Frames of Reference and Time Dilation

[chef99]

Homework Statement

Imagine that you are flying on an airliner on a long flight to Europe, at a constant speed of 300 m/s.



a) You throw a ball towards the back of the plane at 20 m/s. You then shine a beam of light towards the back of the plane. How will these two things—the ball and the light—appear to move, from the earth’s frame of reference? Explain any differences.

b) Would you expect your watch to be affected by time dilation? Explain your reasoning.

Homework Equations

vbe = vbs + vpe

The Attempt at a Solution

a)

vbe = vbs + vpevbe = (-20 m/s) + (300 m/s)vbe = 280 m/sThe ball will appear to move at 280 m/s [forward] from the earth’s frame of reference.

The speed of light would be unaffected, and appear to travel at the constant speed of

3.0 x 108 m/s from both the earth’s and the plane’s frame of reference.The differences in velocity undergone by the ball, depending on the frame of reference, are not experienced by the speed of light. This is because the velocity of objects is dependent on the inertial frame of reference it is viewed/calculated from. Different frames of reference, or direction of the objects travel, will affect the velocity of the object. For example, the ball gains the speed of the plane, minus its own velocity, since the ball is moving in the opposite direction of the plane, in the earth’s frame of reference. If the ball was moving in the direction of the plane [forward], it would have the plane's velocity, plus that of the ball, when viewed in the earth’s frame of reference. In contrast, light is independent of the frame of reference it is viewed from, and as such will travel at the same speed of 3.0 x 108 m/s, regardless of its frame of reference. It is this consistent, independent speed of light, coupled with the dependant speed of the ball, that leads to the differences experienced. b)

There would be a slight time dilation between the time elapsed in the plane to that on the earth, however since the plane is traveling very slowly (compared to the speed of light) the time dilation would be negligible, to the point that any normal (mechanical) watch would not be accurate enough to perceive any difference.

I would appreciate it if someone could check if these answers are correct, I'm confident in my understanding of different frames of reference, but I want to make sure I'm wording my answers correctly.
Also, does anyone know what kind of clock would be used to calculate the time dilation in this sort of scenario?
Thanks

 

[phinds]

Yes, you've got it all correct.

Atomic clocks have been used to measure airplane time dilation.

 

[chef99]

Yes, you've got it all correct.

Atomic clocks have been used to measure airplane time dilation.

Ok great thank you