Work don by a spring problem

[chevyboy86]

A 6000 kg freight car rolls along rails with negligble friction. The car is brought to rest by a combination of 2 coiled springs. Both obey Hooke's law with k1=1600 N/m and k2=3400 N/m. After the first spring compresses a distance of 30 cm, the second springs acts with the first to increase the force as additional compression occurs in the graph.
The car comes to rest 50 cm after first contacting the 2 spring system. Find the car's initail speed.



I have no idea on how to do this problem.

 

[Mindscrape]

Do you know what the work and energy theorem is? You can use the fact that the when you integrate the Force and displacement then you get a work, which will also be a potential energy, which will also be a kinetic energy.

If you use superposition and the above info, then you will be able to get it.

 

[chevyboy86]

but how do I find inital speed, the equations are for work done, not initial speed.

 

[chevyboy86]

ok I'm giving this a shot, I found a similar problem in my book. They show vf= the square root of 2W/m and to find W, they multiplied the force by delta x. So for this problem, I added both forces of the springs to get 5000 N/m and multiplied it by .5m to get 2500J. I then used the books equation to find vf and when I plugged in all the numbers, I get .913 m/s. I'm not sure if this is right, but I took a shot at it.

 

[Astronuc]

A 6000 kg freight car rolls along rails with negligble friction. The car is brought to rest by a combination of 2 coiled springs. Both obey Hooke's law with k1=1600 N/m and k2=3400 N/m. After the first spring compresses a distance of 30 cm, the second springs acts with the first to increase the force as additional compression occurs in the graph.

The car comes to rest 50 cm after first contacting the 2 spring system. Find the car's initail speed.

Well there needs to be more information, such as are the springs acting in series or in parallel. I suspect in parallel.

Each spring stores mechanical energy, as a function of deflection.

The lighter spring deflects 30 cm, then presumably deflects another 50 cm while the stiffer spring is deflecting, for a total of 80 cm. The second spring compresses only 50 cm.

The energy stored in the springs equals the initial kinetic energy of the freight car (1/2 mV²) which was traveling at some speed, V, which is to be determined.

This might help - http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html