Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 3, Problem 2DQ
You happen to visit the Moon when some people on Earth see a total solar eclipse. Who has a better experience of this event, you or the friends you left behind back on Earth? Why?
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8.114 CALC A Variable-Mass Raindrop. In a rocket-propul-
sion problem the mass is variable. Another such problem is a rain-
drop falling through a cloud of small water droplets. Some of these
small droplets adhere to the raindrop, thereby increasing its mass
as it falls. The force on the raindrop is
dp
dv
dm
Fext
=
+
dt
dt
dt
=
Suppose the mass of the raindrop depends on the distance x that it
has fallen. Then m kx, where k is a constant, and dm/dt = kv.
This gives, since Fext
=
mg,
dv
mg = m
+ v(kv)
dt
Or, dividing by k,
dv
xgx
+ v²
dt
This is a differential equation that has a solution of the form
v = at, where a is the acceleration and is constant. Take the initial
velocity of the raindrop to be zero. (a) Using the proposed solution
for v, find the acceleration a. (b) Find the distance the raindrop has
fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of
the raindrop at t = 3.00 s. (For many more intriguing aspects of
this problem, see K. S. Krane, American Journal of…
8.13 A 2.00-kg stone is sliding Figure E8.13
F (kN)
to the right on a frictionless hori-
zontal surface at 5.00 m/s when
it is suddenly struck by an object
that exerts a large horizontal
force on it for a short period of 2.50
time. The graph in Fig. E8.13
shows the magnitude of this force
as a function of time. (a) What
impulse does this force exert on
t (ms)
15.0
16.0
the stone? (b) Just after the force stops acting, find the magnitude
and direction of the stone's velocity if the force acts (i) to the right
or (ii) to the left.
Chapter 3 Solutions
Horizons: Exploring the Universe (MindTap Course List)
Ch. 3 - What is the difference between the daily and...Ch. 3 - If Earth did not rotate, could you still define...Ch. 3 - What would the seasons be like if Earth were...Ch. 3 - Why are the seasons reversed in the Southern...Ch. 3 - Prob. 5RQCh. 3 - Do the phases of the Moon look the same from every...Ch. 3 - What phase would Earth be in if you were on the...Ch. 3 - Why have most people seen a total lunar eclipse,...Ch. 3 - Why isn’t there an eclipse at every new moon and...Ch. 3 - Why is the Moon red during a total lunar eclipse?
Ch. 3 - Why should the eccentricity of Earth’s orbit make...Ch. 3 - Prob. 12RQCh. 3 - Prob. 13RQCh. 3 - How Do We know? Why must a scientific argument...Ch. 3 - You are packing for a vacation on a planet...Ch. 3 - You happen to visit the Moon when some people on...Ch. 3 - Given that Earth is about 4.6 billion (4.6109)...Ch. 3 - Identify the phases of the Moon if on March 20 the...Ch. 3 - Identify the phases of the Moon if at sunset in...Ch. 3 - Prob. 4PCh. 3 - Draw a diagram showing Earth, the Moon, and...Ch. 3 - Phobos, one of the moons of Mars, is about 25 km...Ch. 3 - A total eclipse of the Sun was visible from Canada...Ch. 3 - Prob. 8PCh. 3 - The cartoon in Figure UN 3-4 shows a crescent...Ch. 3 - The photo in Figure UN 3-5 shows the annular...
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