SOLUTION: A load of 6kg stretches a coil spring to a length of 30cm, and a load of 10kg stretches it to a length of 40cm. Find the length of the spring when there is no load.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A load of 6kg stretches a coil spring to a length of 30cm, and a load of 10kg stretches it to a length of 40cm. Find the length of the spring when there is no load.      Log On


   



Question 1002126: A load of 6kg stretches a coil spring to a length of 30cm, and a load of 10kg stretches it to a length of 40cm. Find the length of the spring when there is no load.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the spring when there is no load, in cm.
30-x= stretching of the spring with a 6kg load, in cm.
40-x= stretching of the spring with a 10kg load, in cm.
A very high load, will forever deform, or even break a spring.
However, with reasonable loads, the stretching of a spring is proportional to the load applied, applied, and vice versa.
In equation form, that proportional relation is:
Load in kg = K(strecthing in cm) ,
where K is a constant, i kg/cm.
Without writing the units, the data we are given shows
6=K%2830-x%29
10=K%2840-x%29
dividing one equation by the other, we get
6%2F10=K%2830-x%29%2F%28K%2840-x%29%29 ---> 6%2F10=%2830-x%29%2F%2840-x%29
6%2840-x%29=10%2830-x%29
240-6x=300-10x
10x-6x=300-240+
4x=60+ ---> x=60%2F4 ---> x=15 .
The length of the spring when there is no load is highlight%2815cm%29 .