Question

If a 40 kg brick and a 400 kg brick each dropped from 1 m above a trampoline, find the lowest position of each brick. Assume the trampoline is a simple spring obeying Hooke's law with a k value of 12 000 N/m.

So, I used
mg(h+x)=1/2 k x^2
then solved for x in each case.

and got 2 different values out of the quadratic formula:
-0.223 m and -0.0000242 m
given the question, how can I rule one of the answers out and choose the reasonable answer?

Answer 1

6000x^2-40kx- 40*9.8*1=0 where k is 1, or 10

x= (+40k+-sqrt(1600k^2+9.4E6)/12,000

for k=1
x= (40+-3067)/12000= 25cm ignore the -x, it has no physical meaning, the trampoline will not deform upward.
for k=10
x= (+400+-sqrt(160000+9.4E6)/12000
x=(400+-3093)/12000=29cm

check my math.

Answer 2

you lost be. k= 12 000 N/m
where are you getting 1 or 10