Question

A 2.3 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. The force is given by F with arrow(x) = (2.6 − x^2) N, where x is in meters and the initial position of the block is x = 0.

(a) What is the kinetic energy of the block as it passes through x = 2.1 m?

(b) What is the maximum kinetic energy of the block between x = 0 and x = 2.1 m?


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(a) K naught should tacitly be equal to 0, so when finding W, we should in essence find the final K.
F(x=2.1m)=(2.6-(2.1)^2) = -1.81N
If I plug -1.81N for the scalar product or use integration, I get -3.80J. This is incorrect however.

(b) Finding the max K in (0, 2.1] should be related to finding the zeros of its derivative, since that indicates either a max or min in the interval. The only solution for F'(x) is 0, however.

I am confused..

Any redirection or indication of screw-ups is greatly appreciated.

Answer 1

integration is the correct approach

work (energy) = F(x) dx

the force goes to zero at √2.6, and then goes negative
... this is also the point of max energy