Show that Newton's 2nd Law is Not valid in accelerating reference frame

• Tonia
In summary, the conversation discusses the validity of Newton's Second Law in a reference frame moving past the laboratory frame with a constant acceleration. The problem states that in the laboratory frame of reference, the law is valid, and the task is to show that it is also valid for an observer moving at a constant speed relative to the laboratory frame. The conversation also mentions the equations F=ma and dx^1/dt = dx/dt-v, as well as the concept that F and m would change while a would remain the same in an accelerating frame.
Tonia

Homework Statement

Show that Newton's Second Law is NOT valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration?
Problem 1: In a laboratory frame of reference, an observer notes that Newton's Second Law is valid. Show that it is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.
dx^1/dt = dx/dt-v
d^2x^1/dt^2= d^2x/dt^2
force new = force old
acceleration = d^2x/dt^2 and if v is constant = dv/dt = 0

F = ma

The Attempt at a Solution

I am not sure how to solve it

Last edited by a moderator:
If F1 = m1a1 measured in the Lab reference frame 1, which of F, m, and a, would be the same and which would be different if they are measured in an accelerating frame 2? If F1 = F2 and m1 = m2, but a1 ≠ a2, then you can say the F2 ≠ m2a2

Would the F and m be the same in the accelerating frame? If so, why?

Let me try this again: F would change, and m would stay the same?

1. How does Newton's 2nd Law change in an accelerating reference frame?

In an accelerating reference frame, Newton's 2nd Law states that the net force on an object is equal to its mass times its acceleration plus the fictitious force due to the acceleration of the frame of reference. This means that the traditional form of the law, which only includes the mass and acceleration of the object, is not completely valid in an accelerating reference frame.

2. Can you provide an example of when Newton's 2nd Law is not valid in an accelerating reference frame?

Imagine a person standing in a train car that is accelerating forward. According to Newton's 2nd Law, the person should experience a force in the opposite direction of the train's acceleration. However, in reality, the person will not feel this force because they are also accelerating at the same rate as the train.

3. Why is it important to consider an accelerating reference frame when applying Newton's 2nd Law?

In many situations, objects are not in a state of constant motion and may be accelerating due to various forces. When analyzing these situations, it is crucial to take into account the frame of reference in which the acceleration is occurring. Failure to do so can lead to incorrect predictions and understanding of the motion of objects.

4. Does this mean Newton's 2nd Law is not a valid law?

No, Newton's 2nd Law is still a valid law of physics. However, it is important to understand that it may need to be modified or adjusted when dealing with accelerating reference frames. In these cases, the law can be extended to include the fictitious force due to the acceleration of the frame of reference.

5. How does the concept of inertia tie into Newton's 2nd Law not being valid in an accelerating reference frame?

Inertia, the tendency of an object to resist changes in its motion, is a key concept in Newton's 2nd Law. In an accelerating reference frame, the concept of inertia still applies, but it may be more complex due to the presence of the fictitious force. The object's inertia will determine how it responds to this additional force and how its motion is affected in the accelerating frame of reference.

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