# How does the object move if forces between two objects are equal and opposite?

Overall01
Hello,

If forces between two objects are equal and opposite, then how can a van pull a car if they were attached with, say, some rope (e.g)?

Surely the force of the car on the rope is equal and opposite to the force of the rope on the car. So is it because the van and car are of different masses or something to do with friction?

I'm not entirely sure, so any help would be much appreciated. Please base advice to secondary school (year 11) /high school student (10th grade). Thanks.

## Answers and Replies

Gold Member
By Newton's 3rd, if object A exerts a force on object B, then object B will exert an equal and opposite force on object A. The key point is that these forces are acting on different bodies. So the motion of some object depends only on the forces that are acting on that object.

Overall01
By Newton's 3rd, if object A exerts a force on object B, then object B will exert an equal and opposite force on object A. The key point is that these forces are acting on different bodies. So the motion of some object depends only on the forces that are acting on that object.

Thanks for the reply.

I understand that it's because they are of different bodies (and hence masses) but could you please explain this with regards my example, since this is where I don't understand.

If a van is attached to a (stationary) car which is say, stuck in some mud, with rope and the van begins accelerating, why does the car also move? I believe it may be due to the force of the ground on the van, and the force of the mud on the car, but I'm quite confused. Does this mean friction?

Mentor
If forces between two objects are equal and opposite, then how can a van pull a car if they were attached with, say, some rope (e.g)?
What determines whether an object accelerates is the net force on it (per Newton's 2nd law). The fact that all forces between any two objects are always equal and opposite (per Newton's 3rd law) is irrelevant.

So, for the van to accelerate, there must be a net force in the forward direction. Most likely friction, as you suggest. Net force on van = Friction - force of car pulling back on van (via the rope).

Since they are attached via the rope, the van and car must both move forward. So that means that the net force on the car must be in the forward direction as well.

azizlwl
http://imageshack.us/a/img825/8569/19182213.jpg [Broken]

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hav0c
http://imageshack.us/a/img825/8569/19182213.jpg [Broken]

azizlwl
isn't the horse and cart system acting effectively as the same object?

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Overall01
What determines whether an object accelerates is the net force on it (per Newton's 2nd law). The fact that all forces between any two objects are always equal and opposite (per Newton's 3rd law) is irrelevant.

So, for the van to accelerate, there must be a net force in the forward direction. Most likely friction, as you suggest. Net force on van = Friction - force of car pulling back on van (via the rope).

Since they are attached via the rope, the van and car must both move forward. So that means that the net force on the car must be in the forward direction as well.

http://imageshack.us/a/img825/8569/19182213.jpg [Broken]
Thanks for the reply guys.

I'm still a little confused though with regards:

http://s15.postimage.org/6nn54clt7/Inthemud.jpg [Broken]

What is the force of ground on tractor and force of mud on car? Is that friction? There's only one arrow, so is that the net force?

Just another thing, it doesn't mention the car moving due to the pull of rope on car; only because of the force of ground on tractor is greater than force of mud on car? So which is it?

Sorry for all the questions but I'd appreciate any help.

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azizlwl
Another example is an Arwood's Machine.
The tension on both sides are equal for whatever mass A and mass B.

If mass A is heavier than mass B, even though the tension on both side are equal, mass A and mass B will be accelerating.

Gold Member
Thanks for the reply guys.

I'm still a little confused though with regards:

http://s15.postimage.org/6nn54clt7/Inthemud.jpg [Broken]

What is the force of ground on tractor and force of mud on car? Is that friction?
Yes.
There's only one arrow, so is that the net force?
No, there will also be the pull from the rope (tension force). As Doc Al said, net force on car will be in same direction as the net force acting on the object moving it.

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Mentor
What is the force of ground on tractor and force of mud on car? Is that friction?
You can think of that as friction.
There's only one arrow, so is that the net force?
There are two arrows. One on the tractor going forward; one on the car going backward. The vector sum of those is the net force on the system of 'tractor plus car'.

Just another thing, it doesn't mention the car moving due to the pull of rope on car; only because of the force of ground on tractor is greater than force of mud on car? So which is it?
It's up to you to choose the system you want to analyze. Looking at the car by itself, the two forces are the force from the rope pulling forward and the force from the mud pulling backward. Only if the force from the rope is greater will the car accelerate forward.

But if you look at tractor + car as a single system you can ignore the force of the rope, since it would be internal to the system.

But regardless of how you analyze it, the answer must be the same.