Trouble understanding nonconservative forces

[September24]

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I know that nonconservative forces do not conserve mechanical energy, but do they cause a change in overall energy?

For a system with conservative forces, W=dME (mechanical energy).

For a system with nonconservative forces, W=dME (mechanical energy)+dIE (internal energy).

When friction acts on something, work done will cause a change in mechanical energy (KE-->PE or vice versa), but some energy will be lost due to friction or a nonconservative force.


However, when friction acts on a system, it generates heat. Will this heat increase the temperature of an object or will it just dissipate into the environment. In other words, does frictional heat enter the system? I ask this because I know that dE=W+Q. Mechanical energy or work may decrease due to friction so W decreases, but to maintain overall change in energy, Q increases (heat generated enters system).


Sorry, nonconservative forces just confuse me. I know that they lower mechnical energy, but I'm confused about how "internal energy" and the heat part works.

 

[Chrisz]

Conservative force is a force such that E=U+KE,
Delta E=Delta U+Delta KE
Delta E=0
so, Delta U=-Delta KE

The above reasoning is that if total energy is constant, Change in potential energy =-change in KE

Another property of conservative force is that no matther which path way you take, as long as the starting point and end point is the same, the system always gain or release certain amount of energy. Path Independence.

frictional force is non-conservative, it is path dependent. For example, you slide a box from point A to point B. One route is very frictional while the other is less friction. If you take route A, more heat is generated by frictional force on the first route while less heat is generated by frictional fore on the second route.


Examples are Gravity or and Springs

Assuming, we throw a ball from a cliff with maximum height Y. There is no air resistance, so no energy is lost as heat

Initally, Total Energy E=U=mgY . As ball drops, E=mgY=mgY2+1/2mv^2. when it is about to touch the ground E=mgY=1/2mv^2. Once it bounce back, E=U=mgY again. It will fall down and bounce back to Y till the end of the world, if total energy is kept constant.

Heat is a very random energy, it is really hard to make it harvested. When it releases, it gets eventually dissipated into the surrounding. When you rub something fast, you feel it is warm, because heat is being released into the surrounding

 

[September24]

Conservative force is a force such that E=U+KE,
Delta E=Delta U+Delta KE
Delta E=0
so, Delta U=-Delta KE

The above reasoning is that if total energy is constant, Change in potential energy =-change in KE

Another property of conservative force is that no matther which path way you take, as long as the starting point and end point is the same, the system always gain or release certain amount of energy. Path Independence.

frictional force is non-conservative, it is path dependent. For example, you slide a box from point A to point B. One route is very frictional while the other is less friction. If you take route A, more heat is generated by frictional force on the first route while less heat is generated by frictional fore on the second route.


Examples are Gravity or and Springs

Assuming, we throw a ball from a cliff with maximum height Y. There is no air resistance, so no energy is lost as heat

Initally, Total Energy E=U=mgY . As ball drops, E=mgY=mgY2+1/2mv^2. when it is about to touch the ground E=mgY=1/2mv^2. Once it bounce back, E=U=mgY again. It will fall down and bounce back to Y till the end of the world, if total energy is kept constant.

Heat is a very random energy, it is really hard to make it harvested. When it releases, it gets eventually dissipated into the surrounding. When you rub something fast, you feel it is warm, because heat is being released into the surrounding

Thanks for the help. I was wondering if you can answer a couple follow up questions. One is unrelated but I didnt want to make another topic.


1. What does it mean that friction changes "internal energy"?

2. Speaking of nonconservative forces, I read that if two projectiles of different masses are launched straight up with the same initial velocity, the heavier mass will go higher since it has more inertia and resists change. What about when there is no air resistance. Will the heavier object still go higher? I was under the impression that mass doesnt affect projectile motion.

 

[syoung]

September, in reply to #2, think about that statement you just made. Under no circumstances could you make the heavier of two projectiles (assume same shape) of different masses go higher... Let's approach this from 2 different ways.

Let's look at it from an energy standpoint.

You impart the same 100 J of energy on both objects (obviously different initial velocities). One is 1 kg, the other is 10 kg.

If we had to look at how high the 100 J could take the 1 kg object, it would reach 10 m. The 10 kg object would reach 1 m.

Let's look at it from the same velocity standpoint

You throw both objects up with 9 m/s. They both reach a maximum height at 0.9 s, and land at 1.8 s.

Adding in air resistance, as long as the shapes of them are the same and the velocities are the same, it won't make a difference, since air resistance is mostly affected by velocity and surface area of the object.

 

[September24]

Thanks for knocking some sense into this. I got this from EK and thats the answer they came up with.

From the energy standpoint its 1/2mv^2=mgh. The masses cancel out so shouldn't they go the same height given the same initial velocity?

I'm seeing a couple topics over mass input into kinematics/projectiles today. It seems like many people are confused as am I. It seems like if you apply the same force or "energy" to two objects of different masses, like say you kick two objects with same force, the lighter object will have a larger initial velocity and will go further.

But what if you kick things with the SAME initial velocity. If two things have the same initial velocity, regardless of mass, will their range/height be the same?

 

[September24]

September, in reply to #2, think about that statement you just made. Under no circumstances could you make the heavier of two projectiles (assume same shape) of different masses go higher... Let's approach this from 2 different ways.

Let's look at it from an energy standpoint.

You impart the same 100 J of energy on both objects (obviously different initial velocities). One is 1 kg, the other is 10 kg.

If we had to look at how high the 100 J could take the 1 kg object, it would reach 10 m. The 10 kg object would reach 1 m.

Let's look at it from the same velocity standpoint

You throw both objects up with 9 m/s. They both reach a maximum height at 0.9 s, and land at 1.8 s.

Adding in air resistance, as long as the shapes of them are the same and the velocities are the same, it won't make a difference, since air resistance is mostly affected by velocity and surface area of the object.

Just adding the quote to send the alert. I'm unsure if SDN requires a quote to alert a user.

 

[Chrisz]

Thanks for the help. I was wondering if you can answer a couple follow up questions. One is unrelated but I didnt want to make another topic.


1. What does it mean that friction changes "internal energy"?

2. Speaking of nonconservative forces, I read that if two projectiles of different masses are launched straight up with the same initial velocity, the heavier mass will go higher since it has more inertia and resists change. What about when there is no air resistance. Will the heavier object still go higher? I was under the impression that mass doesnt affect projectile motion.

1. To answer your question, I am assuming what you mean by internal energy is the total energy of the system.
Friction is a force that does a work on a moving object in the opposite direction of the moving object. So when, friction does work on the moving object, the object slows down, so it is taking energy out of the system and release it as heat. So the system, in this case, the object loses energy to the surrounding. If you consider both the object and surrounding as the entire system, energy is conserved.

2 there are so many ways to answer this question, actually gravity is conservative force.
So, as stated earlier, delta E=0 in a conservative system, so -delta K= delta U,
Therefore, -(0-0.5mv^2)=mgh at highest point. So with the same velocity, they reach the same height. If the have two object are given the same kinetic energy, the heavier object has lower initial velocity and the lighter has higher initial velocity, so heavier reach a lower maximum height than the lighter one does.

 

[September24]

1. To answer your question, I am assuming what you mean by internal energy is the total energy of the system.
Friction is a force that does a work on a moving object in the opposite direction of the moving object. So when, friction does work on the moving object, the object slows down, so it is taking energy out of the system and release it as heat. So the system, in this case, the object loses energy to the surrounding. If you consider both the object and surrounding as the entire system, energy is conserved.

2 there are so many ways to answer this question, actually gravity is conservative force.
So, as stated earlier, delta E=0 in a conservative system, so -delta K= delta U,
Therefore, -(0-0.5mv^2)=mgh at highest point. So with the same velocity, they reach the same height. If the have two object are given the same kinetic energy, the heavier object has lower initial velocity and the lighter has higher initial velocity, so heavier reach a lower maximum height than the lighter one does.

Okay. Again thanks for your help. I know you're answering questions like this in other topics, so I apologize for being redundant. Is there a way I can easily tell when mass will have an impact on these projectiles. Like if same force=mass has an impact, same velocity, no impact. Whenever I see an mcat questions and it says "mass is doubled, how will range/height,etc" change with etc. being "projectile related variables", I usually assume that there is no change. As a BR student, I'm told that mass doesn't affect projectiles, but after today, I've seen many occasions on which that is not the case. Or a good source on this might suffice as well.

 

[Chrisz]

Okay. Again thanks for your help. I know you're answering questions like this in other topics, so I apologize for being redundant. Is there a way I can easily tell when mass will have an impact on these projectiles. Like if same force=mass has an impact, same velocity, no impact. Whenever I see an mcat questions and it says "mass is doubled, how will range/height,etc" change with etc. being "projectile related variables", I usually assume that there is no change. As a BR student, I'm told that mass doesn't affect projectiles, but after today, I've seen many occasions on which that is not the case. Or a good source on this might suffice as well.

To be honest, physics is a way to quantify natural phenomenons in mathematical expressions. Mass does not affect projectile when initial velocity of two objects are the same both in magnitude and direction. Br might refer to this specific condition. For physics, you have to apply concepts on conditional basis. I think you took non-calculus based general physics. Actually, a lot of students have done this way. For non-calculus based physics, the students are given formulas with a verbal explanation and some simple examples. I took cal-based physics, so I had to mathematically derive every single formula, with different conditions specified, including the formulas used in non-cal based physics class. In order to make up the difference in understanding, one has to be very careful about the verbal explanations and do a lot of exercise.

 

[syoung]

Gotta do more problems. Experience.