An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3 a-2 b), the value of tension will be _______ N.

Solution

Physics sir · 3 steps

Hooke's law acts on the extension, not the length, so bring in the natural length and let it cancel.

1. Set up Hooke's law. Let the natural length be L and the spring constant be k. Tension is k times the extension, so 3 = k(a - L) and 2 = k(b - L).
2. Find k and L. Subtracting the two equations gives k(a - b) = 1. Then a - L = 3/k = 3(a - b), so L = 3b - 2a.

   T = k[(3a - 2b) - (3b - 2a)] = 5k(a - b)

3. So. Since k(a - b) = 1, the tension is T = 5 × 1 = 5 N.

The idea to keep. When a spring's lengths are given under different loads, the natural length is a hidden unknown. Write T = k(ℓ - L) for each case, and the differences will give k and L.

Answer from the NTA final answer key. Solution by PrepWiser.