work done by a general force

[missrikku]

Hello again! I just want to check if this is correct..

A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the pos direction of an x axis is applied to the block. The force is given by F(x) = (2.5 - x^2)i N, where x is in m and the initial position of the block is x = 0.

a) what is the kinetic energy of the block as it passes through x = 2.0 m?

b) what is the maximum kinetic energy of the block between x = 0 and x = 2.0 m


Wouldn't I get the same answer for both a and b?

I did the following:

** S = integral sign

W = S F(x)dx = Kf - Ki

with xi = 0 and xf = 2.0:

S F(x)dx = 2.5x -x^3/3 --> 2 1/3 J

Wouldn't the ans for both a and be be 2 1/3 J?

Thanks!

[HallsofIvy]

Yes, since this is a horizontal surface, there is no change in potential energy so the change in kinetic energy must be the work done by the force. Integrating the force form the initial point to the last gives that work.

"Wouldn't the ans for both a and be be 2 1/3 J?"

Would it? Certainly the speed and energy will be increasing as long as the force is in the same direction but they will start decreasing when the force changes direction. Where does the force change direction?