A 0.19- kg block on a wooden table is given a sharp blow with a hammer. The bloc

Question

A 0.19- kg block on a wooden table is given a sharp blow with a hammer. The block then slides across the table to a stop. The coefficient of friction between the block and table is 0.35. The hammer's force on the block as a function of time is well approximated by an isosceles triangle with it's base on the horizontal time axis. The length of the base is 0.0075 s and the maximum force is 44.1 N. How far does the block go? Use a graphical technique.

Explanation / Answer

Given that      m = 0.19 kg      = 0.35     base = 0.0075 s     height = 44.1 N The change in momentum of the block is equal to the area of the isosceles triangle        m v - 0 = 0.5 * base * height        v = 0.5 * base * height / m           = 0.5 * 0.0075 * 44.1 / 0.19           = 0.8703 m/s According to conservation of energy        0.5 m v2 = m g x ==>          x = 0.5 v2 / g                     = 0.5 * 0.8703 * 0.8703 / 9.8 * 0.35                     = 0.1104 m                     = 11.04 cm

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