# Force and Change in Momentum

## Homework Statement

A net external force acts on an object of mass m. Is this information
sufficient to conclude that
(i) the velocity of the object changes?
(ii) the kinetic energy of the object changes?
(iii) the speed of'the object changes?

## Homework Equations

Conservation of momentum.

Conservation of Kinetic Energy.

## The Attempt at a Solution

My solution was that, insufficient information was given to determine velocity as direction of force was not given.

Kinetic Energy and Speed can be found as they are unreliant on direction (KE relying on V^2)

Could anybody tell me if I am on the right track? Or am I way way off?

It seems like a pretty simple question, I just wanted to check if my understanding is correct.

Any help, Much appreciated =)

cepheid
Staff Emeritus
Gold Member

## Homework Statement

A net external force acts on an object of mass m. Is this information
sufficient to conclude that
(i) the velocity of the object changes?
(ii) the kinetic energy of the object changes?
(iii) the speed of'the object changes?

## Homework Equations

Conservation of momentum.

Conservation of Kinetic Energy.

## The Attempt at a Solution

My solution was that, insufficient information was given to determine velocity as direction of force was not given.

Kinetic Energy and Speed can be found as they are unreliant on direction (KE relying on V^2)

Could anybody tell me if I am on the right track? Or am I way way off?

It seems like a pretty simple question, I just wanted to check if my understanding is correct.

Any help, Much appreciated =)

I think you're missing the point of the question. Take part (i), for example. They're not asking you to determine what the velocity is. They're just asking you if there is enough information to determine whether the velocity changes in this situation. Do you have enough information to determine whether it will change?

I see what you mean. Hmm.. I would say that yes, there is sufficient information as with force, the acceleration of the object (if it accelerates or moves) can be found.

For Kinetic Energy, insufficient as I would need work done, and that requires distance the object travels.

Would that be a better way of approaching the problem?

cepheid
Staff Emeritus
Gold Member
I see what you mean. Hmm.. I would say that yes, there is sufficient information as with force, the acceleration of the object (if it accelerates or moves) can be found.

You can pose the question in another (equivalent way) that might help:

Q. You know that there is NET force acting on an object. Is this enough information for you to conclude that its velocity will change (yes or no)?

A. Yes, we know with certainty that the velocity of the object will change, because a net force means a non-zero acceleration. If the object is accelerating, then its velocity is changing.

For Kinetic Energy, insufficient as I would need work done, and that requires distance the object travels.

You're still not quite getting what the question is asking. These are all yes/no questions. Let's try this again:

Q. You know that there is NET force acting on an object. Is this enough infomation for you to conclude that its kinetic will change (yes or no)?

A. ____________________________

If there is a net force acting on the object, the object moves. Work done can be determined and so change in Kinetic Energy?

cepheid
Staff Emeritus
Gold Member
The key thing here is that you're not being asked if there is enough information to conclude how much the change in the quantity will be. You're only being asked if there is enough information to conclude whether the quantity will change at all.

In other words, given this information you don't have be able to find out how much the KE will change (if it changes). You just have to be able to find out whether it will change or not. Do you have enough info to say whether it will change or not?

EDIT: emphasized the key word.

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In other words, is it possible for me to calculate a change if there is any, with the information given?

I would say yes, I would have enough information to know if the kinetic energy changes, given the external force and the mass of the object.

cepheid
Staff Emeritus
Gold Member
In other words, is it possible for me to calculate a change if there is any, with the information given?

NO!!!!!

This is what I've been trying to get across here. You're NOT being asked if you have enough info to calculate the change. You're JUST being asked whether you have enough info to state with certainty that a change will occur. Can you state with certainty that a change will occur? Yes or no? That is the question.

I would say yes, I would have enough information to know if the kinetic energy changes, given the external force and the mass of the object.

Matterwave
Gold Member
Since it's pretty obviously that there are situations in which a net-force means kinetic energy changes (e.g. accelerating a particle from rest), try to think of a situation where a net force results in no kinetic energy change. If such a situation were possible, then it's impossible to determine if kinetic energy changes or not. If there is no such situation, then you can say for sure that the kinetic energy will change.

Ok I think I got it. I do NOT have to calculate any values, but determine whether or not a change in Kinetic Energy would occur, given the information above?

So there isn't sufficient information provided, but why is it so?

I'm sorry if it's getting frustrating =S

I really do appreciate your help, i've been trying to wrap my head around this question for awhile.

If there is a net force, we know the object moves. Wouldn't that constitute in a change in Kinetic Energy?

If an object is in motion and the force applied is not in the direction of motion, than there will be no work done as such no kinetic energy change. So with the problem not stating what situation the object and force are in, it is insufficient to determine whether KE would change. Am I closer?

cepheid
Staff Emeritus
Gold Member
Ok I think I got it. I do NOT have to calculate any values, but determine whether or not a change in Kinetic Energy would occur, given the information above?

...whether or not a change in kinetic energy would be certain to occur. But yes, you understand now.

So there isn't sufficient information provided, but why is it so?

I'm sorry if it's getting frustrating =S

I really do appreciate your help, i've been trying to wrap my head around this question for awhile.

If there is a net force, we know the object moves. Wouldn't that constitute in a change in Kinetic Energy?

At this stage, Matterwave's advice is a good thing to consider. Hint: what has to change in order for KE to change? In other words, what quantities does KE depend on? Can you think of a situation where there is a net force on the particle, and yet none of the quantities that KE depends on are changing?

cepheid
Staff Emeritus
Gold Member
If an object is in motion and the force applied is not in the direction of motion, than there will be no work done as such no kinetic energy change. So with the problem not stating what situation the object and force are in, it is insufficient to determine whether KE would change. Am I closer?

Uh yeah. You are indeed much closer. But it's not enough that the two aren't in exactly the same direction. There has to be a very specific relationship between their directions in order for NO work to be done.

The two forces are perpendicular to each other, as such no work is done and there will be no change in kinetic energy.

Since the problem doesnt state the relationship between the net force and the direction of motion of the object, we cannot determine if Kinetic Energy changes?

cepheid
Staff Emeritus
Gold Member
The two forces are perpendicular to each other, as such no work is done and there will be no change in kinetic energy.

Bingo! Can you think of a physical situation where this occurs? A net force acts on a body...its velocity is continuously changing, but its speed remains constant...because the force is always perpendicular to the direction of motion.

Since the problem doesnt state the relationship between the net force and the direction of motion of the object, we cannot determine if Kinetic Energy changes?

You got it! That is why the answer to (ii) (and hence (iii)) is, "No."

Oh Snap! I got it! haha

One example would be if the object is in uniform circular motion. The centripetal force is always perpendicular to the velocity of the ball. So kinetic energy does not change.

Thank you so much for the time and patience cepheid and Matterwave =) really appreciate it.

cepheid
Staff Emeritus