Mass dropped onto vertical spring what is the max compression?

  • Thread starter MathHelpa
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  • #1
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Homework Statement


A mass m = 0.5 kg is dropped from a height of 1.5m above the end of an uncompressed vertical spring with k = 500 N/m. What is the maximum compression of the spring?


Homework Equations


f_sp = -kx
W_sp = 1/2 kx^2
W_nc = ΔK + ΔU
K = 1/2 mv^2
U = mgh
W = Fdcos∅
p = mv


The Attempt at a Solution


My friend and me were in different groups and they did the problem differently and came to a different answer. We set up ours as mg(h_0 + Δx) = 1/2hΔx^2 and came to a answer of .18 and rounded to .20 for Δx. My friend got much higher number so I was wondering what the answer really was and how to do it correctly if we are wrong.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
6,054
391
What are 'h' and 'h_0' in you formula?
 
  • #3
ehild
Homework Helper
15,543
1,914

Homework Statement


A mass m = 0.5 kg is dropped from a height of 1.5m above the end of an uncompressed vertical spring with k = 500 N/m. What is the maximum compression of the spring?


Homework Equations


f_sp = -kx
W_sp = 1/2 kx^2
W_nc = ΔK + ΔU
K = 1/2 mv^2
U = mgh
W = Fdcos∅
p = mv


The Attempt at a Solution


My friend and me were in different groups and they did the problem differently and came to a different answer. We set up ours as mg(h_0 + Δx) = 1/2hΔx^2

You meant 1/2 kdx^2....


and came to a answer of .18 and rounded to .20 for Δx. My friend got much higher number so I was wondering what the answer really was and how to do it correctly if we are wrong.

Your solution is correct.

ehild
 

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