An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. the spring stretches by 0.250 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?

Each spring would stretch by 0.125 m.

Explanation:

Let an object having mass m be hanging from the spring having spring constant k. Due to the weight of the object acting downwards, the spring would stretch by amount, x = 0.250 m.

⇒ m g = -k x       - (1)

Now the spring is cut into two equal halves and attached between the object and the ceiling. It means the springs are connected in parallel.

For parallel combination:

k' = k₁ + k₂

Since, same spring is being used, k₁ = k₂ = k

k' = 2 k

The extension of the two springs would also be equal:

⇒ m g = - k'x'

⇒m g = - 2 k x'

⇒ -k x = - 2 k x'      (from 1)

⇒x' = x/2 = 0.5 × 0.250 m = 0.125 m

Therefore, each spring would stretch by 0.125 m.

.25/4

Explanation:

All you have to do is divide by 4 instead of 2 for the previous response.

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