The ends of a spring are attached to blocks of mass 3 kg and 2 kg as shown in the figure. The 3 kg block rests on a horizontal surface and the 2 kg block which is vertically above it is in equilibrium

Question

The ends of a spring are attached to blocks of mass 3 kg and 2 kg as shown in the figure. The 3 kg block rests on a horizontal surface and the 2 kg block which is vertically above it is in equilibrium producing a compression of 2 mm of the spring. It is found that the 2 kg mass must be compressed further by at least x ( in mm ) so that when it is released, the 3kg block may be lifted off the ground. Find the value of x in mm.

TestHub · Accepted Answer

Equilibrium: k × 0.002 = 20 , so k = 1 0 4 N/m To lift the 3 kg block, spring extension e needs k e = 30 N, so e = 3 mm Energy from compression ( x + 2 ) mm to extension 3 mm: 2 1 ​ k [ ( x + 2 ) 2 − 3 2 ] = m g ( x + 5 ) (mm units) ( x + 2 ) 2 − 9 = 4 ( x + 5 ) , giving x 2 = 25 , so x = 5 mm

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