Question involving conservation law and springs

[mizzy]

A freight car of mass 1800kg is timed at 4.2m/s just after it runs into a spring-loaded bumper at the end of the track. The bumper consists of an 800kg mass that the car runs into, and a pair of large springs. The car travels 2.4m before coming to rest.

 

[kuruman]

And what are the questions that the problem asks?

 

[mizzy]

a)using an appropriate conservation law, find the speed of the freight car before it struck the bumper.
b)Find the time taken for the car to be brought to rest.

 

[kuruman]

OK. You can use energy conservation to find the spring constant k. You need to say that the mechanical energy immediately after the collision (when the spring is still uncompressed) is equal to the mechanical energy at maximum compression (when the masses are instantaneously at rest). This should give you k which you can then use to find the period.

 

[mizzy]

So...

PEs + KE = PEs + KE
0 +1/2mv^2 = 1/2kx^2 = 0

where v is the speed found from part a and x is the distance given before it comes to rest. Then find x and solve for T.

is that right?

 

[mizzy]

i'm sorry...the speed should be 4.2m/s because that is the speed right after collision.

I get a k of 7962.5N/m and therefore T = 3.60s

Can you confirm this?

THANKS FOR ALL YOUR HELP! =)

 

[kuruman]

Confirmed. Don't forget that 3.60 s is not the time you are looking for.