Let’s assume we have 2 different observers. Observer 1 sits in space and observer 2 sits in a space lab which is in a free fall state toward the Earth. We further assume that observer 2 in the space lab does not have any information regarding its surrounding. 1. Is there anyway that observer 2 can figure out whether any frame attached to the space lab can be regarded as an inertial or non-inertial frame? 2. Lets assume there is a 1kg ball inside the space lab which is also free falling together with the space lab? Observer 1 (with its true inertial frame) can measure the acceleration of the ball and deduce that 9.8Newton force is acting on the ball. On the other hand, observer 2 measures the acceleration of the ball as 0, and hence, deduces that the net force acting on the ball is 0. As th

Faith Welch 2022-07-16 Answered
Let’s assume we have 2 different observers. Observer 1 sits in space and observer 2 sits in a space lab which is in a free fall state toward the Earth. We further assume that observer 2 in the space lab does not have any information regarding its surrounding.
1. Is there anyway that observer 2 can figure out whether any frame attached to the space lab can be regarded as an inertial or non-inertial frame?
2. Lets assume there is a 1kg ball inside the space lab which is also free falling together with the space lab? Observer 1 (with its true inertial frame) can measure the acceleration of the ball and deduce that 9.8Newton force is acting on the ball. On the other hand, observer 2 measures the acceleration of the ball as 0, and hence, deduces that the net force acting on the ball is 0. As the observer 2 has no way of knowing that space lab is not an inertial frame, he will not have any doubt about his force measurement. Does this mean that definition of force is dependent on the frame of reference?
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Answers (1)

kamphundg4
Answered 2022-07-17 Author has 20 answers
Looks like you understand the situation already and only need slight confirmation/clarification.
Let's start with simple case. There is an inertial frame of reference, there are some objects, there are forces acting between objects. Objects are moving around, accelerated by the forces.
In any other inertial frame of reference, the forces between objects are the same.
Next case is more complicated. Consider the same set of objects in some non-inertial frame of reference. You can't just use usual Newton laws any more because you are not in an inertial frame of reference! But it may be very convenient for your purposes to use this frame, no matter is it inertial or not. F.e you describe what's going on inside a space station orbiting Earth. Using inertial frame of reference would be very inconvenient for this purpose!
It turns out that it is possible to use Newton's laws even in this situation. You only have to add some additional, "fictional" forces to the equations.
You switch to inertial frame of reference - these additional forces disappear. You switch back - the forces are back. Very real, you can feel how this force pushes you into the chair in airplane. So, the existence of force depends on frame of reference if there is no restriction that frames of reference must be inertial.
And sometimes it's not possible to decide, if your frame of reference is inertial or not. There is no way to find out if the force acting on all the objects in a room is a gravitational force produced by some real planet or is it a "fictional" force existing only because the room is accelerating.
Bottom line: forces do not change if you switch between inertial frames of reference, forces may change if you switch between non-inertial frames, sometimes it's tricky to find you if your frame of reference is inertial or not.

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