Question

A position dependent force f is F = 7-2x +3x2 N acts on a small body of mass 2 kg and displaces it from x=3 to x=7 , find the work done in joules

Answer 1

A position dependent force, F = (7 - 2x + 3x²) N

we have to find workdone of small body of mass 2kg.

use concept,

Work done = ∫F dx

= $\int\limits^7_3{(7-2x+3x^2)}\,dx$

= $\left[7x-\frac{2x^2}{2}+\frac{3x^3}{3}\right]^7_3$

= $[7x-x^2+x^3]^7_3$

=7(7 - 3) - (7² - 3²) + (7³ - 3²)

= 7 × 4 - (49 - 9) + (343 - 27)

= ( 28 - 40 + 316 ) J

= 304 J

hence, work done by the object is 304 J if object is displayed from x = 3 to x = 7