A spring has a natural length of 12 cm. If a 28-N force is required to keep it stretched to a length of 18 cm, how much work W is required to stretch it from 12 cm to 15 cm

The Work required to stretch the spring W = 0.42 J

Explanation:

Natural length = 12 cm

Stretched length = 18 cm

Change in length ( x ) = 18 - 12 = 6 cm = 0.06 m

Force required = 28 N

We know that spring force F = k x --------- (1)

⇒ k =

⇒ k =

⇒ k = 466.67

This is the stiffness of the spring.

Now the force required to stretch the spring F = k

⇒ = change in length of spring = 15 - 12 = 3 cm = 0.03 m

⇒ F = 466.67 × 0.03

⇒ F = 14 N

Now the work required to stretch the spring W = F ×

⇒ W = 14 × 0.03

⇒ W = 0.42 J

This is the Work required to stretch the spring from 12 cm to 15 cm.

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