Another approach to velocity transformations. In Fig. 37-31, reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocities of one frame relative to another with a two-letter subscript. For example, v AB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, ß AB (= v AB /c ) is the speed parameter corresponding to v AB (a) Show that β A C = β A B + β B C 1 + β A B β B C . Let M AB represent the ratio (1 − ß AB ) / ( 1 + ß AB ), and let M BC and M AC represent similar ratios. (b) Show that the relation M AC = M AB M BC is true by deriving the equation of part (a) from it. Figure 37-31 Problem 65, 66 and 67.
Another approach to velocity transformations. In Fig. 37-31, reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocities of one frame relative to another with a two-letter subscript. For example, v AB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, ß AB (= v AB /c ) is the speed parameter corresponding to v AB (a) Show that β A C = β A B + β B C 1 + β A B β B C . Let M AB represent the ratio (1 − ß AB ) / ( 1 + ß AB ), and let M BC and M AC represent similar ratios. (b) Show that the relation M AC = M AB M BC is true by deriving the equation of part (a) from it. Figure 37-31 Problem 65, 66 and 67.
Another approach to velocity transformations. In Fig. 37-31, reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocities of one frame relative to another with a two-letter subscript. For example, vAB is the x component of the velocity of A relative to B. Similarly, represent the corresponding speed parameters with two-letter subscripts. For example, ßAB (= vAB/c) is the speed parameter corresponding to vAB (a) Show that
β
A
C
=
β
A
B
+
β
B
C
1
+
β
A
B
β
B
C
.
Let MAB represent the ratio (1 − ßAB)/(1 + ßAB), and let MBC and MAC represent similar ratios. (b) Show that the relation
MAC= MABMBC
is true by deriving the equation of part (a) from it.
A 238U nucleus is moving in the x direction at 5.0×105 m/s when it decays into an alpha particle (4He) and a 234Th nucleus. If the alpha particle moves off at 22 degrees above the x axis with a speed of 1.1×107 m/s, a) What is the speed of the thorium nucleus and b) What is the direction of the motion of the thorium nucleus ( degrees clockwise from the x axis)?
An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by
r(t)= R cos(wt)i + R sin(wt)j + vztk
R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame.
In vector form:
A)What is the path of the partical in the moving frame?
B)what is the velocity of the particle as a function of time relative to the moving frame?
C)What is the acceleration of the particle in each frame?
D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?
A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1 = 1 would be the end of
the first year. If a is the displacement of the wood in the first 5 years and b is the distance traveled in the first 5 years, what is
a- b?
None of the listed answers
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