Problem 19P

A certain spring has a force constant k. (a) If this spring is cut in half, does the resulting half spring have a force constant that is greater than, less than, or equal to k? (b) If two of the original full-length springs are connected end to end, does the resulting double spring have a force constant that is greater than, less than, or equal to k?

Solution 19P

Step 1 of 3

a)

Here we need to check whether the spring constant will decrease, increase or remains same as we cut the spring into half.

From the Hooke’s law we know that,

-----------------------(1)

--------------------------(2)

Where is the potential energy stored in the spring when we extend the spring by a distance of .