1) The compression of the spring is 0.14 m
2) The mass is 50 kg
Explanation:
We can find the amount of compression of the spring by using Hooke's law. In fact, the magnitude of the restoring force in the spring is given by:
[tex]F=kx[/tex]
where
F is the restoring force
k is the spring constant
x is the compression of the spring
In this problem, we have:
F = 490 N is the restoring force
k = 3500 N/m is the spring constant
Solving for x, we find the compression of the spring:
[tex]x=\frac{F}{k}=\frac{490}{3500}=0.14 m[/tex]
2)
At equilibrium, the weight of the mass on the spring is equal to the restoring force in the spring, therefore we can write:
[tex]mg = kx[/tex]
where
m is the mass of the object
g is the acceleration of gravity
kx is the restoring force
We know that
kx = 490 N at equilibrium (restoring force)
[tex]g=9.8 m/s^2[/tex] (acceleration of gravity)
Solving for m, we find the unknown mass:
[tex]m=\frac{kx}{g}=\frac{490}{9.8}=50 kg[/tex]
#LearnwithBrainly
