Calculate Maximum Spring Compression: 0.4 kg Object, 80 N/m Constant

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To calculate the maximum compression of a spring when a 0.4 kg object traveling at 8 m/s strikes it, the kinetic energy formula (Ek = 0.5 * k * x^2) should be used rather than Hooke's law. The initial kinetic energy of the object can be converted into potential energy stored in the spring at maximum compression. Using the values provided, the kinetic energy is 12.8 J, which can be equated to the potential energy in the spring to find the compression distance. The spring constant (80 N/m) plays a crucial role in determining how far the spring compresses. Ultimately, energy conservation principles guide the solution to this problem.
cooney88
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Q. An object of mass o.4kg slides at 8m/s across a frictionless path before striking one end of a spring that is fixed at the other end. the spring constant is 80N/m. the maximum distance, in metres, by which the spring compressed is : ans?




I a not sure wether to use hookes law (f=ks) or the kinetic energy formula Ek = .5kmv^2

when i used hookes law i got an answer of 0.04 but when i use the kinetic energy forumla i got 0.57. I know it doesn't really make any sense to use hookes law as u can't find the force, only the momentum (0.4x 8)

any help with this would be greatly apreciated



The Attempt at a Solution

 
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It sounds like you're answering your own question. :wink:
 
so its the kinetic formula cos it wouldn't make sense to use the hookes law right? but since when can u have the spring constant in a kinetic energy formula?
 
cooney88 said:
so its the kinetic formula cos it wouldn't make sense to use the hookes law right?
Yes, you'll need to use energy conservation.
but since when can u have the spring constant in a kinetic energy formula?
Consider the potential energy stored in a compressed spring--that's where the spring constant appears.
 
cheers buddy
 
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