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

1 Answer
Aug 19, 2017

Answer:

#W = 8.39# #"J"#

Explanation:

We're asked to find the work necessary to move an object with a varying force.

Since the force varies, we must know that work is the integral of force with respect to displacement, and use the equation

#W = int_(x_1)^(x_2) F(x)*dx#

Here,

  • #x_1# is the original position (#1#)

  • #x_2# is the final position (#2#)

  • #F(x) = 1 + xe^x#

Thus we have

#color(red)(W) = int_1^2 1 + xe^xcolor(white)(l)dx = color(red)(ulbar(|stackrel(" ")(" "8.39color(white)(l)"J"" ")|)#