Two blocks of masses m and M (M m) are placed one over the other on a frictionless horizontal table. The lower block M is attached to a spring of constant k, and the coefficient of friction between the blocks is μ. The system is slightly displaced and released. Consider: (A) T = 2π√[(M+m)/k]; (B) a = -kx/(M+m); (C) the friction magnitude on the upper block is mμ|x|/(M+m); (D) maximum amplitude without slipping is μ(M+m)g/k; (E) maximum frictional force can be μ(M+m)g. Choose the correct set.

Question

Two blocks of masses m and M (M > m) are placed one over the other on a frictionless horizontal table. The lower block M is attached to a spring of constant k, and the coefficient of friction between the blocks is μ. The system is slightly displaced and released. Consider: (A) T = 2π√[(M+m)/k]; (B) a = -kx/(M+m); (C) the friction magnitude on the upper block is mμ|x|/(M+m); (D) maximum amplitude without slipping is μ(M+m)g/k; (E) maximum frictional force can be μ(M+m)g. Choose the correct set.

G1 Physics · Accepted Answer

If there is no slipping, both blocks move together as one system of mass M+m. Equation of motion: (M+m)a = -kx. Therefore, a = -kx/(M+m), so B is correct. The angular frequency is ω = √[k/(M+m)], so T = 2π√[(M+m)/k]. Thus A is correct. For the upper block, the required friction is f = m|a| = mk|x|/(M+m). Therefore statement C, which contains μ instead of k, is incorrect. No slipping requires f ≤ μmg. At maximum displacement Aₘ, mkAₘ/(M+m) = μmg. Thus, Aₘ = μ(M+m)g/k. So D is correct. The maximu…