Newton's Law conceptual question

[StevenStone]

Homework Statement

Two boxes of masses m and 3m are stacked.
The surface between the more massive box and
the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide
on the more massive box, what is t
he static friction force on the less massive box?
A) F
B) F/2
C) F/3
D) F/4

The answer is D.

Homework Equations

∑F=F=Ma
Ff=m(F3m)

So F= (F/3)

The Attempt at a Solution

∑Flarge=F=Ma
Ff=m(F3m)
∑Fsmall=Ff=ma
So F= (F/3)

I keep getting C as the answer. However, the solutions manual claims that the answer is D (I also asked my professor and he too said it is) Can anyone explain to me why it is D? Thank you.

 

[sankalpmittal]

Homework Statement

Two boxes of masses m and 3m are stacked.
The surface between the more massive box and
the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide
on the more massive box, what is t
he static friction force on the less massive box?
A) F
B) F/2
C) F/3
D) F/4

The answer is D.

Homework Equations

∑F=F=Ma
Ff=m(F3m)

So F= (F/3)

The Attempt at a Solution

∑Flarge=F=Ma
Ff=m(F3m)
∑Fsmall=Ff=ma
So F= (F/3)

I keep getting C as the answer. However, the solutions manual claims that the answer is D (I also asked my professor and he too said it is) Can anyone explain to me why it is D? Thank you.

You are applying force "F" on which block ? Is it not mentioned in the problem ?

 

[StevenStone]

I am applying it on the larger box. A diagram the question shows can be found here: http://s3.amazonaws.com/answer-board-image/03f392f4f851dd431c2243239c1a02af.jpg

 

[BvU]

Hello Steven, and welcome to PF.
You forgot to tell us what F is, but I can guess.
Did you make a drawing and a free body diagram for
1) the assembly of the two boxes
2) the less massive box on top by itself ?

If you want to, you can also make one for the large box by itself. In the horizontal direction there is not only F and ma but yet another force in play !
(And in the vertical direction there are two mg forces and N, the normal force).

 

[sankalpmittal]

I am applying it on the larger box. A diagram the question shows can be found here: http://s3.amazonaws.com/answer-board-image/03f392f4f851dd431c2243239c1a02af.jpg

Good, now find the acceleration of the whole system.

F=∑m x a..

 

[StevenStone]

Isn't it just a=FM? So if the mass is 3M is it A=F/3M? Or do you do A=F/(Small box + Big box) so A=F/(3M+1M)?

 

[sankalpmittal]

Isn't it just a=FM? So if the mass is 3M is it A=F/3M? Or do you do A=F/(Small box + Big box) so A=F/(3M+1M)?

I said acceleration of the whole system. Thus we have,

F=(3m+m)a => a=F/4m

Note that even i apply force F anywhere, it will still be net force on whole system. (Just treat two blocks as one single block.)

Now,

We switch to frame of small block kept on larger one. What is the pseudo force acting on that ?

 

[BiGyElLoWhAt]

If I push 2 boxes of mass m and 3m with an acceleration of 1 m/s^2 and they move as one, how much force am I exerting on the system?

 

[StevenStone]

I said acceleration of the whole system. Thus we have,

F=(3m+m)a => a=F/4m

Note that even i apply force F anywhere, it will still be net force on whole system. (Just treat two blocks as one single block.)

Now,

We switch to frame of small block kept on larger one. What is the pseudo force acting on that ?

The static friction?

 

[sankalpmittal]

The static friction?

Yes, the pseudo force will be equal and opposite to static friction in the frame of smaller block. Once you find the pseudo force, you have your answer. :)

 

[StevenStone]

Yes, the pseudo force will be equal and opposite to static friction in the frame of smaller block. Once you find the pseudo force, you have your answer. :)

This is where I'm confused. How do I find the pseudo force?

 

[sankalpmittal]

This is where I'm confused. How do I find the pseudo force?

Ok, if you observe from ground you see that acceleration of both the block is F/4m. Now question states that smaller block does not slip on the bigger one. Hence if you stand on the bigger block, you'll see that you are in rest with respect to smaller one. But, there is a net force acting on it right, because it is accelerated w.r.t ground. So in the frame of small block you apply force "mass of smaller block times acceleration in it" opposite to the force F because in that frame it is at rest.
The force which you apply just for the sake of frame change is the pseudo force.

 

[StevenStone]

Ok, if you observe from ground you see that acceleration of both the block is F/4m. Now question states that smaller block does not slip on the bigger one. Hence if you stand on the bigger block, you'll see that you are in rest with respect to smaller one. But, there is a net force acting on it right, because it is accelerated w.r.t ground. So in the frame of small block you apply force "mass of smaller block times acceleration in it" opposite to the force F because in that frame it is at rest.
The force which you apply just for the sake of frame change is the pseudo force.

So what is the acceleration in it? Is it just 3 because of the bigger box?

 

[sankalpmittal]

So what is the acceleration in it? Is it just 3 because of the bigger box?

The acceleration in both the block is same and that is F/4m. Now pseudo force in the smaller box is F_p = m(mass of smaller block) * F/4m(acceleration)...

This should equal and opposite to static friction if in this frame small block is not slipping. Will it not be ?

 

[StevenStone]

The acceleration in both the block is same and that is F/4m. Now pseudo force in the smaller box is F_p = m(mass of smaller block) * F/4m(acceleration)...

This should equal and opposite to static friction if in this frame small block is not slipping. Will it not be ?

Thank makes sense! Thank you very much!

 

[Andrew Mason]

I said acceleration of the whole system. Thus we have,

We switch to frame of small block kept on larger one. What is the pseudo force acting on that ?

This is where I'm confused. How do I find the pseudo force?

More to the point, what are you calling a pseudo force? The large mass exerts a real force (through static friction) on the smaller (this force = ma). The smaller mass exerts a real force on the larger mass of -ma. This reduces the net force on the larger mass to 4ma - ma = 3ma.

There is no reason to analyse this in the accelerating frame of the masses. The forces should be analysed in an inertial frame of reference.

AM

 

[HallsofIvy]

I don't see anything particularly complicated about this (but, then, I am not a physicist!). There is a total mass of 4m and a force of F is applied to it. The acceleration of the entire body is F/(4m). Since the object of mass m does not slip, it accelerates at F/4m. To accelerate a body of mass m and a= F/(4m) we must have a force of F= ma= mF/(4m)= F/4. There is no external force on the body of mass m so that must come from friction.

As a check, in order to accelerate just the 3m object at a= F/4m, there must be a total force 3m(F/4m)= (3/4)F on it. That is, in fact, the original force, F, minus the F/4 friction force the upper object, of mass m, is applying (opposite to the F force) on it.

(Now that I review, that is what Sankalpmittal said.)

 

[sankalpmittal]

Andrew Mason and HallsofIvy you both are correct.

Andrew Mason, if you see a thing from the ground, you'll see that the total mass(the system) accelerates by F/4m and in the frame of the smaller block it is at rest relatively. You can also solve this problem by inertial frame (of what I did from accelerating frame). I think that is what you did.

No one is WRONG here.

P.S. I am not a physicist as such. I am just an ordinary high school pass out.

 

[PhanthomJay]

Andrew Mason and HallsofIvy you both are correct.

No one is WRONG here.

P.S. I am not a physicist as such. I am just an ordinary high school pass out.

Pretty good for a high school pass out! As a general rule , though, pseudo forces should be used sparingly at the Intro level . Why use the pseudo force concept of F_net - ma = 0 when
the simple F_net = ma will suffice here. They say the same thing, but sooner or later you'll use the pseudo force concept once too often, and it will sting you. Ouch!

 

[sankalpmittal]

Pretty good for a high school pass out! As a general rule , though, pseudo forces should be used sparingly at the Intro level . Why use the pseudo force concept of F_net - ma = 0 when
the simple F_net = ma will suffice here. They say the same thing, but sooner or later you'll use the pseudo force concept once too often, and it will sting you. Ouch!

Ummm thanks for the first statement..

And why will it sting ? Umm curious...

 

[PhanthomJay]

Ummm thanks for the first statement..

And why will it sting ? Umm curious...

1. The key to the proper application of Newton's three laws at the intro level lies in the use of good free body diagrams. Free Body Diagrams show real forces, both contact forces like tension, normal, friction forces, etc., and non contact action at a distance forces like gravity. They do not show make - believe pseudo inertial forces.

2. Many an error has been made, both in homework problems and real world applications, by the improper use of the minus sign. The use of the negative inertial force compounds that error.

3. One good example where the pseudo force will sting you is the circular motion problems with its net inward center seeking centripetal force. Using the fictitious centrifugal force instead, will work against you.

 

[AlephZero]

PhantomJay has given this advice in previous threads on PF, but I think it depends what you want to achieve. If you want to pass a high school level exam with the minimum amount of understanding the subject, then "always work in an inertial coordinate system" might be a good "formula" to follow. On the other hand if you want to learn real-world Newtonian mechanics, you will not be able to hide from accelerating frames of reference for ever, so learn how to use them.

1. The key to the proper application of Newton's three laws at the intro level lies in the use of good free body diagrams. Free Body Diagrams show real forces, both contact forces like tension, normal, friction forces, etc., and non contact action at a distance forces like gravity. They do not show make - believe pseudo inertial forces.

Free body diagrams are a tool for solving problems, not an end in themselves. Restricting yourself to "the one and only correct way" to draw them is similar to the old saying, "if the only tool you have is a hammer, you have to treat every problem as if it was a nail".

2. Many an error has been made, both in homework problems and real world applications, by the improper use of the minus sign. The use of the negative inertial force compounds that error.

Sure, all errors (not "many") are made by making errors. Again, hiding from minus signs might get you through high school, but it won't get you far beyond that.

3. One good example where the pseudo force will sting you is the circular motion problems with its net inward center seeking centripetal force. Using the fictitious centrifugal force instead, will work against you.

There are many real-world situations which are much easier to model in a non-inertial coordinate system. The fact that high school level problems are often no harder to do either way should not be an excuse for not learning how to do both.

I would estimate about 90% of the mechanics I do in real life is done in non-inertial coordinate systems, because that is the only practical way to deal with them. IMO don't hide from them - just learn to use them correctly.

 

[PhanthomJay]

"Ahem, well then", said the old man, straightening himself up as much as he could," I haven't picked up a modern day intro physics text in thirty year, but I'd be surprised if they encouraged the use of inertial pseudo forces in basic level problems. I may need some enlightenment."

 

[sankalpmittal]

A side question, it has been glitching me since years!

In non inertial frames, we need to modify Newton's first two laws by introducing pseudo forces.

Now is Newton's third law applicable in non inertial frame ? Also do pseudo forces obey Newton's third law ?

My answer is no but I could be wrong.

Thanks!

 

[PhanthomJay]

A side question, it has been glitching me since years!



Now is Newton's third law applicable in non inertial frame ?

Newton's 3rd law applies to forces exerted by objects either accelerating or non-accelerating in both inertial and non inertial frames.

do pseudo forces obey Newton's third law ?

no.

Newton 3rd law essentially states that if object A exerts a force on object B, then object B exerts an equal but opposite force of like kind on object A. Pseudo forces are not forces exerted by objects. They have no third law force pair.

In your example, drawing a free body diagram of the top block, three forces act on it: the friction and normal forces of the lower block on the top block , and the force of the Earth (weight) acting on the top block. Real forces. Forces exerted by objects on another object.
With a force pair for each. So when you look at the lower block in a free body diagram, then in addition to the applied force and its weight acting on it, also the friction and normal force from the top block act on it.

Now if you again look at the top block FBD with pseudo forces shown, labeled as such, you have the same three real forces acting on it as noted above, plus the pseudo force ma acting on the top blocks com directed opposite the net force direction. When you now look at the lower 3m block in a FBD with pseudo forces shown, you have the same real forces acting plus a pseudo force of its own, 3ma , acting at its com. There is no Newton 3 pseudo force pair

 

[sankalpmittal]

Thanks a lot!