Work-Energy Theorem in Inertial Reference Frames

In summary: In frame A the particle moves 1 unit in x and y directions. In frame B the particle moves 2 units in x and y directions.
  • #1
Quelsita
49
0
OK, I'm working on a question regarding IRFs, but I seem to be a little confused.

Question:
Observer A is on the ground and Observer B in on a train moving with uniform velocity v wrt the ground. Each observes that a particle of mass m, initially at rest wrt the train, is acted upon by a constant force F applied to it in the forward direction for a time t.
a)What is the work done on the particle by F in referece frame A and B? Are they equal?
b)What are the changes in kinetic energy observed by A and B?
c)Does the Work-energy theorem hold in reference frames of observers A and B?

So, as I understand it, the particle is on the train as it is initially at rest wrt the train (i.e. it is moving with the train). The Force applied in the positive direction indicates that the train has slowed or stopped causing it to jerk forward.

Here is where I get confused, how is the work different for each reference frame? If the train is moving in the +x direction, then the particle is also moving in the +x direction, then does A see the train move in the +x and B see the train move in -x direction?

How does this change kinetic energy?

Thanks!
 
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  • #2
Quelsita said:
So, as I understand it, the particle is on the train as it is initially at rest wrt the train (i.e. it is moving with the train). The Force applied in the positive direction indicates that the train has slowed or stopped causing it to jerk forward.

No, I don't think that's the situation here. Imagine a food cart resting in the aisle of the train, stationary as seen by observer B on the train, but moving (in the +x direction) as seen by observer A on the ground. A train attendant comes along and pushes the cart down the aisle. Imagine that we can ignore friction, so if the attendant pushes with a constant force, the cart accelerates (in both reference frames).
 
  • #3
I see your point, that does make sense.

So, the particle is moving wrt to both reference frames, but I'm still stuck on how the different reference frames affect work...
 
  • #4
Hi Quelsita! :smile:
Quelsita said:
…The Force applied in the positive direction indicates that the train has slowed or stopped causing it to jerk forward.

No … where do you get that from? :confused:
Here is where I get confused, how is the work different for each reference frame? If the train is moving in the +x direction, then the particle is also moving in the +x direction, then does A see the train move in the +x and B see the train move in -x direction

Hint: Force = rate of change of momentum, which you can fairly easily prove is the same for both frames.

But the work done = force x distance moved by the point of application of the force (the particle), which is different for both frames.

How far does the particle move in time t in frame A? and how far in frame B? :smile:
 

1. What is the Work-Energy Theorem in Inertial Reference Frames?

The Work-Energy Theorem in Inertial Reference Frames is a fundamental principle in physics that states that the net work done on an object is equal to the change in its kinetic energy. This theorem is valid in all inertial reference frames, meaning frames of reference that are not accelerating.

2. How is the Work-Energy Theorem derived?

The Work-Energy Theorem is derived from Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. By integrating this equation with respect to displacement, we can obtain the Work-Energy Theorem.

3. What is the significance of the Work-Energy Theorem in physics?

The Work-Energy Theorem is a powerful tool that allows us to analyze and understand the motion of objects. It helps us determine the work done by forces on an object, as well as the resulting change in its kinetic energy. This theorem is also essential in many real-world applications, such as in the design of machines and structures.

4. Can the Work-Energy Theorem be applied to non-inertial reference frames?

No, the Work-Energy Theorem is only valid in inertial reference frames. In non-inertial frames, the net work done on an object may not equal its change in kinetic energy due to the presence of fictitious forces, which are forces that arise from the acceleration of the reference frame itself.

5. How is the Work-Energy Theorem related to the Law of Conservation of Energy?

The Work-Energy Theorem is closely related to the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transferred or transformed. The Work-Energy Theorem shows that the work done on an object is equal to the change in its kinetic energy, and this energy transfer is a manifestation of the Law of Conservation of Energy.

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