Calculating the Compression Distance in an Inelastic Collision with a Spring

[dancing123]

A ball of clay of mass m = 0.5 kg strikes a block of mass M = 8.0 kg which slides on a frictionless table as it compresses a spring with spring constant k = 60 N/m. The initial speed of the ball of clay is v = 12 m/s. The spring is initially at its relaxed length.



W= delta K = 1/2mv^2
W = 1/2kx^2
These are the equations I tried using.



I tried setting delta K equal to the Work but the answer it gave me was too big. I got 4.5 m as my answer and it's wrong. Can someone show me how to do this problem step by step?

 

[tiny-tim]

welcome to pf!

hi dancing123! welcome to pf!

(have a delta : ∆ and try using the X² icon just above the Reply box )

I tried setting delta K equal to the Work but the answer it gave me was too big. I got 4.5 m as my answer and it's wrong.

Show us your full calculations, and then we'll see what went wrong, and we'll know how to help!

 

[dancing123]

Hi! Thank you for helping me. :)

This is what I tried to do:
W = 1/2kx^2
K = 1/2mv^2

1/2kx^2 = 1/2(m+M)v^2
x^2 = [(m+M)v^2]/k
x = sqrt{[(m+M)v^2]/k}
x = sqrt{[(0.5+8.0)12^2]/60}
x = 4.5166 m

 

[tiny-tim]

ah, you have to split the problem into two parts …

the first is an inelastic collision so there's no conservation of energy, instead you use conservation of momentum to find the speed immediately after the collision …

from that time on, you can use energy

 

[dancing123]

Sorry I got back to you so late but thank you so much. I was able to figure it out :) My answer turned out to be 0.266 m, which was the correct answer.