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

To find the stretch of each spring, use the formula F/k, where F is the weight of the object attached to the spring and k is the force constant of the spring.

Step-by-step explanation:

To find the stretch of each spring, we need to consider the conservation of mechanical energy. When the original spring is cut into two identical springs, the total length of the springs remains the same, but the number of coils is divided equally between the two springs. Therefore, each spring will have 50 coils.

Since the original spring and the two identical springs are in series, they share the same force constant. We can use the formula for the force constant of a spring to find the value of k:

k = (F/x)

where F is the force applied to the spring and x is the stretch of the spring. In this case, the force applied to the spring is the weight of the object, which is equal to the gravitational force acting on it.

Using the formula for the force constant, we can find the stretch of each spring:

x = (F/k)

Answer 2

`x' = 0.085 m`

Step-by-step 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' = (x)/(2)`

`x' = (0.170)/(2)`

`x' = 0.085 m`