Understanding Spring Constant: 8.0kg Stone Compression

AI Thread Summary
An 8.0kg stone compresses a spring by 10.0cm, leading to confusion over the spring constant calculation. The initial calculation incorrectly equates gravitational force to spring potential energy without proper unit consideration. The correct relationship involves recognizing that the spring force is proportional to the displacement, leading to a spring constant of 0.8 instead of 1.6. The mistake stems from misinterpreting the units and the energy equations. Understanding the proper application of these formulas is crucial for accurate results in spring constant problems.
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The first part of this problem says that a 8.0kg stone rests on top of a spring, and compresses it by 10.0cm. It then asks what the spring constant is. This is the work I did (assuming g = 10m/s^2, not 9.8m/s^2):

(8.0kg)(10m/s^2) = 1/2k(10cm)^2; 80N = 50cm; k = 1.6

But, the textbook says the answer is .8. I don't understand why it's half my answer. Any help would be greatly appreciated.
 
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On the left hand side, you have the gravitational force,
F_g = m g
On the left hand side, you have the spring potential energy,
W_s = \frac12 k x^2
Try taking the force exerted by the spring as well
F_s = k x

Actually, you could have noticed this mistake by looking at the units... you wrote down 80N = 50cm. Even if you meant
80 N = 50 cm^2 * k (N/cm)
you would have equated N to N cm.
Try to train yourself in spotting these mistakes: unless you know how to convert Newtons into Newtons times centimeters, an alarm bell should go off automatically.
 
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