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</p>

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 .

Step 2 of 3</p>

Now after cutting the spring into two halfs,

--------------------------(3)

Where and is the new spring constant.

From equation (3),

.

So, we got that,

.

The spring constant increases by 4 times.