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A particle of mass m movesthrough a region of space where it is subjectforceto aF(x) = Foe-kx?where F and k are constants(a) How much work does the force do on theoo?mass to move it fromT = 0 to x =(b) If it starts from rest, how fast is the massmoving when it is infinitely far away?

Question
A particle of mass m moves
through a region of space where it is subject
force
to a
F(x) = Foe
-kx?
where F and k are constants
(a) How much work does the force do on the
oo?
mass to move it from
T = 0 to x =
(b) If it starts from rest, how fast is the mass
moving when it is infinitely far away?
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A particle of mass m moves through a region of space where it is subject force to a F(x) = Foe -kx? where F and k are constants (a) How much work does the force do on the oo? mass to move it from T = 0 to x = (b) If it starts from rest, how fast is the mass moving when it is infinitely far away?

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Step 1

(a)

According to the question force acts on particle along positive x direction and work done by given force is given by:

W = F(x)-(de)i
(1)
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W = F(x)-(de)i (1)

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Step 2

Substitute limits given in question and value of force into equation (1) we get,

-
F
- kr
e
W
F
-( a)
e
-0-11
k
(2)
k
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- F - kr e W F -( a) e -0-11 k (2) k

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Step 3

(b)

According to work energy theorem work done by all forces are equ...

W, (K.E),-(KE)
(3)
F
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W, (K.E),-(KE) (3) F

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