Question

question 4
you need to replace a broken spring in a toy at home (on earth), and must determine its spring constant. you take an identical spring from the toy and attach a mass and observe it stretch. if the spring stretches 1.5 cm when 25 g is attached, what is the spring constant (in n/m)?
a 0.1635
b 16.35
c 163.5
d 16350

Explanation:

Step1: Convert units

Convert mass \(m = 25g=0.025kg\) and stretch \(x = 1.5cm = 0.015m\).

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

Since \(F = mg\) (force due to gravity) and \(F = kx\) (Hooke's law), then \(mg=kx\).
We can solve for \(k\): \(k=\frac{mg}{x}\).
Substitute \(m = 0.025kg\), \(g = 9.8m/s^{2}\), \(x=0.015m\) into the formula:
\(k=\frac{0.025\times9.8}{0.015}\)
\(k=\frac{0.245}{0.015}\approx16.33\approx16.35\) (due to rounding differences in intermediate steps)

Answer:

B. 16.35