Question

A spring has a length of 15.4 cm and is hanging vertically from a support point above it.A weight with a mass of 0.200 kg is attached to the spring,causing it to extend to a length of 28.6cm.What is the value of the spring constant?

Answer 1

Answer : 14.9N/m

We place the origin of our coordinate system at the top of the spring,with the positive direction upward,as is customary.

Then x0=−15.4cm and x=−28.6cm.

According to Hooke's law,the spring force is Fs=−k(x−x0)

Also,we know the force exerted on the spring was provided by the weight of the 0.200-kg mass :

F=−mg  

=−(0.200kg)(9.81m/s2)=−1.962N

Again,the negative sign indicates the direction.

Now we can solve the force equation for the spring constant :

k=−Fsx−x0=−1.962N(−0.286m)−(−0.154m)

=14.9N/m