Answer
(a) The spring scale reads 49 N
(b) $k = 1450~N/m$
(c) The scale will read zero when the spring is compressed by 3.4 cm
Work Step by Step
(a) The spring scale will show the weight of the object. Let $T$ be the tension from the scale pulling up on the object.
$T = mg$
$T = (5.0~kg)(9.80~m/s^2)$
$T = 49~N$
The spring scale reads 49 N.
(b) Let $F_s$ be the force of the spring pushing up on the object.
$F_s +T = mg$
$F_s = mg-T$
$F_s = 49~N-20~N$
$F_s = 29~N$
We can find the spring constant of the spring.
$kx = F_s$
$k = \frac{F_s}{x}$
$k = \frac{29~N}{0.020~m}$
$k = 1450~N/m$
(c) The scale will read zero when the spring is supporting the full weight of the object.
$F_s = mg$
$F_s = 49~N$
We can find the distance the spring is compressed when the spring is pushing with this force.
$kx = F_s$
$x = \frac{F_s}{k}$
$x = \frac{49~N}{1450~N/m}$
$x = 0.034~m = 3.4~cm$
The scale will read zero when the spring is compressed by 3.4 cm.
