How Fast Was the Freight Car Moving Before Hitting the Springs?

[klmartin]

Homework Statement

A 8000 kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law with k1 = 1600 N/m and k2 = 3000 N/m. After the first spring compresses a distance of 15.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the car's initial speed.

Homework Equations

U=1/2kx^2
KE=1/2mv^2

The Attempt at a Solution

i tried to set U and KE equal and solve for v but its not really working out. i tried the equation 1/2(k1)(x1)^2+1/2(k2)(x2)^2=1/2mv^2. the problem is confusing because k2 and x2 are not explicitly expressed.

 

[dynamicsolo]

You aren't working out of Serway & Jewett, by any chance? (I just went through this problem with students last week... ;-) )

You have to break this problem into two parts. (You can use conservation of mechanical energy because we are ignoring friction and air resistance.)

At the beginning of part 1, the freight car just begins to make contact with the longer spring. What is the kinetic energy of the car and the potential energy in the springs at that moment? (We can skip gravitational potential energy, since the rails are horizontal, so there is no change in this PE.)

At the end of part 1/start of part 2, the car has compressed spring 1 by 15 cm. and is just beginning to contact spring 2. What are the energies at this point?

At the end of part 2, the car has been brought to rest. By what distance has each spring been compressed? What are the energies now?

How would you use the information about the amount and kind of energy at the end to tell you how fast the freight car was moving at the beginning?