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posted by  DDB1010 on 1/6/2008 9:56:45 AM  |  status: Live  

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Question Details:
A glider of mass 0.230 kg moves on a horizontal frictionless air track. It is permanently attached to one end of a massless horizontal spring, which has a force constant of 9.0 N/m both for extension and for compression. The other end of the spring is fixed. The glider is moved to compress the spring by 0.180 m and then released from rest.
(a) Calculate the speed of the glider at the point where it has moved 0.180 m from its starting point, so that the spring is momentarily exerting no force.
m/s
(b) Calculate the speed of the glider at the point where it has moved 0.250 m from its starting point.
m/s
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posted by physics is phun! on 1/6/2008 12:05:34 PM  |  status: Live
Asker's Rating: Helpful   
DDB1010's comment:
"B was wrong"
Response Details:
Well...
 
The potential energy formula for a spring is:
 
You have the spring constant (k) and the displacement of the spring (x)
Sub in these units to find the potential energy before the glider is released:
 
Solve:
 
 
Now, since at the 2 extremes of displacement in a spring system the potential energy is equal to its kinetic energy (U=K)
 
Now use the kinetic energy formula to solve for velocity:
 
   
now divide by the mass  and then take the square root of the product.
 
 
V = 1.1259778359053076 m/s     THIS  IS  THE  ANSWER  TO  A)
 
 
B) Since the glider is on a perfectly horizontal track, gravity does not slow it down any. Also, the question states it is on a frictionless track, this means there is no friction to slow it down either.
 
So, the answer to this question would be the same as the answer in part a.
 
HOPE THIS HELPS. Please RATE my answer. Thanks.
 
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posted by physics is phun! on 1/7/2008 11:25:25 AM  |  status: Live
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DDB1010's comment:
"it worked"
Response Details:
 
SORRY!  I mis-read the beginning of the question. It's still attached to the spring. So, If it is still attached, it must be slowing down since the spring should now be pulling on it.
 
It asks you for its speed .25 m from its starting point. Well, we know how far the spring was compressed and therefore how far the glader has moved since that point.
 
So subtract the .18 m from the .25m and you should get .07m as a distance traveled since.
 
Now use the information from part A to detirmine the rate change of velocity due to the force of the spring.
 
If   v = 1.1259778359053076 m/s at the end of the .18m then to find acceleration, we use:
 
now sub in your info:
    2*.18 =
DIVIDE BY .36m
 
 
Now use this to do the rest of the problem:
 
If that was its acceleration when it was increasing its speed, then the negative of that would be its "decelleration" when the spring pulling on it is slowing it down.
 
 
Now use the same formula you did above:
 
     your initial velocity is the final velocity in part A)
 
Take the square root:
 
  This is your answer for part B)
 
Hope this helps a little more. Sorry about before. Please let me know if it works!
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"Genius is more often found in a cracked pot than in a whole one." -
  -E.B. White
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