In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is moving at 75.00% the speed of light in the laboratory reference frame, find the speed of the emitted electron relative to the laboratory reference frame if the electron is emitted (a) in the same direction that the nucleus is moving and (b) in the opposite direction from the nucleus’s velocity, (c) In each case in parts (a) and (b), find the kinetic energy of the electron as measured in (i) the laboratory frame and (ii) the reference frame of the decaying nucleus.
In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is moving at 75.00% the speed of light in the laboratory reference frame, find the speed of the emitted electron relative to the laboratory reference frame if the electron is emitted (a) in the same direction that the nucleus is moving and (b) in the opposite direction from the nucleus’s velocity, (c) In each case in parts (a) and (b), find the kinetic energy of the electron as measured in (i) the laboratory frame and (ii) the reference frame of the decaying nucleus.
In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is moving at 75.00% the speed of light in the laboratory reference frame, find the speed of the emitted electron relative to the laboratory reference frame if the electron is emitted (a) in the same direction that the nucleus is moving and (b) in the opposite direction from the nucleus’s velocity, (c) In each case in parts (a) and (b), find the kinetic energy of the electron as measured in (i) the laboratory frame and (ii) the reference frame of the decaying nucleus.
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
A ball is thrown with an initial speed v, at an angle 6, with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.
(a) the time interval during which the ball is in motion
2R
(b) the ball's speed at the peak of its path
v=
Rg 2
√ sin 26, V 3
(c) the initial vertical component of its velocity
Rg
sin ei
sin 20
(d) its initial speed
Rg
√ sin 20
×
(e) the angle 6, expressed in terms of arctan of a fraction.
1
(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.
hmax
R2
(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.
Xmax
R√3
2
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in the figure, but that the ball's speed after the bounce is one-half of what it was before the bounce.
8
(a) Assuming the ball is always thrown with the same initial speed, at what angle & should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a ball thrown upward at 35.0° with no bounce (green path)?
24
(b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
Cone-bounce
no-bounce
0.940
Chapter 37 Solutions
Mastering Physics with Pearson eText -- Standalone Access Card -- for University Physics with Modern Physics (14th Edition)
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