Conceptual questions about Newton's Laws....

[PrathameshR]

Homework Statement

I can't find answers to following questions in the book Concepts of Physics by H. C. Verma.1. The apparent weight of an object increases in an elevator accelerating upward. A peanut seller sells his peanuts using a beam balance in an elevator. Will he gain more if elevator is accelerating up?

2.According to Newtons third law each team pulls the other team with equal force in a tug of war. Why then one team wins?

3.Can two particles be in equilibrium under the action of their mutual gravitation?

4.The weight of an object is more at poles than at equator. Is it beneficial to purchase goods at equator and sell at pole( Do not consider other factors like transportation expenses)? Does it matter whether a spring balance or beam balance is used?

Homework Equations

NA

The Attempt at a Solution

1. I think the apparent acceleration should not matter. This can be viewed as using beam balance on another planet. But somebody had given me a convincing reason of why he should gain. I don't remember the logic as it was 4 years ago. so now I'm confused.

2. I think it has something to do with friction.

3. I think the answer is no.But I'm not sure. Obviously the two masses can go around the c.m. but does that classify as equilibrium?

4. I don't know how to start thinking on this question.

 

[berkeman]

1. I think the apparent acceleration should not matter. This can be viewed as using beam balance on another planet. .

I think your answer is correct, but it would be better to discuss how a beam balance works, compared to a spring balance for weighing objects...

2. I think it has something to do with friction.

Friction may be part of it, but can you draw a Free Body Diagram (FBD) of the rope to help answer this question?

3. I think the answer is no.But I'm not sure. Obviously the two masses can go around the c.m. but does that classify as equilibrium?

What if they are touching...?

4. I don't know how to start thinking on this question.

Since there is a difference in apparent weight, if the goods are sold by weight, they would have different values at the two locations, right? Why are things lighter at the equator compared to the poles? And refer to your answer to #1 to compare the beam balance and spring balance...

 

[Alloymouse]

Homework Statement

I can't find answers to following questions in the book Concepts of Physics by H. C. Verma.1. The apparent weight of an object increases in an elevator accelerating upward. A peanut seller sells his peanuts using a beam balance in an elevator. Will he gain more if elevator is accelerating up?

2.According to Newtons third law each team pulls the other team with equal force in a tug of war. Why then one team wins?

3.Can two particles be in equilibrium under the action of their mutual gravitation?

4.The weight of an object is more at poles than at equator. Is it beneficial to purchase goods at equator and sell at pole( Do not consider other factors like transportation expenses)? Does it matter whether a spring balance or beam balance is used?

Homework Equations

NA

The Attempt at a Solution

1. I think the apparent acceleration should not matter. This can be viewed as using beam balance on another planet. But somebody had given me a convincing reason of why he should gain. I don't remember the logic as it was 4 years ago. so now I'm confused.

2. I think it has something to do with friction.

3. I think the answer is no.But I'm not sure. Obviously the two masses can go around the c.m. but does that classify as equilibrium?

4. I don't know how to start thinking on this question.

1) Yes, you do have the right idea! The acceleration experienced by all objects in the elevator will be the same, therefore, there will be no changes in moments about the beam balance.

2) Beyond friction (which indeed is a factor), consider Newton's second law (including the simplified version - I'll leave that to you). Think along the lines of why you can open a door, but not move a skyscraper by just pulling on it.

3) As @berkeman mentioned, consider the case where they are in contact. For the case where they are orbiting each other, in a sense yes, it is like an equilibrium as by N3L, the forces on each other are equal too.

4) Similar to (1), consider how the apparent weights can result in differences in spring balance and beam balance.

 

[conscience]

For the case where they are orbiting each other, in a sense yes, it is like an equilibrium as by N3L, the forces on each other are equal too.

This is incorrect .

A particle is in equilibrium when net force acting on it is zero . Clearly this is not the case when the two particles are orbiting about their CM .

Not sure why you are bringing Newton's 3rd law while analysing the state of an object ( whether it is in equilibrium ) .

 

[Alloymouse]

This is incorrect .

A particle is in equilibrium when net force acting on it is zero . Clearly this is not the case when the two particles are orbiting about their CM .

Not sure why you are bringing Newton's 3rd law while analysing the state of an object ( whether it is in equilibrium ) .

Oh, I was going on the lines of the system not experiencing a net force - I'm bundling both bodies together as a system, and gravitational force becomes somewhat of an "Internal force", due to N3L making the forces equal and opposite. Kinda like tension.

 

[conscience]

Oh, I was going on the lines of the system not experiencing a net force - I'm bundling both bodies together as a system, and gravitational force becomes somewhat of an "Internal force", due to N3L making the forces equal and opposite. Kinda like tension.

Consider two masses ( kept on a frictionless surface ) at the ends of a massless spring oscillating .

Do you think the two masses are in equilibrium ?

If you think so , your definition of equilibrium is not right .

 

[conscience]

What if they are touching...?

Do two particles touching each other make sense ?

OTOH OP's idea of the particles orbiting each other is alright .

 

[Alloymouse]

Consider two masses ( kept on a frictionless surface ) at the ends of a massless spring oscillating .

Do you think the two masses are in equilibrium ?

If you think so , your definition of equilibrium is not right .

The masses are indeed not in equilibrium individually, but for the system as a whole, I believe they are in equilbrium - there's no net force, and no net torque. But yes, it's pointless thinking about the system as a whole I suppose.

In that respect, then that would mean that neither body will be in equilibrium (ref to OP's question): they will always experience a net force.

Clarification: In my comments, I interpreted equilibrium as translational and rotational - no net force acting on the system/object, and no net torque at any point on the system/object. I just realized that there's another form of equilibrium that you guys are talking about, which is static equilibrium. I hope the OP would clarify what equilibrium is required in this context.

 

[conscience]

but for the system as a whole, I believe they are in equilbrium

Generally equilibrium is discussed for individual masses .

In that respect, then that would mean that neither body will be in equilibrium (ref to OP's question): they will always experience a net force.

Why ?

A book kept on a table is in equilibrium . A wheel rolling with constant linear speed is in equilibrium .

In my comments, I interpreted equilibrium as translational and rotational - no net force acting on the system/object, and no net torque at any point on the system/object.

I am also going with the same definition .

I just realized that there's another form of equilibrium that you guys are talking about, which is static equilibrium.

No . I am referring to dynamic equilibrium .

Do you think a particle undergoing circular motion has no net force acting on it ?

 

[Alloymouse]

Generally equilibrium is discussed for indidividual masses .Why ?

A book kept on a table is in equilibrium . A wheel rolling with constant linear speed is in equilibrium .
I am also going with the same definition .
No . I am referring to dynamic equilibrium .

Do you think a particle undergoing circular motion has net zero force acting on it ?

Alright, looks like the only confusion here was the first point - I was referring to the system, while you were referring to the individual body. So yes that was where we had some mismatch in ideas.

However, I am curious to find out why something in circular motion is interpreted to be at equilibrium - isn't there always a net force acting on it that changes its absolute velocity? (Direction change)

 

[conscience]

isn't there always a net force acting on it that changes its absolute velocity? (Direction change)

When did I object to this ?

My objection was regarding your discussion about equilibrium of the system as a whole and bringing up Newton's 3rd law in this , which I think is irrelevant .

 

[Alloymouse]

When did I object to this ?

My objection was regarding your discussion about equilibrium of the system as a whole and bringing up Newton's 3rd law in this , which I think is irrelevant .

Yes, I did realize lol. Anyways, let's just put that past us now :)

TLDR To OP: consider circular motion and whether it is at equilibrium for (3)

 

[conscience]

OK

 

[PrathameshR]

If they are touching each other it means that they are not in equilibrium solely due to gravity. Electromagnetic contact forces are also involved.

 

[Sanchez]

Equilibrium means net force acting on an object (particle) is zero, according to Newton's first law of motion.
Net force is zero when object is at rest or moving at constant velocity (no acceleration)

Equilibrium also means that net torque acting on an object is zero.

 

[Sanchez]

∑F = 0 and ∑τ = 0