Time for pulse to travel a length

[anglum]

Train problem

Homework Statement

005 (part 1 of 1) 10 points
A 23-car train standing on the siding is started
in motion by the train's engine. There are
4 cm of slack between cars. The cars are 9 m
long. The engine is tightly connected to the
first car and moves at a constant speed of
22 cm/s.
How much time is required for the pulse to
travel the length of the train? Answer in units
of s.

Homework Equations

i used the t = d/v

The Attempt at a Solution

i calculated the distance of the train to be 9m * 23 cars + 4cm slack* 22 cars slack is between = Distance and then converted to cm

and used the Velocity as 22 cm/s

and solved for T

is this the correct approach

 

[anglum]

are my calculations for the distance of the train correct?

and is it correct to use the formula t=d/v to solve for the time the pulse travels

 

[anglum]

i get my calculations for the length of the train to be 20,788 cm

so to solve for the time i took 20,788 cm / 22cm/s

is this correct?

 

[berkeman]

I don't think the length of the train cars matters. I believe only the slack matters. What answer do you get if you make that assumption?

 

[anglum]

i get 4 seconds... but why would the length of the train cars not matter? seems strange to me

 

[anglum]

4 seconds was the correct answer ... i just am confused y the length of the cars doesn't matter

 

[berkeman]

i get 4 seconds... but why would the length of the train cars not matter? seems strange to me

I don't think the length of the cars matters, because they are rigid bodies. All you have to do is move the first car forward 4cm to transfer the impulse to car 2, then another 4cm to transfer the impulse to car 3, and so on. I could be wrong, but I get the 4 seconds answer as well.

 

[dynamicsolo]

i get 4 seconds... but why would the length of the train cars not matter? seems strange to me

As berkeman says, the railcars are rigid objects. This means that the leading and trailing ends of each car move *together*. So as soon as the slack in the coupling at the leading end of a car is used up, this will mean that the trailing end of that car is (almost) instantly beginning to take out the slack in the next coupling at that end. In an idealized situation, there is *no* delay in the pulse passing from one coupling to the next, so the lengths of the cars is irrelevant.

Realistically, "rigid" objects don't move all in one piece. The sudden application of force to one end of the object is communicated by a "shock" traveling at the speed of sound in the material through the body of the object (the molecular bonds are disturbed at one end of the object first, which then disturbs the bonds of molecules further along the object, and so on...). This speed would be somewhere upward of 1000 m/sec, so it takes several milliseconds for the trailing end of a railcar to respond to the fact that the leading edge was yanked forward. In the real world, the length of the cars *would* matter, but the added total delay to the travel time of the pulse would be proportionally small.

I also agree with your result of 4 seconds (I was amused that they chose the values so that the 22's would cancel). The total delay from the "shock" traveling through the bodies of the railcars adds perhaps about another 0.1 second.