Answered: A 3.1 kg object is initially at rest…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A 3.1 kg object is initially at rest and is experiencing a net force of magnitude 4.7e^-t/2 N. As time approaches infinity, notice that the net force decays toward 0 N, which tells us that the acceleration is also dropping to 0 m/s^2 (and so the velocity is leveling off to a terminal speed). What is the terminal speed? (Ans.= 3.0 m/s)

ent_id=_1183944 1&course_id%3D_18813 1
Problem: A 3.1 kg object is initially at rest and is experiencing a net force of magnitude
4.7e N. As time approaches infinity, notice that the net force decays toward 0 N, which tells
us that the acceleration is also dropping to 0 m/s² (and so the velocity is leveling off to a
terminal speed). What is this terminal speed? (ANS. = 3.0 m/s)
(A) Pictorial
Representation
(B) Physical
Representation
(C) Math
Representation
and Solution
2:

Expert Solution

Step 1

Solution:

Let net force acting on the body be dF

Since it is given that,

$d F = 4.7 e^{- t / 2} N$

Now,

since,

$\begin{array}{rcl} d F & = & m a \\ = & m \frac{d v}{d t} \end{array}$

Then

$m \frac{d v}{d t} = 4.7 \times e^{\frac{- t}{2}} m d v = 4.7 e^{\frac{- t}{2}}$

$A s v e l o c i t y v v a r i e s f r o m 0 t o t e r m i n a l v e l o c i t y (v), t h e n t i m e v a r i e s f r o m 0 t o \infty$ , therefore,

$m \int_{0}^{v} d v = 4.7 \int_{0}^{\infty} e^{\frac{- t}{2}} d t m [v - 0] = 4.7 \times \frac{{[e^{- t / 2}]}_{0}^{\infty}}{\frac{- 1}{2}} m v = 4.7 \times - 2 [0 - 1] 3.1 \times v = 4.7 \times 2 v = 3.03 m / s \approx 3 m / s$

Terminal velocity on the mass=3m/s

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