Answer:
16kg
Step-by-step explanation:
This problem is borers on elasticity of materials.
according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."
[tex]F= ke[/tex]
where F is the applied force in N
k is the spring constant N/m
e is the extension in meters
Given data
mass m= 24kg
extensnion=15cm in meters= [tex]\frac{15}{100}[/tex]= [tex]0.15m[/tex]
we can solve for the spring constant k
we also know that the force F = mg
assuming [tex]g=9.81m/s^{2}[/tex]
therefore
[tex]24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\[/tex]
We can use this value of k to solve for the mass that will cause an extension of [tex]10cm= 0.1m[/tex]
[tex]x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg[/tex]
