A particle slides along a straight track under the influence of a position-dependent…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A particle slides along a straight track under the influence of a position-dependent force given by

F(x)=k\,x\,e^{-x/L},\qquad 0\le x\le 5L,

where

k

and

L

are positive constants. (a) Write an expression for the total work

W

done by the force in moving the particle from

x=0

x=5L

. (b) Evaluate

W

in closed form, expressing your answer in terms of

k

and

L

only. (c) Suppose

L

is doubled while

k

remains fixed. Determine the factor by which the work changes and justify your conclusion algebraically.