Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 4, Problem 54P
To determine
To Show:The terminal velocity,
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An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If g is the acceleration due to gravity, then the downward force on the object is mg − cv, where c is a positive constant, and Newton's Second Law gives
m(dv/dt)=mg-cv
Solve this as a linear equation. (Use v for v(t).)
What is the limiting velocity? lim t → ∞
Find the distance the object has fallen after t seconds. (Use s for s(t).)
An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If
s(t)
is the distance dropped after t seconds, then the speed is
v = s'(t)
and the acceleration is
a = v'(t).
If g is the acceleration due to gravity, then the downward force on the object is
mg − cv,
where c is a positive constant, and Newton's Second Law gives
m
dv
dt
= mg − cv.
(a) Solve this as a linear equation. (Use v for v(t).)
v=mgC(1−e−(Cm)t)
(b) What is the limiting velocity?
lim t → ∞ v(t) =
mgc
(c) Find the distance the object has fallen after t seconds. (Use s for s(t).)
A 40 kg wooden crate is being pulled across a wooden surface by a force (of magnitude F) that is angled 20° above the horizontal. The coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.3.
(a)Calculāte the minimum force F (in N) that must be exerted to get the crate moving.
(b)What is the acceleration (in m/s?) of the crate once it starts to move, if that force (F) is maintained?
Chapter 4 Solutions
Physics Fundamentals
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
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