# Difficulty understanding the spring mass system with friction

I am doing to a practical and having a hard time understanding the physics behind the actual response. A block is attached to the spring and mass is attached at the end of the spring. There is friction in the table and block. During the loading cycle, mass is increased gradually (say 100 grams) till the spring reaches the required extension. During the unloading cycle, it is observed that the block does not move until a specific amount of weight is removed (say 300 grams). Afterward, the spring moves with every 100 grams. Due to this reason, if I note the displacement x, half the way, there is a difference due to the initial response of the spring. I am trying to understand the physics behind the problem but failed to understand why there is no initial movement after I remove the 1st 100 gram. If its the static friction causing the initial delay, then why it does not happen afterward too. I would really appreciate some insight as I am stuck.

• Static friction (non-moving) is higher than dynamic friction (while-slipping). When it stops slipping, static friction again is in control. Jul 14, 2021 at 13:53
• Thank you for the response. you are absolutely right. the thing that confused me though was why the system did not respond immediately to the weight removal and why it did not happen consistently. Jul 14, 2021 at 13:57
• This is an example of hysteresis - see en.wikipedia.org/wiki/Hysteresis. Jul 14, 2021 at 14:26

Static frictional forces are equal and opposite to the net force on the block, up to a certain limit. The block only starts moving when the net force on the block is above the friction limit.

At the start, the forces on the block are in equilibrium: the force exerted by the mass is equal and opposite to the force of the spring, and so there is no net force on the block.

After removing the first 100 gram from the weight, the spring force is now larger than the force of the weight, and so there is a net force on the block to the left. But that net force is still below the limiting frictional force, and so the block does not move.

After removing enough weight, the net force will rise above the frictional limit and the block moves. But the block moving will shorten the spring, and therefore reduce the force of the spring. The block will stop moving as soon as the spring force is equal to the frictional force plus the weight. The net force on the block in that situation is equal to the limiting frictional force (or actually a little less, because a moving block has less friction than a stationary one).

So this situation is not equal to the initial situation, where there was zero net force on the block. The block will immediately start moving again when you remove more weight, because the net force will immediately rise above the limit again.

• Thank you very much for the detailed response. So if I understand correctly, the distance traveled by the block during the unloading cycle (when weights are removed) would always be less than the distance traveled during the loading cycle (when weights are added). On a side note, should I try to tackle the problem by having force equilibrium, a free body diagram of the system at the initial and final position or by doing conservation of energy to determine the travel 'x' of the block? Jul 14, 2021 at 13:51