What are the forces at play in an elevator cab?

In summary: No, that is not what I was thinking. I was thinking that either:1. You introduce a fictitious force equal to ma due to the acceleration of the cab. Now Newton's second law holds good. But this fictitious force has no third law partner. So Newton's laws do not all hold.or2. You do not introduce this fictitious force. But now, as you point out, an object subject to a downward force of mg and upward force of mg + ma has zero acceleration. So Newton's second law fails.
  • #36
Steve4Physics said:
A person, P, in an elevator cab’, stands on weighing-scales calibrated in Newtons.
Take:
g = 10m/s² (downwards relative to the ground)
Mass of P= 50kg
Reading on scales = 600N
Assuming the cab is at rest,
1.a. 500 b.500 c. No d. 0 e. 0
2. same as 1 for all.
 
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  • #37
rudransh verma said:
Why it is necessary to have all three laws hold to be a inertial frame. What is the meaning of inertial frame. Also what is the relation between frames and speed/velocity ?
It's by definition. An inertial frame is defined as one in which Newton's laws of motion hold.

Let's leave out general relativity and curved spacetime for now and stick to plain Newtonian mechanics.

Say Alice is at rest in one reference frame, and Bob is at rest in another. Alice finds that Newton's laws hold from her perspective, and Bob finds that the laws hold for him as well. Both Alice and Bob would see the other is moving at a constant velocity. Carlos, on the other hand, tests Newton's laws and find they don't hold from his perspective. Both Alice and Bob will find Carlos is accelerating from their perspective.

Clearly, Alice and Bob are at rest in one type of reference frame, which we call inertial, and Carlos is at rest in another type, where Newton's laws of motion don't appear to work. As others have explained, Carlos can introduce fictitious forces to make the 1st and 2nd law hold again, but at the cost of the 3rd law.

rudransh verma said:
(You said rest frame, frame moving up with constant v, moving down with constant v are three different frames). Why are they different?
Why do you think they're not different?
 
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  • #38
rudransh verma said:
Assuming the cab is at rest,
Incorrect assumption. Read the question carefully and think about the values given.
rudransh verma said:
1.a. 500 b.500 c. No d. 0 e. 0
2. same as 1 for all.
Many mistakes due to the incorrect assumption.

Try again if you want.
 
  • #39

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