Energy Conservation: Kinetic Energy After Collision

[newTonn]

Energy can be neither created nor destroyed.
What is energy?. ability to do work.
what is work ? work = force x displacement.
Consider a body of mass 'm' moving at a uniform velocity 'v'.work done here is zero(no acceleration).So energy is zero.
DONT SAY KINETIC ENERGY is there.please check the derivation of kinetic energy.

Since work = F*d
and
F = m*a
then
work = m*a*d.

From kinematics we know that
d = 1/2 * a*t2
and
t = v/a.

so d = (1/2* a *v2)/ a2 = (1/2* v2)/ a

so work = m* a * (1/2* v2)/ a = 1/2 * m * v2.

in this derivation please note that t = v/a, is only applicable when initial velocity is zero. here initial and final velocity are v ,and kinetic energy will be zero.

now come back to the point.what will happen ,if this body hits another body at rest.?(mass is irrelevant-body at rest have no energy stored,isn't it?).

After collision, both of the bodies have energy(since there is an acceleration).

from where does this energy comes from.?

 

[russ_watters]

How did the body come to be moving at a velocity 'v'?

 

[Doc Al]

Energy can be neither created nor destroyed.
What is energy?. ability to do work.
what is work ? work = force x displacement.
Consider a body of mass 'm' moving at a uniform velocity 'v'.work done here is zero(no acceleration).So energy is zero.
DONT SAY KINETIC ENERGY is there.please check the derivation of kinetic energy.

You'd better check the definition of kinetic energy. If the body is moving, it has kinetic energy.

 

[Feldoh]

now come back to the point.what will happen ,if this body hits another body at rest.?(mass is irrelevant-body at rest have no energy stored,isn't it?).

After collision, both of the bodies have energy(since there is an acceleration).

from where does this energy comes from.?

If the collide then the law of conservation of momentum comes into play, no energy is gained or lost?

$$m_{a}v_{oa}+m_{b}v_{ob} = m_{a}v_{fa}+m_{b}v_{fb}$$

If one car has a velocity of 0, then the other car would have to have some sort of velocity to hit it. Since one of your cars is not moving:

$$m_{a}v_{oa} = m_{a}v_{fa}+m_{b}v_{fb}$$

This means that since the masses cannot change there wil be a change in velocities, the change is going to vary depending on a few factors such as is the collision elastic or inelastic? Technically speaking if there was no friction or gravity the cars would never stop (I think), basically what I'm getting at is that there is no acceleration as a result of the collision, just from friction of the street (I'm assuming your cars are on a road) which is why the cars are going to accelerate negatively until their velocities are 0 and both are at rest.

 

[newTonn]

If the collide then the law of conservation of momentum comes into play, no energy is gained or lost?

$$m_{a}v_{oa}+m_{b}v_{ob} = m_{a}v_{fa}+m_{b}v_{fb}$$

If one car has a velocity of 0, then the other car would have to have some sort of velocity to hit it. Since one of your cars is not moving:

$$m_{a}v_{oa} = m_{a}v_{fa}+m_{b}v_{fb}$$

This means that since the masses cannot change there wil be a change in velocities, the change is going to vary depending on a few factors such as is the collision elastic or inelastic? Technically speaking if there was no friction or gravity the cars would never stop (I think), basically what I'm getting at is that there is no acceleration as a result of the collision, just from friction of the street (I'm assuming your cars are on a road) which is why the cars are going to accelerate negatively until their velocities are 0 and both are at rest.

whatever way you look,you admit there is a change in momentum,which means a force and displacement is there.this finally means a work is done.So role of energy is relevent.

 

[newTonn]

You'd better check the definition of kinetic energy. If the body is moving, it has kinetic energy.

This is not the way ,a scientist should look at the things.If you say there is kinetic energy in a moving body, you have to substantiate this with some logic or calculations

As i mentioned in my previous post, acceleration,a = (v2 - v1)/t , or t = a/(v2 - v1). In this case since v2 = v1 ; t = 0 ; so if you substitute this ,we can find out the kinetic energy is zero.

Otherwise Could you please derivate the kinetic energy formula ,for a body moving with a uniform velocity?or please give me a link.

 

[Feldoh]

whatever way you look,you admit there is a change in momentum,which means a force and displacement is there.this finally means a work is done.So role of energy is relevent.

Change in momentum yes, but no energy is "gained" or "lost" it's simply (forgive me but it's the best word I could think of) transfered.

This is not the way ,a scientist should look at the things.If you say there is kinetic energy in a moving body, you have to substantiate this with some logic or calculations

As i mentioned in my previous post, acceleration,a = (v2 - v1)/t , or t = a/(v2 - v1). In this case since v2 = v1 ; t = 0 ; so if you substitute this ,we can find out the kinetic energy is zero.

Otherwise Could you please derivate the kinetic energy formula ,for a body moving with a uniform velocity?or please give me a link.

$$a = \frac {\Delta{v}}{\Delta{t}}$$
Since it's a change in time I'd venture to guess that's an average acceleration not an instantaneous one. But last time I checked the forumla was

$$KE = \frac{1}{2}mv^{2}$$

If a body is moving it has a velocity that is NOT 0, therefore it has kinetic energy. You proved it yourself, acceleration doesn't matter you derived the equation in a why which acceleration "cancels out".

 

[rcgldr]

derivate the kinetic energy formula ,for a body moving with a uniform velocity?

This formula is independent of a (non-accelerating) frame of reference:

$$work = 1/2\ m\ (\ V_1^2\ -\ V_0^2\ )$$

The simpler form

$$KE = 1/2\ m\ (\ V_1^2\ )$$

Is really just the first equation with $$V_0 = 0$$, so by definition, KE is the equivalent of the work it takes to accelerate or decelerate an object from $$V_0$$ to $$V_1$$. This allows KE to be defined (not derived) as a form of potential energy relative to a (non accelerating) frame of reference moving at $$V_0$$.

 

[newTonn]

Change in momentum yes, but no energy is "gained" or "lost" it's simply (forgive me but it's the best word I could think of) transfered.



$$a = \frac {\Delta{v}}{\Delta{t}}$$
Since it's a change in time I'd venture to guess that's an average acceleration not an instantaneous one. But last time I checked the forumla was

$$KE = \frac{1}{2}mv^{2}$$

If a body is moving it has a velocity that is NOT 0, therefore it has kinetic energy. You proved it yourself, acceleration doesn't matter you derived the equation in a why which acceleration "cancels out".

This formula is independent of a (non-accelerating) frame of reference:

$$work = 1/2\ m\ (\ V_1^2\ -\ V_0^2\ )$$

The simpler form

$$KE = 1/2\ m\ (\ V_1^2\ )$$

Is really just the first equation with $$V_0 = 0$$, so by definition, KE is the equivalent of the work it takes to accelerate or decelerate an object from $$V_0$$ to $$V_1$$. This allows KE to be defined (not derived) as a form of potential energy relative to a (non accelerating) frame of reference moving at $$V_0$$.

Thank you Jeff,that's it.
I was expecting the same answer from many.
I will come to my point based on this answer.
What will happen if we use the same concept for force?
say the force acting on the mentioned body,moving with a uniform velocity v1 is F= mass x acceleration (from zero to final velocity).
So now force on the body is F = m * v1/t.
now consider this body accelerated to a velocity of v2 in the next interval of 't1' seconds.
Now at this instance , force on body is F2 = m*v2/t1
force on body if it was still traveling at v1 for t1 seconds will be F1 = m*v1/t1.
so what is the net force /residual force or whatever,which caused this acceleration?

net F = (m*v2/t1) - (m*v1/t1) = m * a .

Why? and what is the use of changing the perspective.

Isn't it a clear answer for Inertia of body moving at uniform speed?Is it because of this force(already acting),a body which is at rest or in uniform motion tries to resist any changes in the motion?

Well ,i hope it is clear.please don't see it with a prejudice and correct me ,if i am wrong anywhere

 

[Doc Al]

This is not the way ,a scientist should look at the things.If you say there is kinetic energy in a moving body, you have to substantiate this with some logic or calculations

You're kidding me, right?

As i mentioned in my previous post, acceleration,a = (v2 - v1)/t , or t = a/(v2 - v1). In this case since v2 = v1 ; t = 0 ; so if you substitute this ,we can find out the kinetic energy is zero.

You are confusing change in kinetic energy with kinetic energy. From one second to the next, a body moving at constant speed has zero change in KE. The kinetic energy is certainly not zero.

Otherwise Could you please derivate the kinetic energy formula ,for a body moving with a uniform velocity?or please give me a link.

Look up the work-energy theorem, which relates work done to the change in KE. (http://hyperphysics.phy-astr.gsu.edu/hbase/work.html#wepr") As far as KE itself, it is defined to be $1/2 m v^2$ (at least in Newtonian physics).

 

[Doc Al]

Thank you Jeff,that's it.
I was expecting the same answer from many.
I will come to my point based on this answer.
What will happen if we use the same concept for force?
say the force acting on the mentioned body,moving with a uniform velocity v1 is F= mass x acceleration (from zero to final velocity).
So now force on the body is F = m * v1/t.

This is gibberish. Is the body moving with constant velocity or not? Acceleration is change in velocity over time, not a particular velocity over a particular time.

If the body is moving at a constant velocity, the net force on it is zero.

now consider this body accelerated to a velocity of v2 in the next interval of 't1' seconds.
Now at this instance , force on body is F2 = m*v2/t1
force on body if it was still traveling at v1 for t1 seconds will be F1 = m*v1/t1.
so what is the net force /residual force or whatever,which caused this acceleration?

net F = (m*v2/t1) - (m*v1/t1) = m * a .

In order for a body to change its velocity, a net force must act on it. That force is given by $F_{net} = m a$. Basic stuff! No need for vague concepts such as "residual force".

Isn't it a clear answer for Inertia of body moving at uniform speed?Is it because of this force(already acting),a body which is at rest or in uniform motion tries to resist any changes in the motion?

Nope. Newton figured this out centuries ago. No force is needed to maintain a constant velocity.

 

[K.J.Healey]

What will happen if we use the same concept for force?
say the force acting on the mentioned body,moving with a uniform velocity v1 is F= mass x acceleration (from zero to final velocity).

So we're saying F=m*a, which I'm sure you know is equivalent to F=dp/dt. I am just putting it out there for later use...

So now force on the body is F = m * v1/t.

I'm sure you mean F = m*dv/dt = m*a. Why that v1? Don't answer yet, I'll get to it in a second.

now consider this body accelerated to a velocity of v2 in the next interval of 't1' seconds.
Now at this instance , force on body is F2 = m*v2/t1

Remember F= m*dv/dt, mass times the Change in velocity over the Change in time. So with your method you'd say : F = m*(V2-V1)/(t2-t1)

force on body if it was still traveling at v1 for t1 seconds will be F1 = m*v1/t1.
so what is the net force /residual force or whatever,which caused this acceleration?

The force doesn't change. Its stays constant so long as acceleration (change in velocity) is constant.

net F = (m*v2/t1) - (m*v1/t1) = m * a .

Simplify that. F=m*(v2-v1)/t1=m*(dv)/(dt)= m*a
This is correct. Given a force F the mass "m" will accelerate from "v1" to "v2" over some period of time "t1" is correct.

You can't think of it as F(v), Force isn't a changing function of "v".
F(v1)=F(v2)=ma >> its constant in this example.

Why? and what is the use of changing the perspective.
Isn't it a clear answer for Inertia of body moving at uniform speed?Is it because of this force(already acting),a body which is at rest or in uniform motion tries to resist any changes in the motion?

Well ,i hope it is clear.please don't see it with a prejudice and correct me ,if i am wrong anywhere

I don't see what you're asking. Any mass needs a force to change its velocity. Thats Newtons 1st Law.

 

[rcgldr]

Say the force acting on the mentioned body,moving with a uniform velocity v1 is F= mass x acceleration (from zero to final velocity). So now force on the body is F = m * v1/t.

Ok, so v0 = 0 in your example. The way you've written it, the component (v1/t) doesn't look like an acceleration. It should be
F = m * (v1 - v0) / (t1 - t0)
so that it's clear that the acceleration is represented as a change in velocity versus a change in time, even if v0=0 and t0=0.

net F = (m*v2/t1) - (m*v1/t1) = m * a

This is almost correct, write it as
F = m *(v2 - v1)/(t2 - t1).

These examples are assuming a constant force.

 

[newTonn]

Nope. Newton figured this out centuries ago. No force is needed to maintain a constant velocity.

What is the cause of inertia?Does anybody figured this before?
Inertia,for a body moving at constant velocity ,is the force acting on it ,which is the cause of displacement of the body.(whatever may be the cause.somebody pulled it or push it).
Our force in regular equation,F = m*a;is the additional force required to change its velocity in a given interval.
Inertia, for a body at rest (in space,where there is no gravitational field- A body at rest is a concept ony,it can be relatively at rest)is zero.

 

[newTonn]

Ok, so v0 = 0 in your example. The way you've written it, the component (v1/t) doesn't look like an acceleration. It should be
F = m * (v1 - v0) / (t1 - t0)
so that it's clear that the acceleration is represented as a change in velocity versus a change in time, even if v0=0 and t0=0.
This is almost correct, write it as
F = m *(v2 - v1)/(t2 - t1).

These examples are assuming a constant force.

please... t , t1 ,t2 etc. mentioned here are time intervals.(may be i am using wrong notations)

 

[russ_watters]

What is the cause of inertia?Does anybody figured this before?
Inertia,for a body moving at constant velocity ,is the force acting on it ,which is the cause of displacement of the body.(whatever may be the cause.somebody pulled it or push it).

That's still gibberish. Inertia is a stand-alone physical property of matter. "Cause" is irrelevant. Newton's first law states explicitly that no force is required to keep a body in motion, only to accelerate it. Don't think that because you are asking a question that physics doesn't care about that that automatically makes it new and profound. It isn't - it is simply irrelevant. I'm not sure how we can make you accept how inertia works, but you can see it in everyday life. It just does.

Our force in regular equation,F = m*a;is the additional force required to change its velocity in a given interval.

I don't see "additional force" in that equation, I only see "force". "Additional force" is something you have made up and it doesn't exist. It doesn't matter what you call it - "additional force" or "residual force": it doesn't exist.

Inertia, for a body at rest (in space,where there is no gravitational field- A body at rest is a concept ony,it can be relatively at rest)is zero.

A body is always at rest with respect to itself. Newton's first law is not picky on this point: whether at rest or just in a uniform/constant state of motion, it works the same.

Heck, this is a pretty clear flaw in your idea that uniform motion requires a constant force. Since you understand that uniform motion is frame of reference dependent, so too would the force be frame of reference dependent. And you can't have force be frame dependent. A scale reads what a scale reads and only that value.

please... t , t1 ,t2 etc. mentioned here are time intervals.(may be i am using wrong notations

No. They are not time intervals, they are just times - what you see when you stare at your watch. t0=0 seconds, t1=1 second, t2= 2 seconds, etc. The interval from t1 to t2 is (t2-t1)=2-1=1 second. So the acceleration over that interval is the change in velocity divided by the time interval in which the change occurred.

Jeff wrote it exactly correctly.

 

[newTonn]

That's still gibberish. Inertia is a stand-alone physical property of matter. "Cause" is irrelevant. Newton's first law states explicitly that no force is required to keep a body in motion, only to accelerate it. Don't think that because you are asking a question that physics doesn't care about that that automatically makes it new and profound. It isn't - it is simply irrelevant. I'm not sure how we can make you accept how inertia works, but you can see it in everyday life. It just does. I don't see "additional force" in that equation, I only see "force". "Additional force" is something you have made up and it doesn't exist. It doesn't matter what you call it - "additional force" or "residual force": it doesn't exist. A body is always at rest with respect to itself. Newton's first law is not picky on this point: whether at rest or just in a uniform/constant state of motion, it works the same.

Heck, this is a pretty clear flaw in your idea that uniform motion requires a constant force. Since you understand that uniform motion is frame of reference dependent, so too would the force be frame of reference dependent. And you can't have force be frame dependent. A scale reads what a scale reads and only that value. No. They are not time intervals, they are just times - what you see when you stare at your watch. t0=0 seconds, t1=1 second, t2= 2 seconds, etc. The interval from t1 to t2 is (t2-t1)=2-1=1 second. So the acceleration over that interval is the change in velocity divided by the time interval in which the change occurred.

Jeff wrote it exactly correctly.

Why weight?-because of gravity(everybody knows)
Why conductivity?-because of valence electrons(everybody knows)
Why Inertia?-Nobody knows-so don't ask that question-it is irrelevant.

Is that what you mean?

And Let us consider one of everyday situation.You are traveling in a car.Suddenly you applied break.(You forget to wear your seat belt).You are throwned forward.
why? because of inertia.-finished.
If i say,that force which was acting on you,which cause you to move at a velocity equal to that of the car is still acting on you and remains until another force acts upon you,is there anything wrong?-you can call it inertia.
if there was no gravity ,or any other forces,the force will continuously act on you ,keeping you to move at same velocity.
And regarding rest, i stated that relatively a mass can be at rest.
you stated it in another way that a body is always at rest with respect to itself(relatively at rest).
Finally,regarding the time intervals ,it was something regarding my derivation and i have all the right to tell somebody that by that notations i mean time intervals (i remember i appologise for using wrong notations).

 

[Doc Al]

Why weight?-because of gravity(everybody knows)
Why conductivity?-because of valence electrons(everybody knows)
Why Inertia?-Nobody knows-so don't ask that question-it is irrelevant.

You are welcome to ponder the "ultimate" source and meaning of inertia, but first learn a bit of physics.

And Let us consider one of everyday situation.You are traveling in a car.Suddenly you applied break.(You forget to wear your seat belt).You are throwned forward.
why? because of inertia.-finished.

Somewhere you've picked up the misconception that a force is required to keep you moving forward. Some ancient Greeks thought this, but we've since discovered otherwise.

If i say,that force which was acting on you,which cause you to move at a velocity equal to that of the car is still acting on you and remains until another force acts upon you,is there anything wrong?-you can call it inertia.

You seem nominally interested in physics, but not enough to pick up a textbook and learn what we already know. Constant velocity does not require a force!

if there was no gravity ,or any other forces,the force will continuously act on you ,keeping you to move at same velocity.

Nope. Again: Learn (or at least read about) Newton's laws. Learn what we mean by a "force". A force requires an agent: something doing the pushing or pulling. If you are moving at a constant velocity either all the forces acting on you have canceled out or there are no forces acting on you. (For the latter, imagine a spaceship coasting in outer space, away from all masses.)

And regarding rest, i stated that relatively a mass can be at rest.
you stated it in another way that a body is always at rest with respect to itself(relatively at rest).

What's relevant here is whether the body is accelerating or not.

 

[newTonn]

You are welcome to ponder the "ultimate" source and meaning of inertia, but first learn a bit of physics..

What would have been the scenario if human beings stopped thinking out of box(from what they learned till then).?

Somewhere you've picked up the misconception that a force is required to keep you moving forward. Some ancient Greeks thought this, but we've since discovered otherwise..

Tell me why you require a force to stop an object moving at uniform velocity?
With your force you have to cancel some other force.what is the other force.it is inertia.if you try to find an equation to find out that force,you will end up with my conclusion.

You seem nominally interested in physics, but not enough to pick up a textbook and learn what we already know. Constant velocity does not require a force
Nope. Again: Learn (or at least read about) Newton's laws. Learn what we mean by a "force". A force requires an agent: something doing the pushing or pulling. If you are moving at a constant velocity either all the forces acting on you have canceled out or there are no forces acting on you. (For the latter, imagine a spaceship coasting in outer space, away from all masses.)


What's relevant here is whether the body is accelerating or not.

Ok.A force require an agent.yes did i told you no?
To achieve a constant velocity,you require a force .isn't it?Agents role is finished there.
shall i explain?
consider a golf ball (at rest-relatively).
you hit it with the club(sorry if i am right-club is the stick i mean)
Now the ball is accelerating positively ,then negative acceleration and ultimately comes to a hault.
If you see any intervals,you can see there is a force acting on the ball.
But you cannot say,the club was hitting on the ball throughout the way.
Learning is something and understanding is something else.
Please don't undermine peoples.There is something to learn from every layman.

 

[Doc Al]

What would have been the scenario if human beings stopped thinking out of box(from what they learned till then).?

You should open the box and see what's in it. But first you must find the box.

Tell me why you require a force to stop an object moving at uniform velocity?

If you are asking why the world is the way it is, I can't answer that.

With your force you have to cancel some other force.

There is no force (at least no net force) acting on an object moving at uniform velocity. So there is no "other force" that you have to cancel.

what is the other force.it is inertia.if you try to find an equation to find out that force,you will end up with my conclusion.

Your conclusion is based on misunderstanding.

Ok.A force require an agent.yes did i told you no?
To achieve a constant velocity,you require a force .isn't it?

No!

Agents role is finished there.
shall i explain?
consider a golf ball (at rest-relatively).
you hit it with the club(sorry if i am right-club is the stick i mean)
Now the ball is accelerating positively ,then negative acceleration and ultimately comes to a hault.
If you see any intervals,you can see there is a force acting on the ball.
But you cannot say,the club was hitting on the ball throughout the way.

I have no idea what this example is supposed to tell us. If you wish to accelerate the golf ball, you must exert a force on it. True. So?

Learning is something and understanding is something else.
Please don't undermine peoples.There is something to learn from every layman.

Might I dare suggest that there is something to learn from studying basic physics?

 

[newTonn]

THE CLUB IS NOT HITTING THE BALL THROUGHOUT THE WAY OF BALL.BALL IS MOVING BECAUSE AGENT(CLUB) EXERTED A FORCE ON IT IN PAST,BUT THE FORCE REMAINS UNTIL THE END OF EVENT(UNTIL FORCE DIMINISHES AND BODY COMES TO REST WITH THE EFFECT OF GRAVITY).This has to be true if there is no gravity as well.
Now if you couldn't understand what my example is telling you..

(We can wake up a man who is sleeping.But we cannot wake up a man who is pretending so.)

 

[Doc Al]

THE CLUB IS NOT HITTING THE BALL THROUGHOUT THE WAY OF BALL.BALL IS MOVING BECAUSE AGENT(CLUB) EXERTED A FORCE ON IT IN PAST,BUT THE FORCE REMAINS UNTIL THE END OF EVENT(UNTIL FORCE DIMINISHES AND BODY COMES TO REST WITH THE EFFECT OF GRAVITY).This has to be true if there is no gravity as well.
Now if you couldn't understand what my example is telling you..

Using bold caps does not help.

As soon as the club loses contact with the ball, it no longer exerts a force on the ball. If there are no other forces acting on the ball--such as gravity and air resistance--the ball will continue in a straight line at constant speed forever. But there are other forces acting on the ball. And when the ball hits the ground, the ground and grass exert other forces on the ball, eventually bringing it to rest. Once the ball is at rest, the net force on it is zero. So what?

(We can wake up a man who is sleeping.But we cannot wake up a man who is pretending so.)

Can't you hear the alarm clock ringing? Time to wake up!

 

[russ_watters]

You should open the box and see what's in it. But first you must find the box.

It's over there! You can lead newTonn to a box, but you can't make him open it?

 

[Nancarrow]

THE CLUB IS NOT HITTING THE BALL THROUGHOUT THE WAY OF BALL.BALL IS MOVING BECAUSE AGENT(CLUB) EXERTED A FORCE ON IT IN PAST,BUT THE FORCE REMAINS UNTIL THE END OF EVENT(UNTIL FORCE DIMINISHES AND BODY COMES TO REST WITH THE EFFECT OF GRAVITY).This has to be true if there is no gravity as well.

Except that it isn't true.

Er, sorry, I meant:

EXCEPT THAT IT ISN'T TRUE.

 

[Ariste]

Using your golf ball example:

You seem to think that once the ball is in the air, there must be some force acting on it to keep it moving. Unfortunately, Isaac Newton has told us that this isn't true.

The club exerts a force on the ball and accelerates it. It does work on the ball. This work is the transfer of energy from the club to the ball. After this work is done, the ball contains kinetic energy, with a magnitude of 1/2mv^2.

Work is then done by various forces to stop the ball. This work is done against the energy that was transferred to the ball by the club, not some force that is keeping the ball in motion. The ball, according to the law of inertia, will stay in motion until some net force acts upon it. In this case, air resistance and friction (once the ball hits the ground) will cause the ball to stop moving. Again, the work done by air resistance and friction is done against the work the club originally did on the ball, not against any force that has continued to act on the ball throughout its flight.

THE CLUB IS NOT HITTING THE BALL THROUGHOUT THE WAY OF BALL.BALL IS MOVING BECAUSE AGENT(CLUB) EXERTED A FORCE ON IT IN PAST,BUT THE FORCE REMAINS UNTIL THE END OF EVENT(UNTIL FORCE DIMINISHES AND BODY COMES TO REST WITH THE EFFECT OF GRAVITY).This has to be true if there is no gravity as well.

Here's where you're wrong: the force does not remain with the ball throughout its flight. The energy transferred to the ball by the force remains with the ball until it stops moving. The club does work on the ball, transferring energy to it. Once the ball is in the air, there is no force acting on it in the direction that it was originally hit. The forces of friction and air resistance now perform work against this moving body. This work is done to counteract the work that was originally done by the club - against the kinetic energy that the ball now contains. The work of air resistance and friction is not against any continuing force on the ball.

And just to be clear, gravity does not bring the ball to rest. It brings the ball down. Friction and air resistance bring the ball to rest.

 

[K.J.Healey]

Remember also that when you hit a golf ball, the ball accelerates WHILE the club is touching the ball. As soon as it leaves the face of the club, it WILL NOT SPEED UP. It will maintain its velocity forever and ever and ever. Unfortunately, there are natural FORCES that will CHANGE THE VELOCITY of the ball. Thats what a force does, by definition. It CHANGES VELOCITY. F = MA where A is the CHANGE IN VELOCITY. So this ball that would go forever and ever at some constant velocity V unfortunately gets pulled on by Gravity and Air resistance. Which Change its Velocity V.

If you are applying a SINGLE FORCE on an object, it will forever ACCELERATE and its velocity will always increase (assuming no speed limit of light, but don't even ask about that yet).

You have to realize that THAT is what a force is.

 

[rcgldr]

Tell me why you require a force to stop an object moving at uniform velocity?

Because any change in velocity will require a force, whether it's to increase or decrease the velocity.

With your force you have to cancel some other force. What is the other force.

The other force is the "reactive force" of an accelerating or decelerating object, which correpsonds to inertia. This acceleration or deceleration can be linear (rate of movment) or angular (rate of rotation). When forces applied to an object do not cancel each other out, the object's velocity and/or rate of rotation changes. This "reactive force" is always equal to the imbalance in forces applied to an object, regardless of the inertia of an object. Inertia (mass times linear and angular movement) isn't considered to be a force, just a factor into how an object will react to external forces (with mass determining the rate of change versus applied forces).

 

[newTonn]

Using bold caps does not help.

As soon as the club loses contact with the ball, it no longer exerts a force on the ball. If there are no other forces acting on the ball--such as gravity and air resistance--the ball will continue in a straight line at constant speed forever. But there are other forces acting on the ball. And when the ball hits the ground, the ground and grass exert other forces on the ball, eventually bringing it to rest. Once the ball is at rest, the net force on it is zero. So what?


Can't you hear the alarm clock ringing? Time to wake up!

Could anybody draw a freebody diagram of the ball ,just after the club hits the ball.

 

[newTonn]

Using your golf ball example:

You seem to think that once the ball is in the air, there must be some force acting on it to keep it moving. Unfortunately, Isaac Newton has told us that this isn't true.

The club exerts a force on the ball and accelerates it. It does work on the ball. This work is the transfer of energy from the club to the ball. After this work is done, the ball contains kinetic energy, with a magnitude of 1/2mv^2.

Work is then done by various forces to stop the ball. This work is done against the energy that was transferred to the ball by the club, not some force that is keeping the ball in motion. The ball, according to the law of inertia, will stay in motion until some net force acts upon it. In this case, air resistance and friction (once the ball hits the ground) will cause the ball to stop moving. Again, the work done by air resistance and friction is done against the work the club originally did on the ball, not against any force that has continued to act on the ball throughout its flight.



Here's where you're wrong: the force does not remain with the ball throughout its flight. The energy transferred to the ball by the force remains with the ball until it stops moving. The club does work on the ball, transferring energy to it. Once the ball is in the air, there is no force acting on it in the direction that it was originally hit. The forces of friction and air resistance now perform work against this moving body. This work is done to counteract the work that was originally done by the club - against the kinetic energy that the ball now contains. The work of air resistance and friction is not against any continuing force on the ball.

And just to be clear, gravity does not bring the ball to rest. It brings the ball down. Friction and air resistance bring the ball to rest.

Please coool and try to solve this problem with a freebody diagram(at any instance after the club hits ball).and get confirmed that without showing the force exerted by club,the ball should move in opposite direction.(because all other forces you are mentioning here are acting on the opposite direction).
Forget about the ball.
If you found a body which is accelerating with respect to you,Do you say a force is acting on the body?(we don't know wheather it was hit by something,pulled by something etc)

 

[russ_watters]

This is completely wrong and i think since all forumn members are focused on me,they forget to correct you.please somebody explain healey,that acceleration requires a time interval.A body cannot accelerate instantaneously,by defenition.Somebody please explain him what a banana is.. and then let him come to explain what an apple or orange is.

Sorry, newTonnn, there is a time interval there. The ball is in contact with the club for a finite and measurable amount of time, during which it accelerates.

 

[russ_watters]

Please coool and try to solve this problem with a freebody diagram(at any instance after the club hits ball).and get confirmed that without showing the force exerted by club,the ball should move in opposite direction.(because all other forces you are mentioning here are acting on the opposite direction).
Forget about the ball.
If you found a body which is accelerating with respect to you,Do you say a force is acting on the body?(we don't know wheather it was hit by something,pulled by something etc)[emphasis added]

Assuming you mean after the ball leaves the club-face, the ball will then be in motion with only the force of gravity acting on it. The club is no longer accelerating it.

Yeah, the golf ball accelerates really quickly when hit by a golf club.

 

[Ariste]

Please coool and try to solve this problem with a freebody diagram(at any instance after the club hits ball).and get confirmed that without showing the force exerted by club,the ball should move in opposite direction.(because all other forces you are mentioning here are acting on the opposite direction).
Forget about the ball.
If you found a body which is accelerating with respect to you,Do you say a force is acting on the body?(we don't know wheather it was hit by something,pulled by something etc)

No, no. You're not understanding.

After the ball leaves contact with the club, it has a pretty large velocity in what we'll call the forward direction. Yes, all other forces acting on the ball after it leaves the club are acting in the opposite direction, but these only act in response to the ball's movement relative to them. Through air resistance and friction, which act in the opposite of the direction of the ball's flight, the ball is brought to rest.

I think you are asking me why the ball does not begin to go backwards the other way after friction and air resistance bring it to a stop. You're saying that, if all forces acting on the ball after contact with the club (friction and air resistance) are pushing the ball backwards, the ball should slow to a stop and then begin to move backwards. As you can see in everyday life, though, this isn't the case.

Air resistance and friction only act on a body that is in motion relative to the agent of the air resistance or friction. When you push a box across the floor, the frictional force pushes against your push. When the box is just standing still, though, the frictional force doesn't push it backwards, or in any direction at all. Friction only acts against an applied force. Same with air resistance.

In the case of the golf ball, air resistance and friction bring the ball to rest, and once it's at rest, these forces cease acting, and the ball stays at rest. If you want to understand this in terms of free-body diagrams, you'll need to make at least two. After the ball leaves the club, there will be a force directed against the ball's motion (air resistance) and a force straight down (gravity). This diagram will stay pretty much the same until the ball hits the ground, when the frictional force will add to air resistance and create a greater force opposite the ball's motion. Once the ball comes to a rest, however, there will only be two forces acting on the ball in the diagram: the force of gravity straight down, and the normal force straight up. These forces will be exactly balanced, and there will be no other forces because the ball is not moving and thus friction and air resistance will not act on the ball. Since all forces are balanced, the ball will stay at rest.

 

[rcgldr]

Could anybody draw a freebody diagram of the ball ,just after the club hits the ball.

How about a very slow motion video of the impact? The club doesn't just hit the ball, it compresses the ball about 10% (iron) to 25% (club), and the ball springs back with a reasonably elastic reaction, so the ball leaves the club at a much higher velocity than the club is moving (club at 100mph, ball leaves at 170mph). Many golf broadcasts include "swing videos", such as this one, at the end is a super slow motion close up of the impact. I read that the duration of the interaction is about 5 milliseconds, (1 / 200th of a second), pretty quick. Note that the ball has bounced off the club about the same time that the club has only moved about 1/3rd of it's width over the tee.



As already posted, once the ball leaves the club, then the forces acting on it are aerodynamic drag and gravity, until the ball impacts with the ground (or trap, tree, spectator, ... ).

 

[Ariste]

How about a very slow motion video of the impact? The club doesn't just hit the ball, it compresses the ball about 10% (iron) to 25% (club), and the ball springs back with a reasonably elastic reaction, so the ball leaves the club at a much higher velocity than the club is moving (club at 100mph, ball leaves at 170mph). Many golf broadcasts include "swing videos", such as this one, at the end is a super slow motion close up of the impact. I read that the duration of the interaction is about 5 milliseconds, (1 / 200th of a second), pretty quick. Note that the ball has bounced off the club about the same time that the club has only moved about 1/3rd of it's width over the tee.



As already posted, once the ball leaves the club, then the forces acting on it are aerodynamic drag and gravity, until the ball impacts with the ground (or trap, tree, spectator, ... ).

Hey, pretty neat video :) I didn't realize the ball compresses like that.

 

[newTonn]

Assuming you mean after the ball leaves the club-face, the ball will then be in motion with only the force of gravity acting on it. The club is no longer accelerating it.

Yeah, the golf ball accelerates really quickly when hit by a golf club.

You didn't answer all my questions
let me ask it in a simple manner?
consider you are at rest or in uniform motion.
A rocket is moving at uniform velocity with respect to you.
Another rocket passed you with an acceleration.
(consider you don't know,wheather a thrust is applied on the rockets during its journey past you-you have been assingned to find out the force acting on these rockets).
What will be the force(net) acting on these rockets?
Do you use f = m*a in the case of second rocket? or do you say a force was acting on that rocket in past.
Please explain me how you will confirm,the acceleration was due to some action in past or it is attained during it was passing you.


regarding golf club really accelerates quickly.it depends on how hard you hit it.forgetting all other forces,we can say ,acceleration takes a time equal to the time required for ball to reach its final velocity from zero velocity.it never can be zero.