Understanding Forces in Different Scenarios: Two Questions Analyzed

[Arquon]

Homework Statement

1.A body becomes weightless. What is the force Earth is pulling it ?
2.A box is on an incline plane and the box is not moving. What are the forces acting on the box ? What is the resultant force ? (Attached a picture of the box)

Homework Equations

Fg = mg

The Attempt at a Solution

These two questions got me a little bit confused so I'd like to know if I got these right.

1. I would say it is mg, because weight is not mass. ( other options were : 0, 2mg, m(g-a) )
2. C - Fn, Fg, and friction. Quite unsure about the resultant force, but it is probably 0, because the object is not moving ? ( other options were: mg, mg - Fn, 2mg)

 

[Orodruin]

I would say it is mg, because weight is not mass. ( other options were : 0, 2mg, m(g-a) )

So what is weight?

(Although I do think the question could have been better posed)

C - Fn, Fg, and friction. Quite unsure about the resultant force, but it is probably 0, because the object is not moving ?

Right.

 

[Arquon]

Weight is the force of gravity ? So if weight is 0, the force at which Earth pulls is as well 0, but acceleration still remains ?

 

[Orodruin]

Weight is the force of gravity ? So if weight is 0, the force at which Earth pulls is as well 0, but acceleration still remains ?

If the object has mass and is weightless, the only logical conclusion is that the gravitational field is zero. This can be changed by changing reference frame to onethat is accelerating relative to the one in which the object is weightless.

 

[Arquon]

So, to my understanding the answer is mg ? Sorry, this question is just really getting me confused.

 

[TomHart]

A body becomes weightless.

What does that statement mean? Does it mean the body is in a free fall near the surface of the earth? Or does it mean that the body is positioned far away from the Earth so that the Earth's gravity has no effect? Or I suppose if something could float at the perfect center of the earth, it would be weightless - but unstable. Or does it mean the body has some superhero gravity-cloaking device?
I think I have to agree with:

I do think the question could have been better posed

I just looked up "Weightlessness" on Wikipedia. There are two different interpretations given. (See below.) I guess you have to decide which one to use.

In Newtonian mechanics the term "weight" is given two distinct interpretations by engineers.
Weight₁: Under this interpretation, the "weight" of a body is the gravitational force exerted on the body and this is the notion of weight that prevails in engineering. Near the surface of the earth, a body whose mass is 1 kg has a weight of approximately 9.81 N, independent of its state of motion, free fall, or not. Weightlessness in this sense can be achieved by removing the body far away from the source of gravity. It can also be attained by placing the body at a neutral point between two gravitating masses.
Weight₂: Weight can also be interpreted as that quantity which is measured when one uses scales. What is being measured there is the force exerted by the body on the scales. In a standard weighing operation, the body being weighed is in a state of equilibrium as a result of a force exerted on it by the weighing machine cancelling the gravitational field. By Newton's 3rd law, there is an equal and opposite force exerted by the body on the machine. This force is called weight2. The force is not gravitational. Typically, it is a contact force and not uniform across the mass of the body. If the body is placed on the scales in a lift (an elevator) in free fall in pure uniform gravity, the scale would read zero, and the body said to be weightless i.e. its weight2 = 0. This describes the condition in which the body is stress free and undeformed. This is the weightlessness in free fall in a uniform gravitational field. (The situation is more complicated when the gravitational field is not uniform, or, when a body is subject to multiple forces which may, for instance, cancel each other and produce a state of stress albeit weight2being zero. See below.)
To sum up, we have two notions of weight of which weight1 is dominant. Yet 'weightlessness' is typically exemplified not by absence of weight1but by the absence of stress associated with weight2. This is the intended sense of weightlessness in what follows below.

A body is stress free, exerts zero weight2, when the only force acting on it is weight1 as when in free fall in a uniform gravitational field. Without subscripts, one ends up with the odd-sounding conclusion that a body is weightless when the only force acting on it is its weight.

 

[Arquon]

What does that statement mean? Does it mean the body is in a free fall near the surface of the earth? Or does it mean that the body is positioned far away from the Earth so that the Earth's gravity has no effect? Or I suppose if something could float at the perfect center of the earth, it would be weightless - but unstable. Or does it mean the body has some superhero gravity-cloaking device?

It only says that the body became weightless in pole. I guess we can simply imagine that object is falling towards pole.

 

[Arquon]

I tried using a formula, and I am getting that the answer is mg:

W = Fg - ma
Fg = W + ma ( W is 0)
Fg = ma ( a = g in this case)

Is this correct ?

 

[Orodruin]

It only says that the body became weightless in pole. I guess we can simply imagine that object is falling towards pole.

And, as I alluded to in #2 and was elaborated on in #6, the question is too vague to have a definite answer. It is then generally not a good idea to just assume something. The better approach would be to ask for clarification.

 

[Arquon]

And, as I alluded to in #2 and was elaborated on in #6, the question is too vague to have a definite answer. It is then generally not a good idea to just assume something. The better approach would be to ask for clarification.

So generally there can be two answers : 0 if the object is far away from Earth, and mg if the object is falling near Earth ?