A person wants to figure out the spring constant of a spring he found in a junky

Question

A person wants to figure out the spring constant of a spring he found in a junkyard so that he can use it to measure the inertias of other objects in the yard. First, he needs to calibrate it (hold a meter stick next to it and take measurements of compression lengths under load). So, he puts an object with inertia 10kg on the spring and measures a compression of 0.1m when it comes to rest . (a)What is the spring constant? (b)This person now puts a box of unknown inertia on the spring, which compresses the spring by 0.15m. What is the inertia of the box? (c)If this person put a 5kg box on the same spring, how much would the spring compress?

Explanation / Answer

here the weight is balanced by spring force

(a) K.X = mg

K = mg/X = (10 x 9.8) / .1 = 980 N/m

(b) mg = K.X

m = K.X / g = (980 x .15) / 9.8 = 15 kg

(c) K.X = mg

X = mg / K = (5 x 9.8) / 980 = .05 m

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