PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Blocks 1 and 2, of masses m1=0.30kg and m2=0.50kg respectively, are attached to separate horizontal springs on identical low-friction tracks. The spring constant for Block 1 is k1=180N/m. The spring constant for Block 2, k2, is unknown. The blocks are set oscillating such that
• Each block reaches the same maximum speed vmax=1.2m/s as it passes through equilibrium.
• The total mechanical energies of the two systems are equal.
Both blocks start from rest at their maximum displacements.
(a) Show that for a block–spring system that starts from rest at its maximum displacement, the total mechanical energy can be written in terms of the block’s mass and its maximum speed.
(b) Calculate the total mechanical energy of Block 1.
(c) Given that Block 2 has amplitude A2=0.11m, determine the spring constant k2 required so that the two systems have equal total mechanical energy.
(d) When each block is instantaneously at one-half of its amplitude from equilibrium and moving toward equilibrium, compute the speed of each block and indicate which is greater. Provide quantitative justification.