A force compresses a spring by 0.280 meters. The spring has a spring constant of 250 newtons per meter. If the same force were applied to a spring with a spring constant of 300 newtons per meter, by how much would the spring compress?Select one:0.268 m.highlight_off0.210 m.highlight_off0.297 m.highlight_off0.233 m.highlight_offImage Source: PhET
Question
A force compresses a spring by 0.280 meters. The spring has a spring constant of 250 newtons per meter. If the same force were applied to a spring with a spring constant of 300 newtons per meter, by how much would the spring compress?Select one:0.268 m.highlight_off0.210 m.highlight_off0.297 m.highlight_off0.233 m.highlight_offImage Source: PhET
Solution
The force exerted on the spring can be calculated using Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. The formula is:
F = k * x
where: F is the force applied, k is the spring constant, and x is the distance the spring is stretched or compressed.
Given that the spring constant k1 is 250 N/m and the spring is compressed by x1 = 0.280 m, we can calculate the force F as follows:
F = k1 * x1 F = 250 N/m * 0.280 m F = 70 N
Now, if the same force is applied to a spring with a different spring constant k2 = 300 N/m, we can find the new compression distance x2 using the same formula, rearranged as follows:
x2 = F / k2 x2 = 70 N / 300 N/m x2 = 0.233 m
So, the spring with a spring constant of 300 N/m would compress by 0.233 meters.
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