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

1 Answer
Aug 27, 2017

Answer:

#W = 5.33# #"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)dx#

We know

  • #F_x = x^2 + 3#

  • #x_1 = 1# #"m"#

  • #x_2 = 2# #"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"" ")|)#