Platform on Springs A platform of mass 0.8 kg is supported on four springs (only two springs are shown in the picture, but there are four altogether). A chunk of modeling clay of mass 0.6 kg is held above the table and dropped so that it hits the table with a speed of v = 0.9 m/s. The clay sticks to the table so that the the table and clay oscillate up and down together. Finally, the table comes to rest 6 cm below its original position, a) What is the effective spring constant of all four springs taken together?
Explanation / Answer
Given thatthe mass of the clay is m = 0.6 kg Mass of theplatform is M = 0.8 kg velocityof the clay is v = 0.9 m/s spring from theiniital poistion is x = 6 cm = 0.06m ----------------------------------------------------------------------- Apply conservationof energy before collision and when the spring is in compressedposition (1/2)mv2 + mgx = 4*(1/2)Kx2 mv2 + 2mgx = 4*Kx2 K = ( mv2 + 2mgx) /4*x2 =----------- N/m