A 3.5 kg block is initially at rest on a horizontal frictionless surface when a

Question

A 3.5 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)= (1.5-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 = 1.9 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 1.9 m?

HINT: Work can be found by integrating a force with respect to position. Work is equal to the change in kinetic energy. Initially the force does positive work. At what position does it begin to do negative work?

Explanation / Answer

a)Kinetic energy= Integral(F.dx)=1.5x-x3/3=0.5637J

b) Differentiating the kinetic energy function for maxima,

1.5-x2=0

x=1.225m

Kinetic energy=1.5*1.225-1.2253/3=1.225J

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