Block attached to spring - calculate how far it will move

  • Thread starter jcjc16
  • Start date
  • #1
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Homework Statement


A spring with spring constant 200 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y = 0. A block of weight 20 N is attached to the lower end, held still for a moment, and then released. How far will the block move before coming momentarily to a stop?


Homework Equations


mg = -kx
mg = 0.5kx^2


The Attempt at a Solution


I tried using the first equation and got x = 0.1m as my ans. which was wrong. I then tried using the second equation instead and still got an incorrect answer. Where am I going wrong? The ans. is 0.2 m.

Thanks in advance!
 

Answers and Replies

  • #2
lewando
Homework Helper
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You need to look at this problem from an energy conservation standpoint.
 
  • #3
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The block comes to a stop when its speed is zero. Your approach is invalid because the speed of the block is not necessarily zero when the net force acting on the block is zero.
 
  • #4
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Hmm ok would it be something like this? mgh = 0.5kx^2 and the x and the h are the same? Cuz then solving for h I get (2mg)/k and when I subbed in the number I got 0.2. Is this the right way of doing this problem?
 
  • #5
lewando
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Looks like a good way to get the answer!
 
  • #6
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Your answer is correct; however, it is important you understand why the approach is valid. Do you?
 

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