Kinetic energy in frames of reference

[daveed]

i was just reading, and i saw this question, and i don't know how to explain it...

how can you describe why when two things go at a velocity v, and one of them accelerates to 2v, the KE gain w/ respect to the Earth and the other object are different, but the work done is constant?

i just don't know how to explain this... it should not be so difficult, no?

 

[SpaceTiger]

how can you describe why when two things go at a velocity v, and one of them accelerates to 2v, the KE gain w/ respect to the Earth and the other object are different, but the work done is constant?

The work, Fx (assuming constant acceleration), isn't constant. The force is the same in both frames, but the distance isn't.

$$x=\int v~dt$$

Moving frame:

$$v=\int a~dt=at$$
$$x=\frac{1}{2}at^2$$

Stationary frame:

$$v=v_0+\int a~dt=v_0+at$$
$$x=v_0t+\frac{1}{2}at^2$$

In your example, this leads to work that's three times larger in the stationary frame, just like the change of kinetic energy.

 

[charng]

Kinetic energy is defined as the energy an object possesses due to its motion. In the context of frames of reference, it is important to understand that kinetic energy is a relative quantity and is dependent on the frame of reference in which it is measured. This means that the kinetic energy of an object will appear differently to observers in different frames of reference.

In the scenario described, two objects are initially moving at a velocity v and one of them accelerates to a velocity of 2v. This means that the change in kinetic energy for this object is greater than the other object, as it has a higher velocity. However, this does not mean that the work done on both objects is different.

Work is defined as the transfer of energy from one object to another. In this case, the work done on both objects is constant because the same amount of energy is being transferred from the accelerating object to the other object, regardless of their different velocities. This is because the work done is dependent on the force applied, and not just the velocity of the object.

To explain why the kinetic energy gain is different for the two objects, we must consider the concept of relative motion. From the perspective of the Earth, the initial velocity of both objects was v. However, when one object accelerates, its velocity relative to the other object changes from v to 2v. This change in relative velocity results in a greater change in kinetic energy for the object that accelerates.

In conclusion, the difference in kinetic energy gain for the two objects can be explained by considering the concept of relative motion and the frame of reference in which the kinetic energy is measured. The work done, on the other hand, remains constant as it is dependent on the force applied, not just the velocity of the object.