Question about Newton's Third Law and and the Force between 2 objects

[MrDickinson]

m1 is the large cruise ship

m2 is the tug boat

The question doesn't state it explicitly, but I assume that both masses are undergoing acceleration because the tug boat is experiencing a change in velocity. I assume the system accelerates uniformly, and I assume that m1 and m2 accelerate together and experience the same Δv/Δt.

Here, the tug boat is causing the large ship to accelerate; therefore, my reasoning is that the force exerted by the tug boat on the cruise ship must be greater than the force exerted by the cruise ship on the tug boat.

Apparently, I am wrong.

Can someone please explain this to me, with equations and free-body-diagrams if possible. Please include a verbal explanation of your reasoning as well, if possible.

Thanks

 

[russ_watters]

Can someone please explain this to me, with equations and free-body-diagrams if possible.

Why don't you start us off by drawing the free body diagrams for the cruise ship and tug. It should become immediately obvious where you are going wrong.

 

[Dale]

What does Newton’s 3rd law say? Quote it exactly from your text.

Apply that statement to the tug boats.

 

[A.T.]

...the tug boat is causing ... therefore, my reasoning is...

Here is where you go wrong. Causation doesn't enter force analysis.

 

[anorlunda]

Even simpler. Make a free body diagram of a one foot section from the middle of the tow line.

But no matter how you do it, you must be careful. Newton's second law, F=ma, tells us two things. For constant velocity, a=0 and the net forces F must be zero. If it is accelerating, then there is an additional force to consider to overcome inertia; its magnitude is F=ma.

I think you may be mixing up these two cases.

 

[Mister T]

Here, the tug boat is causing the large ship to accelerate; therefore, my reasoning is that the force exerted by the tug boat on the cruise ship must be greater than the force exerted by the cruise ship on the tug boat.

The large ship is accelerating because of forces exerted on the large ship. So forces on the tug boat are not relevant here.

Likewise, the tug boat is accelerating because of forces exerted on the tug boat. So forces on the large ship are not relevant here.

 

[sophiecentaur]

Apparently, I am wrong.

I'm afraid you are because:

Newton Three says what it says and no more.

Newton One and Newton Two are both relevant here and they are the ones that dictate what moves and in what direction.

There is tension in the tow rope and the forces on the two boats are not there in isolation - the tug has to be pushing water (or, it were two spaceships, there would be ejected, burnt rocket fuel). Without at least one other force in the system, there would be no tension in the tow rope.

 

[russ_watters]

There is tension in the tow rope and the forces on the two boats are not there in isolation - the tug has to be pushing water (or, it were two spaceships, there would be ejected, burnt rocket fuel). Without at least one other force in the system, there would be no tension in the tow rope.

I was really hoping the OP would be back with an attempt at the free body diagrams, because I think this makes it quite clear.

The FBD for the cruise ship is easy: it has one force, the tension of the tow rope.

The tug has two forces applied to it; the tension of the tow rope is pulling backwards and the force from the propeller pushing forwards, just a little harder than the tension of the tow rope.

 

[sophiecentaur]

I was really hoping the OP would be back with an attempt at the free body diagrams, because I think this makes it quite clear.

The free body diagram is not as straightforward for many people as PF may think. It can be a new idea for some people and it takes some getting used to. (After all, it's MATHS) Of course it's a great way to work thing out for the cognoscenti but it actually assumes some acceptance about what it means. There are many examples of OPs just ignoring explanations that include those three words. If someone is struggling then it may require someone else to draw the FBD for them.

 

[vanhees71]

Aren't free-body diagrams just there to torment students? For me the introduction of d'Alembert's principle and finally the action principle was a revelation ;-)).

 

[sophiecentaur]

Aren't free-body diagrams just there to torment students?

They can be a scary prospect because the student doesn't know what to include and what to leave out - it's the worry about being wrong.

 

[russ_watters]

The free body diagram is not as straightforward for many people as PF may think. It can be a new idea for some people and it takes some getting used to. (After all, it's MATHS) Of course it's a great way to work thing out for the cognoscenti but it actually assumes some acceptance about what it means. There are many examples of OPs just ignoring explanations that include those three words. If someone is struggling then it may require someone else to draw the FBD for them.

I'd say free body diagrams are deceptively simple, and the reason we try to force people to attempt to solve problems themselves is that doing is far more likely to ring the bell than just seeing. Even though it annoys a lot of our newer users.

 

[PeroK]

You don't need a FBD if you can picture the whole thing in your head. If you can't picture it all in your head, you need to draw a diagram.

 

[Dale]

They can be a scary prospect because the student doesn't know what to include and what to leave out - it's the worry about being wrong.

Which is why we assign homework!

 

[sophiecentaur]

Which is why we assign homework!

It really isn't always straightforward for people and they may need 'guidance' to get them over the hump.
Perhaps we should give a suitable link when someone apparently doesn't want to get involved. Like the wiki page ?

 

[vanhees71]

They can be a scary prospect because the student doesn't know what to include and what to leave out - it's the worry about being wrong.

Yes, whenever I had to use forces, I used the more simple principles to check, whether I'm right (as soon as I knew them of course) ;-).

 

[Mister T]

They can be a scary prospect because the student doesn't know what to include and what to leave out - it's the worry about being wrong.

In my experience, students seek first and foremost to make an answer (that is hopefully the correct answer). Most will avoid making free body diagrams because, yes, they don't know how to draw them, but also because they don't see their value. That is, they don't recognize that drawing the diagram will help them get the correct answer. Many students are focused on answer-making rather than sense-making.

The only remedy I've seen used successfully is to assign problems, and have the students draw only the free body diagram. There is no attempt at solving the problem. Then, once they learn how to draw the free body diagram, they can return to those problems and solve them. It takes a lot of extra time. Which is why I don't do it.

Moreover, in the USA for the last 15 years or so, school children have been taught that their standardized test score is all that matters. Those tests involve filling in a bubble. So skills that involve the making of drawings are not emphasized. Drawing vector diagrams to scale and doing ray tracing are a couple more skills that are suffering.

 

[sophiecentaur]

their standardized test score is all that matters.

Multiple choice answers are the death knell of understanding - they just tend to teach kids how to best answer multiple choice test.

 

[vanhees71]

Moreover, in the USA for the last 15 years or so, school children have been taught that their standardized test score is all that matters. Those tests involve filling in a bubble. So skills that involve the making of drawings are not emphasized. Drawing vector diagrams to scale and doing ray tracing are a couple more skills that are suffering.

Not only in the US! In Germany it's called you shouldn't teach people active knowledge but "competences". "Competences" however doesn't mean anything else than being trained to solve standardized problems. It's worst in math, but also in the natural sciences it's destroying all the fun, and finally students don't like STEM subjects, because it's something they cannot understand anyway. I've the impression that this socalled "didactics" has been done more bad than good in developing the high school curricula in these subject than anything else!

 

[Mister T]

Multiple choice answers are the death knell of understanding - they just tend to teach kids how to best answer multiple choice test.

Yes, they emphasize answer-making over sense-making. In general, I'm convinced that conscientious students who have difficulty in their introductory physics classes have focused their learning efforts (in all subjects) on answer-making. For most subjects, knowing how to make answers is evidence of understanding, but that is not necessarily so in physics. And of course, any conscientious physics instructor is emphasizing sense-making. So these students, as bright and studious as they may be, end up confused and think that physics is a hard subject to learn.

 

[Nugatory]

It really isn't always straightforward for people and they may need 'guidance' to get them over the hump.
Perhaps we should give a suitable link when someone apparently doesn't want to get involved. Like the wiki page ?

For this particular problem, the best advice may be to point the original poster at the closely related horse cart-problem - googling for "horse cart Newton" will bring up many good and user-friendly explanations

 

[sophiecentaur]

Along with the free body diagram, comes the general 'Normal Force' confusion. Having had loads of such questions to deal with at School, it's mostly not a problem for me 'cos I went through the regular A level course with Mr Worthington (legend) at a time in history when, however lazy you were, a lot of good stuff was crammed into you.