Answer
(a) To measure up to 5.0 kg, the spring needs to stretch a distance of $0.20~m$
(b) The spring constant is $245~N/m$
Work Step by Step
(a) The spring stretches 1 mm for every 25 grams. We can find the stretch distance for a mass of $5.0~kg$:
$x = \frac{5.0~kg}{0.025~kg/mm} = 0.20~m$
To measure up to 5.0 kg, the spring needs to stretch a distance of $0.20~m$
(b) We can find the spring constant:
$kx = mg$
$k = \frac{mg}{x}$
$k = \frac{(5.0~kg)(9.80~m/s^2)}{0.20~m}$
$k = 245~N/m$
The spring constant is $245~N/m$.
