Question

If I am in an inertial frame of reference, and I experience a force, what will happen is that I will accelerate relative to this inertial frame of reference. Say I am 60 kg and the force is 5 N and initially, I am at rest relative to this inertial frame of reference. This can be described by Newton's laws of motion. My acceleration is 1/12 m/s^2, relative to this inertial frame of reference.

However, if I am in an accelerating frame of reference with a constant acceleration, with absolutely nothing around me, I wouldn't be able to tell I am accelerating. (Imagine I am falling in a uniform gravitational field and the frame of reference is also accelerating with me. A good example will be a falling bottle of water and I am viewing from the angle of one water molecule). In this case, if I am 60 kg and experience a force of 5 N and initially, I am at rest relative to this accelerating frame of reference (imagine that, for some reason, I experience some sort of mysterious stuff that makes me at rest relative to this accelerating frame of reference), what will happen? What is my acceleration relative to this accelerating frame of reference? Do the physics laws still apply and why? Do Newton's second law and third law apply and why?

Then, my next question would be: What will happen if the conditions are the same as stated above, apart from that the frame of reference is accelerating with a changing acceleration. And why?

Answer 1

In an inertial frame of reference, a 5 N force would cause a 60 kg object to accelerate at 1/12 m/s^2. In an accelerating frame with constant acceleration, the observed acceleration from a 5 N force would initially be zero due to fictitious forces. In a non-constant accelerating frame, these fictitious forces become more complex, but Newton's laws still apply with adaptations.

Step-by-step explanation:

If you are in an inertial frame of reference and experience a force of 5 N, according to Newton's second law of motion, you would accelerate relative to the inertial frame. Since F=ma, with your mass being 60 kg, the acceleration would be 5 N / 60 kg = 1/12 m/s2. However, if you are in an accelerating frame of reference, things get more complex.

In an accelerating frame of reference, if you were at rest and experienced the same force, your acceleration relative to that frame would be zero initially, since no relative motion would be observed. This is due to the presence of fictitious forces which must be included in non-inertial frames to apply Newton's laws. Here, the force you experience might be a fictitious force that keeps you at rest relative to the accelerating frame.

When the frame of reference is accelerating with a changing acceleration, the fictitious forces become even more complex, and depend on the exact nature of the frame's acceleration. However, the laws of physics still apply, but they need to be considered with the addition of these fictitious forces to describe the motion correctly. Newton's laws still provide the correct framework but must be adapted correctly to the accelerating frame.