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Problem 35 Hard Difficulty

The force on a particle is directed along an $x$ axis and given by $F=F_{0}\left(x / x_{0}-1\right) .$ Find the work done by the force in
moving the particle from $x=0$ to $x=2 x_{0}$ by $(a)$ plotting $F(x)$ and
measuring the work from the graph and (b) integrating $F(x)$.

Answer

(a) $W=0 \mathrm{J}$
(b) $W=0 \mathrm{J}$

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Video Transcript

here we fuss. Plot the four sources Displacement forces on y axis and displacement on X axis. Here we have. If Lord, this is zero. And here we have minus F. Lord, this is explored and this is two times off. Ex Lord, if you plot then this goes The line goes from picks mod and meet If Lord here given a one dimensional force therefore fix effects which is a function of X The world is simply equal to the area under the curve. So what will be called to integral off Ex Initial two x file force dx for about a The port is shown here we take explored to be a positive and the world done. He's inactive. There's the object moves from ex physical 202 x Is it going to explode? And the world is a positive as it moves from X physical Do it smart two x is equal to two x amount So this is negative here and here. It's a positive since the 80 off a triangle we know any offer trying will be No, he's the one or two times a based I'm altitude. Then the work done from X more acceptable to 02 X is equal to X. Marred is doubly. One is equal to minus X Lord times if no divided by two and the world done from X p Simple to fix Nod two X is equal to to explode is given by W to that easy Cool too well, um two ex lord minus X terms if f more divided by two. This gives us explored F Lord divided by two. The total work is then some off to So not who is one plus w two on this gives us minus one over to f more explored plus one or two explored f mort to be zero but be the integral for the work Done. Who can be written is a w integration from 0 to 2 Ex Lord, This is f into the function we have If more x divided by explored minus one d x are integrating this we get if more times x squared, divided by two ex Lord minus X integrating from zero to to explode this user stance her to be zero

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