Question

A 29.0 cm long spring is hung vertically from a ceiling and stretches to 35.7 cm when a 7.00 kg mass is hung from its free end.

(a)

Find the spring constant (in N/m).

 __N/m

(b)

Find the length of the spring (in cm) if the 7.00 kg weight is replaced with a 165 N weight.

__ cm

Answer 1

(a)

$Δx = 35.7-29.0 = 6.7 \;cm = 0.067 \;m \\ Mg=kΔx \\ 7.0 \times 9.8 = k \times 0.067 \\ k = \frac{68.6}{0.067}=1023.88 \;N/m$

(b)

$Mg = 165 \;N \\ 165 = 1023.88 \times Δx \\ Δx = \frac{165}{1023.88} = 0.1611 \; = 16.11 \;cm$