Bullwinkle in reference frame S' passes you in reference frame S along the common direction of the x' and x axes, as in Fig. 37-9. He carries three meter sticks: meter stick 1 is parallel to the x' axis, meter stick 2 is parallel to the y' axis, and meter stick 3 is parallel to the z' axis. On his wristwatch he counts off 15.0 s, which takes 30.0 s according to you. Two events occur during his passage. According to you, event 1 occurs at and , and event 2 occurs at and . According to your measurements, what is the length of (a) meter stick 1, (b) meter stick 2, and (c) meter stick 3? According to Bullwinkle, what are (d) the spatial separation and (e) the temporal separation between events 1 and 2, and (f) which event occurs first?
The expression of time dilation is given by,
Here, the time according to watch is, , and the time according to Bull winkle is, .
From equation (1),
It is known that then,
The expression to calculate the length is given by,
Substitute 1 m for Lo, and 2 for in equation (2).
Therefore, the length of meter stick 1 is 0.5 m.
The meter stick 2 is along y-axis, and the frame S' is moving along positive x-axis. Therefore, there is no length contraction along y' direction. So, the length of the meter stick parallel to y' axis will remain same.
Hence, according to the measurement of length of the meter stick parallel to y' axis is 1 m.
There is no length contraction for the meter stick placed parallel to z axis. Thus, according to the measurement of length of the meter stick parallel to z' axis is 1 m.
The expression to calculate the spatial separation is given by,
Find as follows.
Find as follows.
Find v as follows.
Substitute 2 for , 20 m for , for , and for v in equation (3).
Therefore, the spatial separation is 19.216 m.
The expression to calculate temporal separation is given by,
Substitute 2 for , 20 m for , for , for c, and for v in equation (4).
Therefore, the temporal separation is -35.46 ns.
The value of temporal separation is negative. Therefore, the event 2 is occurred before event 1 in S'.
You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, on your return, to find Earth as it will be exactly 1000 years in the future. (a) To eight significant figures, at what speed parameter must you travel? (b) Does it matter whether you travel in a straight line on your journey?
An electron of moves along the axis of an evacuated tube that has a length of 3.00 m as measured by a laboratory observer S at rest relative to the tube. An observer S’ who is at rest relative to the electron, however, would see this tube moving with speed v ( ).What length would observer S’ measure for the tube?
Question: Temporal separation between two events. Events and occur with the following spacetime coordinates in the reference frames of Fig. 37-25: according to the unprimed frame, and according to the primed frame, . In the unprimed frame and . (a) Find an expression for in terms of the speed parameter and the given data. Graph versus for the following two ranges of : (b) 0 to 0.01and 0.1 (c) 0.1 to 1. (d) At what value of is minimum and (e) what is that minimum? (f) Can one of these events cause the other? Explain.
94% of StudySmarter users get better grades.Sign up for free