University Physics Volume 1
1st Edition
ISBN: 9781630182137
Author: Samuel J Ling Jeff, Sanny, William Moebs
Publisher: OpenStax
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Textbook Question
Chapter 9, Problem 71P
Find the center of mass of a rectangular material of length a and width b made up of a material of nonuniform density. The density is such that when the rectangle is placed in the xy-plane, the density is given by
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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 9 Solutions
University Physics Volume 1
Ch. 9 - Check Your Understanding The U.S. Air Force uses...Ch. 9 - Check Your Understanding What if we had assumed...Ch. 9 - Check Your Understanding Suppose the second,...Ch. 9 - Check Your Understanding Would the ball’s change...Ch. 9 - Check Your Understanding Even if there were some...Ch. 9 - Check Your Understanding The changes of momentum...Ch. 9 - Check Your Understanding There is a second...Ch. 9 - Check Your Understanding Suppose there had been no...Ch. 9 - Check Your Understanding Suppose the initial...Ch. 9 - Check Your Understanding Notice that the mass of...
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The...Ch. 9 - Prob. 57PCh. 9 - A proton traveling at 3.0106m/s scatters...Ch. 9 - Prob. 59PCh. 9 - A family is skating. The father (75 kg) skates at...Ch. 9 - Prob. 61PCh. 9 - Two cars of the same mass approach an extremely...Ch. 9 - Three point masses are placed at the corners of a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 , move uniformly...Ch. 9 - Two particles of masses m1 and m2 move uniformly...Ch. 9 - Find the center of mass of a one-meter long rod,...Ch. 9 - Find the center of mass of a rod of length L whose...Ch. 9 - Find the center of mass of a rectangular block of...Ch. 9 - Find the center of mass of a rectangular material...Ch. 9 - A cube of side a is cut out of another cube of...Ch. 9 - Find the center of mass of a cone of uniform...Ch. 9 - Find the center of mass of a thin wire of mass in...Ch. 9 - Find the center of mass of a uniform thin...Ch. 9 - Find the center of mass of a sphere of mass M and...Ch. 9 - (a) A 5.00-kg squid initially at rest ejects 0.250...Ch. 9 - A rocket takes off from Earth and reaches a speed...Ch. 9 - Repeat the preceding problem but for a rocket that...Ch. 9 - How much fuel would be needed for a 1000-kg rocket...Ch. 9 - What exhaust speed is required to accelerate a...Ch. 9 - Unreasonable Results Squids have been reported to...Ch. 9 - Two 70-kg canoers paddle in a single, 50-kg canoe....Ch. 9 - Which has a larger magnitude of momentum: a...Ch. 9 - A driver applies the brakes and reduces the speed...Ch. 9 - You friend claims that momentum is mass multiplied...Ch. 9 - Dropping a glass on a cement floor is more likely...Ch. 9 - Your 1500-kg sports car accelerates from 0 to 30...Ch. 9 - A ball of mass m is dropped. 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