A 800 g chunk of modeling clay is held above a table and dropped so that it hits

Question

A 800 g chunk of modeling clay is held above a table and dropped so that it hits the table with a speed of 1.65 m/s. The table (m = 1600 g) is supported on 4 springs. The clay makes an inelastic collision with the table and the table and the clay oscillate up and down. After a long time the table comes to rest 0.06 m below its original position. (a) Draw a Free Body Diagram (b) What is the effective spring constant of all four springs taken all together? (c) What maximum amplitude that the platform oscillates with when it starts bouncing?

Explanation / Answer

momentum conservation in vertical direction

800/1000 * 1.65 = (0.8+1.6 ) V

V= 0.55 m/s

initially equillibrium

4K (x) = 1.6*9.81

final equillibrium

4 * K * (0.06 + x ) = (0.8+1.6 ) *9.81

(x + 0.06)/ x = ((0.8+1.6 ) *9.81)/(1.6*9.81)

1+ 0.06/x = 1.5

0.06/x = 0.5

x = 0.06/0.5 =0.12

4K (x) = 1.6*9.81

4k = 1.6*9.81/(0.12))

130.8 N/m

let maximum amplitude be A

0.5* (130.8) * (A^2) = 0.5*(1.6+0.8) * (0.55^2)

A= 0.07450140072 m

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