Max Compression Distance x: Solving the Compression Distance Problem

[asimon2008]

Problem: An object of mass m1= 10 kg moving to the right with a velocity v1=30 m/s, collides with a second object of mass m2=5kg, which is initially at rest. The 2 objects stick together, and they continue to move with the same velocity V. The moving system of 2 blocks compresses a light spring, having a spring constant k=80 N/m. Calculate the max. compression distance x, of the spring.

m1v1 + m2v2 = (m1+m2)vf
(10)(30)+(5)(0)=(10+5)vf
300=15vf
Vf=300/15=20

KE=U spring

I stuck on how to finish solve the problem.

 

[tramar]

You need to account for the energy stored in the spring. it is given by
$$\frac{1}{2} k x^2$$
where k is the spring constant and x is the distance from the equilibrium position.

 

[Redbelly98]

In other words, after you have found the 20 m/s velocity, this becomes an energy conservation problem to get the spring compression.