Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you need. Find the answers you need quickly and accurately with help from our knowledgeable and dedicated community members.

A force on a particle depends on position such that f(x) = (3. 00 n/m2)x2 + (2. 00 n/m)x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0. 00 m to x = 2. 00 m?.

Sagot :

LammettHashidn

Integrate the force function over the given displacement:

[tex]W = \displaystyle \int_{x=0.00\,\rm m}^{x=2.00\,\rm m} \left(3.00\frac{\rm N}{\mathrm m^2}\right) x^2 + \left(2.00\frac{\rm N}{\rm m}\right) x \, dx[/tex]

[tex]W = \displaystyle \left(1.00\frac{\rm N}{\mathrm m^2}\right) x^3 + \left(1.00\frac{\rm N}{\rm m}\right) x^2 \bigg|_{x=0.00\,\rm m}^{x=2.00\,\rm m}[/tex]

[tex]W = \displaystyle \left(1.00\frac{\rm N}{\mathrm m^2}\right) (2.00\,\mathrm m)^3 + \left(1.00\frac{\rm N}{\rm m}\right) (2.00\,\mathrm m)^2[/tex]

[tex]W = \displaystyle 8.00 \, \mathrm N{\cdot}\mathrm m + 4.00 \,\mathrm N{\cdot}\mathrm m = \boxed{12.0 \, \mathrm J}[/tex]

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.