Moving clocks and time dialation question

[phja]

i'm revising for an exam and have this question posed (this isn't homework)

what is the maximal velocity for a clock being transported from london to new york if the time difference to a stationary clock should be less than 10^-8 seconds.

i'm not allowed to use calculators.

i've tried doing it by t=t'y, but get a velocity of 1/3c, which i think is much too high. anyone have any ideas?

thanks.

 

[gendou2]

care to show how you got the 1/3c?

 

[thomate1]

I would approach this question by first understanding the concept of time dilation and how it relates to the velocity of an object. Time dilation is a phenomenon in which time appears to pass slower for an object in motion compared to a stationary observer. This is due to the effects of special relativity, which states that the speed of light is constant and the laws of physics are the same for all observers in uniform motion.

In order to calculate the maximal velocity of the clock being transported from London to New York, we need to use the formula for time dilation, which is t' = t/sqrt(1-v^2/c^2). Here, t' represents the time measured by the stationary clock, t represents the time measured by the moving clock, v represents the velocity of the moving clock, and c is the speed of light.

Since we want the time difference to be less than 10^-8 seconds, we can set t' = 10^-8 seconds and solve for v. This gives us v = c*sqrt(1-10^-16), which is approximately equal to c. This means that the maximal velocity for the clock being transported from London to New York is the speed of light, c.

It is important to note that this calculation assumes a perfect scenario where there are no external factors affecting the velocity of the clock. In reality, there may be other factors such as air resistance or gravitational effects that could slightly alter the maximal velocity. However, for the purpose of this exam question, assuming a perfect scenario, the maximal velocity for the clock would be the speed of light.

I hope this explanation helps you better understand the concept and approach to solving this question. Good luck on your exam!