Question

question 3
suppose you find a spring in an old box. being the curious type, you decide to determine its spring constant. you hang 350 g from it and it stretches 8 cm. what is its spring constant in n/m?
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integer, decimal, or e notation allowed

question 4
you are visiting an alien planet and want to determine the acceleration of gravity (the alien \g\). you get out a 0.5 kg mass and attach it to a spring with a spring constant of 100 n/m and the spring stretches 4 cm. what is the acceleration due to gravity in m/s^2
add your answer
integer, decimal, or e notation allowed

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Explanation:

Question 3

Step1: Convert units

Convert mass \(m = 350g=0.35kg\) and stretch \(x = 8cm = 0.08m\).

Step2: Use Hooke's law \(F = kx\) and \(F=mg\)

Since \(F = mg\) (force due to gravity) and \(F = kx\) (Hooke's law), then \(mg=kx\). Solve for \(k\): \(k=\frac{mg}{x}\).
Substitute \(m = 0.35kg\), \(g = 9.8m/s^{2}\), \(x=0.08m\) into the formula: \(k=\frac{0.35\times9.8}{0.08}\).
Calculate \(0.35\times9.8 = 3.43\), then \(k=\frac{3.43}{0.08}=42.875\)

Answer:

\(42.875\)

Question 4

Step1: Convert units

Convert stretch \(x = 4cm=0.04m\)

Step2: Use Hooke's law \(F = kx\) and \(F = mg_{alien}\)

Since \(F = kx\) (Hooke's law) and \(F=mg_{alien}\), then \(kx=mg_{alien}\). Solve for \(g_{alien}\): \(g_{alien}=\frac{kx}{m}\)
Substitute \(k = 100N/m\), \(x = 0.04m\), \(m = 0.5kg\) into the formula: \(g_{alien}=\frac{100\times0.04}{0.5}\)
Calculate \(100\times0.04 = 4\), then \(g_{alien}=\frac{4}{0.5}=8\)