Which of these units are equal in this situation

Question

Two objects of different mass are being pushed to opposite sides by a compressed string. Which of these units are equal in this situation.

a) accelerations; b) velocities; c) distances d) forces that act upon both of the objects.

How to solve this kind of problem and why only forces are equal in this case?

Answer 1

The masses are different therefore for objects 1 and 2 the masses are m1 and m2

m1 = F1/a1 m2 = F2/a2 if we assume that F1 = F2, then a1 ≠ a2 , and if F1 ≠ F2, than a1 ≠ a2. So a1 is different than a2 no matter what the forces are, but to maintain equilibrium of the compressed spring, the forces at each end pushing against the objects are of opposite sense and must be equal or the spring will translate in either direction. There forces should be equal such that F1 = F2 = m1a1 = m2a2 with different masses, velocities and accelerations. It is possible that different combinations of masses and accelerations can produce the same force

Ex. if m1 = 3kg, and m2 = 2kg, and a1 = 2 m/s² and a2 = 3 m/s²

F1 = m1 a1 = 3kg ( 2m/s²) = m2 a2 = 2kg ( 3m/s²) = F2 = 6N