# The spring of a toy pistol with a stiffness of k = 1000N / m has a length L0 = 15 cm.

The spring of a toy pistol with a stiffness of k = 1000N / m has a length L0 = 15 cm. To what height will a ball with a mass of m = 10 g fly up vertically from the pistol if its spring has been compressed to L = 5 cm, do not take into account the air resistance.

Data: k (gun spring rate) = 1000 N / m; L0 (original length of the spring) = 15 cm (in SI L0 = 0.15 m); m (ball mass) = 10 g (in SI m = 0.01 kg); L (spring length after compression) = 5 cm (in SI L = 0.05 m).

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

The height to which the ball should take off is determined using the law of conservation of energy: m * g * h = k * ΔL ^ 2/2 = k * (L0 – L) ^ 2/2 and h = k * (L0 – L) ^ 2 / (2 * m * g).

Calculation: h = 1000 * (0.15 – 0.05) ^ 2 / (2 * 0.01 * 10) = 50 m.

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