Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 2, Problem 32EAP
To determine
The particle velocity at
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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.
Please calculate the expectation value for E and the uncertainty in E for this wavefunction trapped in a simple harmonic oscillator potential
Chapter 2 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 2 - For Questions 1 through 3, interpret the position...Ch. 2 - For Questions 1 through 3, interpret the position...Ch. 2 - For Questions 1 through 3, interpret the position...Ch. 2 - FIGURE Q2.4 shows a position-versus-time graph for...Ch. 2 - FIGURE Q2.5 shows a position-versus-time graph for...Ch. 2 - FIGURE Q2.6 shows the position-versus-time graph...Ch. 2 - FIGURE Q2.7 shows the position-versus-time graph...Ch. 2 - FIGURE Q2.8 shows six frames from the motion...Ch. 2 - You’re driving along the highway at a steady speed...Ch. 2 - A bicycle is traveling east. Can its acceleration...
Ch. 2 - (a) Give an example of a vertical motion with a...Ch. 2 - A ball is thrown straight up into the air. At each...Ch. 2 - A rock is thrown (not dropped) straight do from a...Ch. 2 - FIGURE Q2.14 shows the velocity-versus-time graph...Ch. 2 - Alan leaves Los Angeles at 8:00 A.M. to drive to...Ch. 2 - Julie drives 100 mi to Grandmother’s house. On the...Ch. 2 - Larry leaves home at 9:05 and runs at constant...Ch. 2 - FIGURE EX2.4 is the position-versus-time graph of...Ch. 2 - FIGURE EX2.5 shows the position graph of a...Ch. 2 - A particle starts from x0=10matt=0s and moves with...Ch. 2 - FIGURE EX2.7 is a somewhat idealized graph of the...Ch. 2 - FIGURE EX2.8 shows the velocity graph for a...Ch. 2 - FIGURE EX2.9 shows the velocity graph of a...Ch. 2 - FIGURE EX2.7 showed the velocity graph of blood in...Ch. 2 - Prob. 11EAPCh. 2 - FIGURE EX2.1 2 shows the velocity-versus-time...Ch. 2 - a. What constant acceleration, in SI units, must a...Ch. 2 - A jet plane is cruising at 300 m/s when suddenly...Ch. 2 - a. How many days will it take a spaceship to...Ch. 2 - Prob. 16EAPCh. 2 - A speed skater moving to the left across...Ch. 2 - A Porsche challenges a Honda to a 400 m race....Ch. 2 - Acar starts from rest at a stop sign. It...Ch. 2 - Prob. 20EAPCh. 2 - A student standing on the ground throws a ball...Ch. 2 - A rock is tossed straight up from ground level...Ch. 2 - 23. When jumping, a flea accelerates at an...Ch. 2 - Prob. 24EAPCh. 2 - A rock is dropped from the top of a tall building....Ch. 2 - A skier is gliding along at 3.0 m/s on horizontal,...Ch. 2 - A car traveling at 30 m/s runs out of gas while...Ch. 2 - Prob. 28EAPCh. 2 - A snowboarder glides down a 50-m-long, 15° hill....Ch. 2 - A small child gives a plastic frog a big push at...Ch. 2 - FIGURE EX2.31 shows the acceleration-versus-time...Ch. 2 - Prob. 32EAPCh. 2 - A particle moving along the x-axis has its...Ch. 2 - A particle moving along the x-axis has its...Ch. 2 - The position of a particle is given by the...Ch. 2 - The position of a particle is given by the...Ch. 2 - Particles A. B. and C move along the x-axis....Ch. 2 - A block is suspended from a spring, pulled down,...Ch. 2 - A particle’s velocity is described by the function...Ch. 2 - Prob. 40EAPCh. 2 - Prob. 41EAPCh. 2 - A particles velocity is given by the function vx=...Ch. 2 - A ball rolls along the smooth track shown in...Ch. 2 - Draw position, velocity, and acceleration graphs...Ch. 2 - FIGURE P2.45 shows a set of kinematic graphs for a...Ch. 2 - FIGURE P2.46 shows a set of kinematic graphs for a...Ch. 2 - The takeoff speed for an Airbus A320 jetliner is...Ch. 2 - You are driving to the grocery store at 20 m/s....Ch. 2 - You’re driving down the highway late one night at...Ch. 2 - Two cars are driving at the same constant speed on...Ch. 2 - You are playing miniature golf at the golf course...Ch. 2 - The minimum stopping distance for a car traveling...Ch. 2 - A cheetah spots a Thomson’s gazelle, its preferred...Ch. 2 - You are at a train station, standing next to the...Ch. 2 - A 200 kg weather rocket is loaded with 100 kg of...Ch. 2 - A 1000 kg weather rocket is launched straight up....Ch. 2 - A lead ball is dropped into a lake from a diving...Ch. 2 - A hotel elevator ascends 200 m with a maximum...Ch. 2 - A basketball player can jump to a height of 55 cm....Ch. 2 - You are 9.0 m from the door of your bus, behind...Ch. 2 - Ann and Carol are driving their cars along the...Ch. 2 - Amir starts riding his bike up a 200-m-long slope...Ch. 2 - A very slippery block of ice slides down a smooth...Ch. 2 - Bob is driving the getaway car after the big bank...Ch. 2 - One game at the amusement park has you push a puck...Ch. 2 - A motorist is driving at 20 m/s when she sees that...Ch. 2 - Nicole throws a ball straight up. Chad watches the...Ch. 2 - David is driving a steady 30 m/s when he passes...Ch. 2 - A cat is sleeping on the floor in the middle of a...Ch. 2 - Water drops fall from the edge of a roof at a...Ch. 2 - I was driving along at 20 m/s, trying to change a...Ch. 2 - As an astronaut visiting Planet X, you’re assigned...Ch. 2 - Your goal in laboratory is to launch a ball of...Ch. 2 - When a 1984 Alfa Romeo Spider sports car...Ch. 2 - The two masses in FIGURE P2.75 slide on...Ch. 2 - In Problems 76 through 79, you are given the...Ch. 2 - In Problems 76 through 79, you are given the...Ch. 2 - In Problems 76 through 79, you are given the...Ch. 2 - In Problems 76 through 79, you are given the...Ch. 2 - A rocket is launched straight up with constant...Ch. 2 - Careful measurements have been made of Olympic...Ch. 2 - III Careful measurements have been made of Olympic...Ch. 2 - A sprinter can accelerate with constant...Ch. 2 - A rubber ball is shot straight up from the ground...Ch. 2 - The Starship Enterprise returns from warp drive to...
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