A light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a smooth horizontal floor.

Question

You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion?

Answer 1

The distance moved = .5at2=.96 ... t=1.6sec thus a = 0.75 m/s². The force required to accelerate this 12.5 kg box = 12.5*.75 = 9.375 Newtons. The spring will deliver that force when stretched 9.375/2.5= 3.75 cm making the total length of 15+3.75=18.75cm.