A force of 15N stretches a spring to a total length of 30cm. An additional force of 10N stretches the spring 5cm further. Find the natural length of the spr...

A force of 15N stretches a spring to a total length of 30cm. An additional force of 10N stretches the spring 5cm further. Find the natural length of the spring

Answer Details

We can use Hooke's Law, which states that the force exerted by a spring is proportional to its extension, to solve this problem. Let the natural length of the spring be x. When a force of 15N is applied, the spring is stretched by 30cm - x. Therefore, we have: 15N = k(30cm - x) where k is the spring constant. When an additional force of 10N is applied, the spring is stretched by an additional 5cm. Therefore, we have: 25N = k(35cm - x) Dividing the second equation by the first, we get: 25N/15N = (35cm - x)/(30cm - x) Simplifying this equation, we get: 5/3 = (35cm - x)/(30cm - x) Multiplying both sides by 30cm - x, we get: 5(30cm - x) = 3(35cm - x) 150cm - 5x = 105cm - 3x 2x = 45cm x = 22.5cm Therefore, the natural length of the spring is 22.5cm. Answer:  22.5cm.