What are the forces at play in an elevator cab?

[jbriggs444]

What is the meaning of inertial frame.

Other threads in these forums have gone on deeply and at length (some with more than a little heat) about what is meant by the term "frame of reference". I will try to keep thing simpler than that.

One can get through high school (U.S. years 10, 11 and 12) with the notion of "frame of reference" as another name for a cartesian coordinate system. Like a piece of graph paper. The graph paper is free to move, but one is expected to pretend that it is at rest. You can write down the positions of all of your objects of interest in terms of the x and y coordinates found on the graph paper at events of interest. Of course, one is expected to record time stamps as well.

A piece of graph paper can move. It can move smoothly. It can accelerate. It can rotate. A piece of graph paper that translates at constant velocity without rotation can be thought of as defining an inertial frame.

This intuition was enough to get me through first year physics. But it left me somewhat uncomfortable. A frame of reference is not really a full blown coordinate system. Instead, it is more like a standard of rest.

One is not limited to cartesian coordinates. One can still have a standard of rest with polar coordinates. Nor is one limited to a particular scale -- a coordinate system implies a choice of units. But a frame of reference does not need a unit choice. What we need to have a frame of reference is a bit less than what we need to have for a coordinate system.

The picture I like these days is that a frame of reference is a standard of rest that applies at every point (event) in the space-time being considered. It gives you a standard for what "at rest" means at that event. It also gives you a standard for direction and speed. So if you have any object of interest at any point and at any time, the "frame of reference" is the standard that let's you say "that object was moving in such and such direction at such and such speed".

For example, if you have a frozen lake with bunch of stakes pounded in and on each stake is a speed detector and a compass, you have yourself the realization of a frame of reference.

An inertial frame of reference is one where objects free of external forces would have the same velocity vector each time they pass near a stake on the ice. That's Newton's first law.

Newton's second and third laws clarify what we mean by the term "force".

 

[rudransh verma]

@jbriggs444 I have posted a thread named “
'Inertial vs non inertial frames'
https://www.physicsforums.com/threads/inertial-vs-non-inertial-frames.1010363/
” please see it. It says something more about frames. What you wrote is very elementary but I am relieved to know that I don’t have to know much to solve 10+2 problems. I was very worried I won’t be able to solve problems without a firm grasp on frames.
This is the video by the way of that thread.

 

[rudransh verma]

All measured quantities here are either invariant or are relative to our chosen frame. We are not mixing frames in our measurements or calculations.

How is it possible? The acceleration a is relative to Earth whereas the $a_{cab}$ is relative to cab.

 

[Steve4Physics]

How is it possible? The acceleration a is relative to Earth whereas the $a_{cab}$ is relative to cab.

Hi @rudransh verma. Here’s an exercise for you.

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

1. For an observer in the ground frame of reference:
a. What is the gravitational force on P?
b. What force is exerted by the scales on P?
c. Are there any other (real or fictitious) forces on P in this frame? If so, describe.
d. What is the effective resultant force on P measured in this frame?
e. What is P’s acceleration in this frame?

2. For an observer in the cab’ frame of reference:
a. What is the gravitational force on P?
b. What force is exerted by the scales on P?
c. Are there any other (real or fictitious) forces on P in this frame? If so, describe.
d. What is the effective resultant force on P measured in this frame?
e. What is P’s acceleration in this frame?

Edit - minor changes.

 

[jbriggs444]

How is it possible? The acceleration a is relative to Earth whereas the $a_{cab}$ is relative to cab.

I am not inclined to go back and unravel the chain of references to figure out exactly what misunderstanding we were working on.

 

[rudransh verma]

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.

 

[vela]

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.

(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?

 

[Steve4Physics]

Assuming the cab is at rest,

Incorrect assumption. Read the question carefully and think about the values given.

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.

 

[rudransh verma]

Thanks @vela