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Chapter 37: 42P (page 1148)
What is the minimum energy that is required to break a nucleus of 12C (of mass 11.996 71 u) into three nuclei of 4He (of mass 4.001 51 u each)?
The minimum energy to break the nucleus of Carbon nuclei into Helium nuclei is 7.28 MeV.
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Observer reports that an even occurred on theaxis of his reference frame at at time . Observerand her frame are moving in the positive direction of the axis at a speed of. Furtherat. What are the (a) spatial and (b) temporal coordinate of the event according to ? If were, instead, moving in the negative direction of theaxis, what would be that (c) spatial and (d) temporal coordinate of the event according to?
The car-in-the-garage problem. Carman has just purchased the world鈥檚 longest stretch limo, which has a proper length of . In Fig. 37-32a, it is shown parked in front of a garage with a proper length of . The garage has a front door (shown open) and a back door (shown closed).The limo is obviously longer than the garage. Still, Garageman, who owns the garage and knows something about relativistic length contraction, makes a bet with Carman that the limo can fit in the garage with both doors closed. Carman, who dropped his physics course before reaching special relativity, says such a thing, even in principle, is impossible.
To analyze Garageman鈥檚 scheme, an axis is attached to the limo, with at the rear bumper, and an axis is attached to the garage, with at the (now open) front door. Then Carman is to drive the limo directly toward the front door at a velocity of (which is, of course, both technically and financially impossible). Carman is stationary in the reference frame; Garageman is stationary in the role="math" localid="1663064422721" reference frame.
There are two events to consider. Event 1: When the rear bumper clears the front door, the front door is closed. Let the time of this event be zero to both Carman and Garageman: . The event occurs at . Figure 37-32b shows event 1 according to the reference frame. Event 2: When the front bumper reaches the back door, that door opens. Figure 37-32c shows event 2 according to the reference frame.
According to Garageman, (a) what is the length of the limo, and what are the spacetime coordinates (b) and (c) of event 2? (d) For how long is the limo temporarily 鈥渢rapped鈥� inside the garage with both doors shut? Now consider the situation from the reference frame, in which the garage comes racing past the limo at a velocity of . According to Carman, (e) what is the length of the passing garage, what are the spacetime coordinates (f) and (g) of event 2, (h) is the limo ever in the garage with both doors shut, and (i) which event occurs first? (j) Sketch events 1 and 2 as seen by Carman. (k) Are the events causally related; that is, does one of them cause the other? (l) Finally, who wins the bet?
A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the rear car passes the near end of the tunnel (event RN), a device in that car is set to send a signal to the engine room to deactivate the bomb. Train view: (a) What is the tunnel length? (b) Which event occurs first, FF or RN? (c) What is the time between those events? (d) Does the paint bomb explode? Tunnel view: (e) What is the train length? (f) Which event occurs first? (g) What is the time between those events? (h) Does the paint bomb explode? If your answers to (d) and (h) differ, you need to explain the paradox, because either the engine room is covered with blue paint or not; you cannot have it both ways. If your answers are the same, you need to explain why?
One cosmic-ray particle approaches Earth along Earth鈥檚 north-south axis with a speed of toward the geographic north pole, and another approaches with a speed of toward the geographic south pole (Fig. 37- 34). What is the relative speed of approach of one particle with respect to the other?
In Fig. 37-26a, particle P is to move parallel to the x and axes of reference frames S and , at a certain velocity relative to frame S. Frame " width="9">x axis of frame S at velocity v. Figure 37-26b gives the velocity localid="1664359069513" of the particle relative to frame localid="1664359072841" for a range of values for v. The vertical axis scale is set by . What value will have if (a) and (b) ?
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