Jean's wrath

Classical Mechanics Level 4

Wolverine and Jean somehow find themselves in an intense mutant show off in outer space. Assume their positions can be described with coordinate points . Wolverine who was initially standing at the origin ( $0,0,0)$ , decides to avoid the conflict and jumps in a straight line towards the point $(3,3,0)$ .

Jean, angered by this display of cowardice, uses her telekinetic powers to apply a force of $\large{\vec F(x,y,z) = -kxy^2 \hat{\jmath} }$ on Wolverine. This is a force in the negative $y$ direction whose magnitude depends on Wolverine's position $(x,y,z)$ . Calculate the amount of work Jean does on wolverine as he jumps from $(0,0,0)$ towards $(3,3,0)$ . If this work is $W$ , input $|W|$ in joules as your answer.

Take $k=2.50 \frac{N}{m^3}$

The answer is 50.6.

1 solution

Deepanshu Gupta
Nov 7, 2014

${ F }_{ x }\quad =\quad 0\quad \quad \& \quad \quad { F }_{ y }\quad =\quad -kx{ y }^{ 2 }\quad \quad \\ \\ W\quad =\quad \int { { F }_{ x }dx\quad +\quad { F }_{ y }dy } \\ \\ W\quad =\quad \int { \quad { F }_{ y }dy } \quad =\quad \int { -kx{ y }^{ 2 }dy }$ .

Since we know that Coward Wolverine moves along the line

y=x

$W\quad =\quad \int _{ 0 }^{ 3 }{ -k{ y }^{ 3 }dy } \quad =\quad -\quad \cfrac { 81k }{ 4 } \quad =\quad -50.6\\ \\ \left| W \right| \quad =\quad 50.6\quad$ .

So this field is not a conservative field? I can't just add the x and y components for energy?

What would happen if the path followed was more complicated? Say along the curve \(y = frac{1}{3} x^2) ? How would I calculate this then?

Kp Govind - 6 years, 4 months ago

Jean's wrath

The answer is 50.6.

1 solution

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