6.4 Integral Applications
Force and Work Application
Question #2 (Medium): Hooke’s Law and the Spring Constant
Hooke’s Law deals with the force and work done on springs. Force required to stretch a spring by a
length of beyond its natural length is given by: ( ) , where is the spring constant and is
the distance stretched. Usually the spring constant is not provided, so it needs to be calculated.
Because springs are of miniature size, value for the length stretched is usually in or inches. For the
work done, the stretched length needs to be converted to corresponding meters or feet based on the
conversion rate of : ̅ .
If of work is needed to stretch a spring from its natural length of to a length of , then:
1) How much work is needed to stretch the spring from to ?
2) What is the length that would keep the spring stretched beyond its natural length?
If the spring is stretched from its natural length of to 40cm, then x value representing the length
stretched is: .
By Hooke’s Law: ( ) . The question provides work and not force but Work done. So