Blocks A (1 kg) and B (2 kg) are on a frictionless floor with coefficient of friction 0.6 between them. A spring of force constant 900 N m⁻¹ is stretched and the system is released. Find the maximum initial spring extension in cm so that the blocks do not slip relative to each other.

Question

G1 Physics · Accepted Answer

For common motion, total mass is 3 kg, so acceleration due to spring force kx is a = kx/3. The lower 2 kg block is accelerated only by friction, requiring f = 2a = 2kx/3. Limiting friction at the interface is μ(1 kg)g = 6 N. Thus 2kx/3 ≤ 6, giving x ≤ 9/900 = 0.01 m = 1 cm.