Question

An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The spring stretches by 0.170 m. The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object. By how much does each spring stretch?

Answer 1

Answer:

$x' = 0.085 m$

Explanation:

As we know by force balance

$mg = kx$

now we have

$mg = k(0.170)$

now we know that spring constant is inversely depends on the length of the spring

So when length of the spring is half then the spring constant is doubled

so we will have

$mg = (2k) x'$

now we have

$kx = (2k) x'$

$x' = \frac{x}{2}$

$x' = \frac{0.170}{2}$

$x' = 0.085 m$