The force applied on a moving object with a mass of 1 kg 1kg on a linear path is given by F(x)=x^2+3F(x)=x2+3. How much work would it take to move the object over x in [1,2] x[1,2]?

1 Answer
Aug 27, 2017

W = 5.33W=5.33 "J"J

Explanation:

The equation for the work done by a varying force is given by

W = int_(x_1)^(x_2) F_xcolor(white)(l)dxW=x2x1Fxldx

We know

  • F_x = x^2 + 3Fx=x2+3

  • x_1 = 1x1=1 "m"m

  • x_2 = 2x2=2 "m"m

Plugging these in:

color(red)(W) = int_(1color(white)(l)"m")^(2color(white)(l)"m") x^2 + 3color(white)(l)dx = color(red)(ulbar(|stackrel(" ")(" "5.33color(white)(l)"J"" ")|)