Two light, ideal springs with force constants and are connected in series between a…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Two light, ideal springs with force constants k1=200Nm−1 and k2=300Nm−1 are connected in series between a fixed wall and a 2.0kg block on a frictionless horizontal surface. The block is pulled so that the overall extension of the combined spring system becomes 0.15m and is then released from rest.
(i) Derive an expression for the effective force constant keff of two springs connected in series.
(ii) Using the effective constant, calculate the total work done by the spring system on the block as it moves from the stretched position to the equilibrium position.
(iii) Hence determine the speed of the block at the equilibrium position.