answers
part a = 196 N/m
part b = 55 cm or 0.55 m
explanation
we can solve this using Hooke's law where spring force is equal to the product of displacement and spring constant
[tex]F_s =kx[/tex]
part a
rearrange Hooke's law to solve for k (spring constant)
[tex]F_s =kx\\k = \frac{F_s}{x}[/tex]
the spring force caused by the painting here is equal to the weight of the painting
[tex]F_s = mg\\k = \frac{mg}{x}[/tex]
m = 3 kg
g = 9.8 m/s^2
x = 45 - 30 = 15 cm = 0.15m
[tex]k = \frac{3*9.8}{0.15}\\k = 196 \frac{N}{m}[/tex]
part b
since we now know the spring constant, we can find the displacement caused by a 2kg picture by rearranging Hooke's law to solve for x, where spring force is still equal to weight
[tex]F_s =kx\\x = \frac{F_s}{k}\\x = \frac{mg}{k}[/tex]
m = 2 kg
g = 9.8 m/s^2
k = 196 N/m
[tex]x = \frac{2*9.8}{196} \\x = 0.1m[/tex]
the spring is stretched an additional 0.1 meters or 0.1 * 100 = 10 centimeters
45 cm + 10 cm = 55 cm or 0.55 m
