The force applied on a moving object with a mass of #3 kg # on a linear path is given by #F(x)=x^2+1 #. How much work would it take to move the object over #x in [0,2 ] #?

1 Answer
Jan 22, 2017

Answer:

I found: #W=14/3J#

Explanation:

Having a variable force I would use the work in integral form as:
#W=int_(x_1)^(x_2)F(x)dx# along #x#.
We have:
#W=int_0^2(x^2+1)dx=#
Solve it as usual:
#=int_0^2(x^2+1)dx=x^3/3+x=#
Apply the extremes:
#=(2^3/3+2)-(0^3/3+0)=8/3+3=(8+6)/3=14/3#
so we get:
#W=14/3J#