Non-inertial observer inside train

In summary, the observer inside the train cannot directly measure the acceleration of the train. They can only measure the deflection in a spring scale and use that information to calculate the acceleration. This is because they are unable to see the increasing velocity of the train or the boxcar. Additionally, in the perspective of the observer inside the train, the fictitious force acting on the mass until the string becomes taut has a very real effect. However, from an external, inertial frame of reference, this force is considered fictitious because it depends on the mass of the object being acted on, which is not a characteristic of real forces.
  • #1
ChiralSuperfields
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Homework Statement
Pls see below
Relevant Equations
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For part (c) of this problem,
1676851122866.png

The solution is,
1676851157115.png

However, how did they know that the fictitious force that acts on the mass until the string become taut (T = Ma from as observed by an observer at rest outside) has a magnitude of Ma (assuming that the observer has no communication with the outside observer)

Many thanks!

Many thanks!
 
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  • #2
Callumnc1 said:
...
However, how did they know that the fictitious force that acts on the mass until the string become taut (T = Ma from as observed by an observer at rest outside) has a magnitude of Ma (assuming that the observer has no communication with the outside observer)
Someone in the car can only see how much deflection occurs in the spring scale.
That person is unable to see the increasing velocity of the object or the boxcar.
Therefore, a direct measurement of the acceleration can't be made by that person.
 
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  • #3
Callumnc1 said:
how did they know that the fictitious force that acts on the mass until the string become taut (T = Ma from as observed by an observer at rest outside) has a magnitude of Ma (assuming that the observer has no communication with the outside observer)
The observer in the car has to have some way of figuring out the acceleration of the car. Note that they have no way to distinguish a literal acceleration from a constant horizontal gravitational attraction. This is part of the reasoning behind Einstein's GR theory.
 
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Thank you for your replies @Lnewqban and @haruspex !

I guess we could go as far as saying then that there is no way to tell from an non-inertial perspective inside the carriage that there is a fictitious force acting at all. From their perspective it is a very real force, correct?

Many thanks!
 
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  • #5
Callumnc1 said:
Thank you for your replies @Lnewqban and @haruspex !

I guess we could go as far as saying then that there is no way to tell from an non-inertial perspective inside the carriage that there is a fictitious force acting at all. From their perspective it is a very real force, correct?

Many thanks!
In GR, gravity is considered a fictitious force because, like acceleration of the frame, it depends on the mass of the object being acted on. Real forces should not depend on that.
 
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  • #6
Callumnc1 said:
Thank you for your replies @Lnewqban and @haruspex !

I guess we could go as far as saying then that there is no way to tell from an non-inertial perspective inside the carriage that there is a fictitious force acting at all. From their perspective it is a very real force, correct?

Many thanks!
Yes. Furthermore, the person inside the train will be under the impression that the "floor" on which the mass rests is an inclined plane. That's because a plumb bob hanging from the ceiling defines the local direction of "down". When viewed from the inertial frame of the ground, the plumb bob will not be perpendicular to the floor, but will be slanted back. Thus, the "down" direction for the person in the car is not perpendicular to the floor. Also, the body of the person must be aligned with the plumb bob and lean into the "incline" to avoid being toppled over. The effective weight of the train rider is the vector sum ##m\mathbf{g}+m(-\mathbf{a})##.
 
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  • #7
haruspex said:
In GR, gravity is considered a fictitious force because, like acceleration of the frame, it depends on the mass of the object being acted on. Real forces should not depend on that.
Thank you for your help @haruspex !
 
  • #8
kuruman said:
Yes. Furthermore, the person inside the train will be under the impression that the "floor" on which the mass rests is an inclined plane. That's because a plumb bob hanging from the ceiling defines the local direction of "down". When viewed from the inertial frame of the ground, the plumb bob will not be perpendicular to the floor, but will be slanted back. Thus, the "down" direction for the person in the car is not perpendicular to the floor. Also, the body of the person must be aligned with the plumb bob and lean into the "incline" to avoid being toppled over. The effective weight of the train rider is the vector sum ##m\mathbf{g}+m(-\mathbf{a})##.
Thank you for you reply @kuruman !

That is very interesting what you mention about the person having to a higher effective weight. But I guess if the acceleration is purely horizontal in the train's case the normal force from the floor dose not have to increase, correct?

Many thanks!
 
  • #9
Callumnc1 said:
Thank you for you reply @kuruman !

That is very interesting what you mention about the person having to a higher effective weight. But I guess if the acceleration is purely horizontal in the train's case the normal force from the floor dose not have to increase, correct?

Many thanks!
The normal force from the floor does not change, but the person now experiences 'gravity' as being at an angle to the floor, and increased in magnitude.
 
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  • #10
haruspex said:
The normal force from the floor does not change, but the person now experiences 'gravity' as being at an angle to the floor, and increased in magnitude.
Thank you for that @haruspex !
 
  • #11
Callumnc1 said:
Thank you for your replies @Lnewqban and @haruspex !

I guess we could go as far as saying then that there is no way to tell from an non-inertial perspective inside the carriage that there is a fictitious force acting at all. From their perspective it is a very real force, correct?

Many thanks!
Thank you for your reaction @PeroK !

Out of curiosity, what makes you skeptical?

Many thanks!
 
  • #12
Callumnc1 said:
Thank you for your reaction @PeroK !

Out of curiosity, what makes you skeptical?

Many thanks!
You confused force with acceleration. If you are in a car that accelerates forward, then the force you experience is in the forward direction. If something isn't accelerating with the car, then in the reference frame of the car, it is accelerating in the opposite direction. You then must add a fictitious force to explain the relative acceleration in the non-inertial frame.
 
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  • #13
PeroK said:
You confused force with acceleration. If you are in a car that accelerates forward, then the force you experience is in the forward direction. If something isn't accelerating with the car, then in the reference frame of the car, it is accelerating in the opposite direction. You then must add a fictitious force to explain the relative acceleration in the non-inertial frame.
Thank you help @PeroK !
 

1. What is a non-inertial observer inside a train?

A non-inertial observer is an observer who is experiencing acceleration or deceleration. In the case of a train, the observer is inside a closed system that is moving at a constant speed, but the observer feels the effects of acceleration and deceleration as the train starts, stops, or changes direction.

2. How does the motion of the train affect the observations of a non-inertial observer?

The motion of the train can affect the observations of a non-inertial observer in several ways. First, the observer may feel a force pushing them in a certain direction, even though the train is moving at a constant speed. Second, the observer may observe objects outside the train appearing to move in a curved path due to the train's acceleration or deceleration. Third, the observer may experience a change in their perception of time due to the train's motion.

3. How does the concept of relativity apply to a non-inertial observer inside a train?

The concept of relativity states that the laws of physics are the same for all observers, regardless of their state of motion. This applies to a non-inertial observer inside a train as well. The observer may feel the effects of acceleration and deceleration, but the laws of physics still apply to their observations and measurements.

4. Can a non-inertial observer inside a train experience weightlessness?

Yes, a non-inertial observer inside a train can experience weightlessness. This can happen when the train is in free fall or when it is moving at a constant velocity. In both cases, the observer is not experiencing any external forces and therefore feels weightless.

5. How does the concept of inertia relate to a non-inertial observer inside a train?

The concept of inertia states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. In the case of a non-inertial observer inside a train, the observer may feel a force pushing them in a certain direction, even though the train is moving at a constant speed. This is because the train is acting as the external force on the observer, causing them to accelerate or decelerate along with the train's motion.

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