comparison of slings · Physics Brawl 2022 #2

Physics · mechanics

Problem

Lego got bored of bows, so he went to buy a sling. We approximate it as a spring with constant stiffness and a zero rest length. Lego can stretch the sling with force F=31.4F = 31.4 N, and he wants it to store as much energy as possible while it is stretched. There were two slings at the shop, with stiffnesses k1=159k_1 = 159 N/m and k2=265k_2 = 265 N/m. What will be the difference between the potential energies of those slings stretched with force FF? Give a positive result if the sling with k1k_1 has more energy and a negative one if the opposite is true.

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