Question

The force applied against an object moving horizontally on a linear path is described by `F(x)= cospix+x`. By how much does the object's kinetic energy change as the object moves from `x in [ 0, 2 ]`?

Answer 1

I got: `DeltaK=2J`

Explanation:

We can use the Work-K.E. theorem that tells us that:

`W=DeltaK`

or that work done on the system is equal to the change in kinetic energy.

Here we need to evaluate the work of a variable force so we use the integral version of work as:

`W=int_(x_1)^(x_2)f(x)dx=int_0^2[cos(pix)+x]dx=int_0^2[cos(pix)]dx+int_0^2[x]dx=sin(pix)/pi+x^2/s|_0^2=sin(2pi)/pi+2^2/2-0=2J`

So:

`W=DeltaK=2J`