Calculating Time Dilation of a Rocket.

[alex1261]

Homework Statement

The problem was asking to find the time dilation of a rocket traveling upwards at 100,000 m/s with the reference point being Earth for a duration of a day.

Homework Equations

1/√(1-(β^2))
Δt = γΔt'

The Attempt at a Solution

I've calculating gamma to be 1.000000055, but I'm a little confused on where to go next. Do I just multiple gamma by Δt'? However, that gives me an incorrect and unreasonable answer. The answer key says that the answer should be 9ns. Any help is appreciated thanks.

 

[Simon Bridge]

Do I just multiple gamma by Δt'?

Pretty much - decide which observer and which clock.

However, that gives me an incorrect and unreasonable answer.

You probably picked the wrong clock or had the wrong number of nanoseconds in a day or somethinfg like that.
This is why we ask you to show your working - so we can figure out how to instruct you properly.

something The answer key says that the answer should be 9ns.

i.e. over the course of a day, one of the clocks will lose 9ns with respect to the other one. i.e. the question wants the difference between the elapsed times on each clock.

when 1day passes on the Earth, the Earth observer sees the rocket clock to have ticked off 1day+T nanoseconds. How do you find T?

 

[apelling]

I suspect that the supplied answer is incorrect. Nobody's perfect.

 

[Simon Bridge]

I suspect that the supplied answer is incorrect.

I think you are right there.

 

[Nickie]

I would first make sure that the equations used are correct and applicable to the situation. In this case, the equations for time dilation are appropriate for calculating the effects of special relativity on time for objects moving at high speeds.

Next, I would double check the values used for the velocity of the rocket and the duration of a day. It is important to use accurate and consistent units for these values.

Once the values are confirmed, the next step would be to plug them into the equations and solve for the time dilation. It is important to make sure that the units cancel out correctly and the final answer is expressed in the appropriate units.

If the answer still seems unreasonable, I would check for any errors in calculations or potential conceptual misunderstandings. It may also be helpful to consult with a colleague or refer to reliable sources for further clarification.

Overall, as a scientist, it is important to approach problems with a critical and analytical mindset, making sure to double check all steps and assumptions to ensure accurate and meaningful results.