Question

If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm

Answer 1

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."

$F= ke$

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= $\frac{15}{100}$= $0.15m$

we can solve for the spring constant k

we also know that the force F = mg

assuming $g=9.81m/s^{2}$

therefore

$24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m$

We can use this value of k to solve for the mass that will cause an extension of  $10cm= 0.1m$

$x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg$