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Asked • 07/17/19

Bidirectional jerk motion on a stopping vehicle?

A stopping vehicle (say a car) has an apparent retardation (which may/may not be constant in magnitude) when force via brakes is applied. I travel by subway trains, and I noticed an odd phenomenon. The thing about such trains (might be irrelevant) is that, being light-weight, their motion somewhat mimics that of cars, and the effects of motion are more apparent as one usually stands in such trains. The thing I noticed was that I could feel a force pulling me in the initial direction of motion, as the train slowed down. That obviously is the inertia. But as soon as the train halted, I noticed a secondary jerk...this time in the opposite direction, and it was kind of short lasting. I'm curious to know, what causes this secondary jerk backwards as soon as a vehicle comes to rest. I'm guessing it has something to do with the reaction force by the brakes which overcome the forward motion and provide an impulse backwards. But then it has to have a proper force 'mirror' as per the third law of motion. Also, there never is any intentional backwards motion here (the drivers are precise, I guess). So what could it really be?

Lander M.

When a train is being stopped, most of its kinetic energy is dissipated into heat by the frictional action of the braking system - that energy is, at that point, essentially removed from the mechanical situation. However, trains are (thankfully) not completely rigid, so, during the braking process, a smaller amount of energy will be stored in the pseudoelastic deformation of the carriage, suspension, and other mechanical components. That is, the train will act a bit like a giant spring. After the train reaches zero velocity, this stored spring potential energy will produce a small but noticeable reactionary backward movement. If it weren't for damping, this process could create a continuous back-and-forth bouncing effect, but in real life the oscillation is generally negligible after the first backswing.


Stanton D.

Interesting hypothesis, but I think you're feeling the effects of the sudden cessation of an acceleration. While the train is slowing to a stop, you are probably braced in a direction to oppose your inertia. But when the train achieves zero velocity, suddenly your bracing "throws" you in the "opposite" direction. If the train had a "soft" third derivative of position with respect to time, your bracing position could be smoothly adjusted to upright without a "jerk". There's an interesting asymmetry to it: if you've ever listened to the sounds of a freight train starting up, the cars reach the end of their linkage slack and are jerked into motion with an audible clank. The clanks get faster as more cars are moving with the engine, but the frequency of the clanking is not a linear function of time. Why not? What function would you predict, given constant engine power? -- Cheers, Mr. d. P.S. if you want some *real oscillation*, be on a passenger train running over a series of pennies laid on the track. You might think that a penny, or more than one, gets smooshed with no disturbance to the train. You would be right that they get smooshed, and wrong that you wouldn't notice. Been there, heard that! -- Cheers, -- Mr. d. P.P.S. What names might you assign to positive values for successive derivatives of position with respect to time? 1st = velocity, unnoticable; 2nd = acceleration, counteract with a lean; 3rd = brake pedal pushdown speed, gives a smoothly increasing sense of acceleration; 4th = ? 5th =? How far up can you detect? IS there such a thing as a jolt (a true step function, at some level of derivative)?


1 Expert Answer


Jeff K. answered • 05/21/20

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