If you release it, the tension does work on the object as the rubber band springs back. The rubber band 'stored up' the energy you put into it when you pulled the object down, and returned the energy when you released the object. 
The energy that was 'stored up' is called potential energy. When the object was released the potential energy was converted to kinetic energy.
The gravitational force is completely conservative. All the work you did against gravity to lift the object is returned. Gravity exerts just as much force on the return as it did when
The elastic tension force of the rubber band is not completely conservative. The rubber band heats up when it is stretched (and cools when it snaps back), with the net result being that some of the work you do goes into thermal energy (i.e., heat) so the rubber band doesn't manage to 'store' all the energy you put into it and you don't get all your energy back. So the rubber band force can be regarded as 'partially conservative'. It stores energy, but not all of it.
Friction is an example of a force that isn't conservative at all. If you push a box across the floor, it's friction that resists your efforts. However friction doesn't 'store' any of the energy you put into pushing the box. If you push the box from this side of the room to that side, then release it, the box doesn't slide back even a little bit. The energy you expended is simply dissipated (friction heats up the floor and the box, and the resulting thermal energy is just dissipated to the surroundings).

*@

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 ok

 "

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

*********************************************

Question:  `q Define the relationship between the work done by a system against nonconservative forces, the work done against conservative forces and the change in the KE of the system.  How does PE come into this relationship?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 

 

 The work done by a system against nonconservative or conservative forces = KE lost by the system. Only in the case where the

system does work against a conservative force does the PE of the system increase.

Only in the case where the system does work against a nonconservative force is PE lost by the system.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution: 

`a** The system does positive work at the expense of its kinetic and/or potential energy.

The work done by the system against all forces is `dW_net_BY.

`dW_net_BY is equal and opposite to `dW_net_ON, which is in turn equal to `dKE, the change in the kinetic energy of the system.

We conclude that `dW_net_BY = - `dKE.    The change in KE is equal and opposite to the work done by the system against the net force acting on it.

To consider the role of PE, we first review our formulation in terms of the work done ON the system:

`dW_net_ON = `dKE.

The work `dW_net_ON is the sum of the work done on the system by conservative and nonconservative forces:

• `dW_net_ON = `dW_cons_ON + `dW_NC_ON

and `dW_cons_ON is equal and opposite to `dPE, the change in the system's PE.

Thus `dW_net_ON = `dW_NC_ON - `dPE so that `dW_net_ON = `dW_cons_ON + `dW_NC_ON becomes

• `dW_NC ON - `dPE = `dKE so that

• `dW_NC_ON = `dPE + `dKE. 

Since `dW_NC_BY = - `dW_NC_ON, we see that

• -`dW_NC_BY = `dPE + `dKE so that

• `dW_NC_BY + `dPE + `dKE = 0.

Intuitively, if the system does positive work against nonconservative forces, `dPE + `dKE must be negative, so the total mechanical energy PE + KE of the system decreases.  (Similarly, if the system does negative work against nonconservative forces that means nonconservative forces are doing positive work on it, and its total mechanical will increase).

As usual, you should think back to the most basic examples in order to understand all these confusing symbols and subscripts (e.g., if I lift a mass, which you know intuitively increases its gravitational potential energy, I do positive work ON the system consisting of the mass, the conservative force of gravity acts in the direction opposite motion thereby doing negative work ON the system, and the work done BY the system against gravity (being equal and opposite to the work done ON the system by gravity) is therefore positive).

The equation -`dW_NC_BY = `dPE + `dKE isolates the work done by the system against nonconservative forces from the work it does against conservative forces, the latter giving rise to the term `dPE.

If the system does positive work against conservative forces (e.g., gravity), then its PE increases.

If the system does positive work against nonconservative forces (e.g., friction) then `dPE + `dKE is negative:  PE might increase or decrease, KE might increase or decrease, but in any even the total PE + KE must decrease.  The work done against a nonconservative force is done at the expense of at least one, and maybe both, the PE and KE of the system.  (In terms of gravitational forces, the system gets lower or slows down, and maybe both, in order to do the work).

If nonconservative forces do positive work on the system, then the system does negative work against those forces, and `dW_NC_ON is negative.  Thus -`dW_NC_ON is positive, and  `dPE + `dKE is positive.  Positive work done on the system increases one or both the PE and the KE, with a net increase in the total of the two.  (In terms of gravitational forces, the work done on system causes it to get higher or speed up, and maybe both.)

STUDENT RESPONSE WITH INSTRUCTOR COMMENTARY:  The work done by a system against nonconservative forces is the work done to overcome friction in a system- which means energy is dissipated in the form of thermal energy into the 'atmosphere.'

 

Good.  Friction is a nonconservative force. 

 

However there are other nonconservative forces--e.g., you could be exerting a force on the system using your muscles, and that force could be helping or hindering the system.  A rocket engine would also be exerting a nonconservative force, as would just about any engine.  These forces would be nonconservative since once the work is done it can't be recovered.

 

STUDENT RESPONSE WITH INSTRUCTOR COMMENTS:  The work done by a system against conservative forces is like the work to overcome the mass being pulled by gravity.

 

INSTRUCTOR COMMENT:  that is one example; another might be work to compress a spring 

STUDENT QUESTION

ok, alot to absorb but I think I am getting there. So KE is equal to work done ON the system not BY the system...this is a little confusing. I was thinking that when we calculate the dw= fnet * 'ds we were caculated the work done BY the system not on the system.?
INSTRUCTOR RESPONSE

To be very specific

• `dW_net_ON = F_net_ON * `ds

is the work done by the net force acting ON the system, where F_net_ON is the net force acting on the system.
The work-kinetic energy theorem states that

• `dW_net_ON = `dKE

If positive work is done on a system, it speeds up. If negative work is done on the system, it slows down.
From the point of view of the system, if positive work is done by the system then the system has to 'use up' some of its kinetic energy to do the work, so it slows. 
Positive work done BY the system constitutes negative work being done ON the system.
If part of the net force is conservative, then `dW_net_ON can be split into `dW_net_ON_cons and `dW_net_ON_noncons.

The quantity `dPE, the change in PE, is defined to be equal and opposite to `dW_net_ON_cons. That is,

• `dPE = - `dW_net_ON_cons.

It follows that `dW_net_ON = `dW_net_ON_noncons - `dPE, so that the work-kinetic energy theorem can be rewritten as

• `dW_net_ON_noncons - `dPE = `dKE.

This is commonly rearranged to the form

• `dW_net_ON_NC = `dKE + `dPE.

STUDENT COMMENT (confused by too many symbols)

Once again this makes no since to me. All the symbols lost me


We can say this first in words, then translate the words into symbols:

remember that

• work done by all forces acting on a system is equal to the change in the kinetic energy of the system, and

• change in potential energy is equal and opposite to work done by conservative forces.

Now, some forces are conservative and some are nonconservative, so

• work on system by all forces = work on system by nonconservative force + work on system by conservative forces

• work on system by conservative forces = - change in potential energy so

• work on system by all forces = work on system by nonconservative force - change in potential energy

Since work on system by all forces = change in kinetic energy

• work on system by nonconservative force - change in potential energy = change in kinetic energy and thus

• work on system by nonconservative force = change in potential energy + change in kinetic energy

Saying exactly the same thing in symbols:

• `dW_net = `dKE

• `dPE = -`dW_cons_ON

Some forces are conservative and some are nonconservative, so

• `dW_net_on = `dW_nc_on + `dW_cons_on

• `dW_net_on = `dW_nc_on + (-`dPE)

• `dW_net_on = `dW_nc_on - `dPE

Since `dW_net_on = `dKE

• `dW_nc_on - `dPE = `dKE and thus

• `dW_nc_on = `dKE + `dPE

STUDENT QUESTION

I do not understand conservative and nonconservative forces at all. Could you explain this to me in simpler terms?

INSTRUCTOR RESPONSE

The official definition is that conservative forces are path-independent. However that in itself is a tough concept to understand and I don't find it very useful when students first encounter the idea.
The basic idea itself is simple enough. A conservative force 'stores up' the work you do against it. So for example when you lift something you do work against gravity. If you then release it, gravity does equal work on it as it falls back to its original position.
As another example suppose you hang an object from a rubber band and allow it to come to rest at an equilibrium position. If you then pull it further downward you do work against the increasing tension in the rubber band. If you release it, the tension does work on the object as the rubber band springs back. The rubber band 'stored up' the energy you put into it when you pulled the object down, and returned the energy when you released the object. 
The energy that was 'stored up' is called potential energy. When the object was released the potential energy was converted to kinetic energy.
The gravitational force is completely conservative. All the work you did against gravity to lift the object is returned. Gravity exerts just as much force on the return as it did when
The elastic tension force of the rubber band is not completely conservative. The rubber band heats up when it is stretched (and cools when it snaps back), with the net result being that some of the work you do goes into thermal energy (i.e., heat) so the rubber band doesn't manage to 'store' all the energy you put into it and you don't get all your energy back. So the rubber band force can be regarded as 'partially conservative'. It stores energy, but not all of it.
Friction is an example of a force that isn't conservative at all. If you push a box across the floor, it's friction that resists your efforts. However friction doesn't 'store' any of the energy you put into pushing the box. If you push the box from this side of the room to that side, then release it, the box doesn't slide back even a little bit. The energy you expended is simply dissipated (friction heats up the floor and the box, and the resulting thermal energy is just dissipated to the surroundings).

*@

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

 ok

 "

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

#*&!

&#This looks good. Let me know if you have any questions. &#