A 1.3 kg block is initially at rest on a horizontal frictionless surface when a

Question

A 1.3 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(x) = (2.4 - x^2) i 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 = 2.0 m?

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

Explanation / Answer

a(x)=F/m v(x)=(2.4 x -x^3/at3+c)/m integrating acceleration v(0)=0 =>c=0 a>v(2)=[2.4*2-8/3]/1.3=1.64 KE=1/2 *1.3*1.64^2=1.75 b>max velocity when acc=0 =>x^2=2.4 =>x=1.55 max vel=[2.4*1.55-1.55^3/3]/1.3=1.9 max KE=1/2 *1.3*1.9^2=2.36

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