Physics - Spring gun

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A spring gun is made by compressing a spring in a tube and then latching the spring at the compressed position. A 4.87-g pellet is placed against the compressed and latched spring. The spring latches at a compression of 4.87 cm, and it takes a force of 9.13 N to compress the spring to that point. Assume that the spring quits moving when it is back to its relaxed length. How much work is done by the spring when the latch is released and the pellet leaves the tube?

I am not doing this problem right... This is what I did the first time.
k=mg/d
(.00487 kg)(9.8 m/s^2)/.0487 m = .98 N/m

Ws= 0 - 1/2kd^2
= -1/2(.98 N/m)(.0487m)^2
= -1.16E-3

W= f x d
(9.13N)(.0487m) = .445J
Correct answer was .222J

Can anyone tell me where I went wrong??

  • Physics - Spring gun -

    k is force needed to compress spring / distance moved
    k = 9.13/.0487 = 187 N/m

    Work done = potential energy in spring = (1/2) k x^2 = (1/2)(187)(.0487)^2
    = 0.222 Joules

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