Thoughts Experiment about Frame of References

In summary: Earth relative to car which is 0 because it's moving at a constant velocity)3)10 = a - 0a = 10 km/h2 (acceleration of bird relative to me)4)40 = a - 0a = 40 km/h2 (acceleration of bird relative to me)In summary, the observer sitting in a car moving at 30 km/h east relative to Earth will see a bird flying at a velocity of -20 km/h if the bird is also moving east at a velocity of 10 km/h relative to Earth. If the bird is instead moving east at a velocity of 40 km/h relative to Earth, the observer will see the bird
  • #1
kasha
7
0

Homework Statement



The Observer (me) is at Inertial Frame of Reference:

1)
I am sitting at a car moving east v=30 km/h relative to earth
A bird flying east v = 10 km/h relative to earth
What is the speed of bird for me?

2)
I am sitting at a car moving east v=30 km/h relative to earth
A bird flying east v = 40 km/h relative to earth
What is the speed of bird for me?

3)
I am sitting at a car moving east v=30 km/h relative to earth
A bird flying east accelerating at a=10km/h2 relative to earth
What is the acceleration of the bird relative to me?

4)
I am sitting at a car moving east v=30 km/h relative to earth
A bird flying east accelerating at a=40 km/h2 relative to earth
What is the acceleration of the bird relative to me?

Please feel free to correct any stupidity/misconceptions I might have introduced in my questions

Homework Equations


Frames of Reference

The Attempt at a Solution



1) I think (-20km/h)...if the car and the bird started at the same spot, after 1hr, I would have traveled 30 km to the east, while the bird would have traveled only 10km to the east, so the bird is lagging behind me by 20km..looking as the bird is moving 20km/h to the west!2) I think (+10km/h)...if the car and the bird started at the same spot, after 1hr, I would have traveled 30 km to the east, while the bird would have traveled 40km to the east, so the bird is a head of me by 10 km..looking as the bird is traveling 10km/h to the east!

3) 10 km/h2 ?!
4) 40 km/h2 ?!
 
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  • #2
Looks good to me.
 
  • #3
Doc Al said:
Looks good to me.
Thanks but I was looking for more explanation.

for question (1 & 2). we simply use Galilean Transformation (let's not worry about Lorentz transformation)
The Galilean transformation gives the coordinates of the point as measured from the fixed frame in terms of its location in the moving reference frame.
The fixed frame is the Earth, the point moving is the bird, the frame moving (car)
but for the observer inside the car (the fixed frame is the car, the moving frame is the Earth moving at -30 km/h, the point moving is the bird)

x' (position of bird in moving frame "Earth") = x (position of bird measured from my frame "car") - vt (velocity of moving frame "Earth" with respect to mine)

for velocity transformation, we differentiate by t:
d(x')/dt = d(x)/dt - d(vt)/dt
v' (velocity of bird relative to Earth) = v (velocity of bird relative to car) - vs (velocity of car relative to Earth which is -30)

1)
10 = v - (-30)
v = -20 km/h (velocity of bird relative to car)

2)
40 = v - (-30)
v = 10 km/h (velocity of bird relative to car)

for (3&4) the acceleration transformation of the Galilean will be:
a' (acceleration of bird relative to Earth) = a (acceleration of bird relative to me)
 

Related to Thoughts Experiment about Frame of References

1. What is a thought experiment about frame of reference?

A thought experiment about frame of reference is a mental exercise used by scientists to explore and understand the effects of different reference frames on physical phenomena. It involves imagining a hypothetical scenario and analyzing how the laws of physics would apply from different perspectives.

2. Why are thought experiments about frame of reference important in science?

Thought experiments about frame of reference allow scientists to gain a deeper understanding of how the laws of physics work and how they are affected by different reference frames. They also help in developing new theories and concepts, and in testing the validity of existing theories.

3. Can thought experiments about frame of reference be used to solve real-world problems?

Yes, thought experiments about frame of reference can be used to solve real-world problems. They can provide insights and help in making predictions about physical phenomena, which can then be applied to real-world situations. For example, the theory of relativity, which was developed through thought experiments, has numerous practical applications in modern technology.

4. Do you need advanced knowledge of physics to understand thought experiments about frame of reference?

While a basic understanding of physics is helpful, one does not necessarily need advanced knowledge to understand thought experiments about frame of reference. These experiments are designed to be thought-provoking and can be understood by anyone with an open mind and a willingness to think critically.

5. Are there any limitations to thought experiments about frame of reference?

Like any other scientific method, thought experiments about frame of reference have their limitations. They are based on hypothetical scenarios and cannot always be tested or verified experimentally. Additionally, they may not accurately reflect the complexities of the real world. However, they remain a valuable tool for exploring and understanding the fundamental principles of physics.

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