The magnitude of a force F needed to stretch a spring a distance Delta x from it

Question

The magnitude of a force F needed to stretch a spring a distance Delta x from its equilibrium length is described by the equation F = k Delta x, where k is the spring constant, or "stiffness" of the spring. The constant k may be found by applying a force to the spring, and measuring Delta x. The SI units for k are N/m. If the end of the spring is not accelerating, the spring exerts a force that is equal in magnitude and in the opposite direction to Delta x (labeled as Dx in figure). In the figure below, draw a free body diagram for the forces acting on a mass m hanging from the bottom of a spring. A spring stretches by Delta x = 10.0 cm when a mass of 25.0 g is hung from it. What is the spring constant k of the spring? The spring stretches by Delta x = 22.3 cm when a force F is applied to its end. What is the magnitude of the force F?

Explanation / Answer

Part 1

spring stretches by dx = 10 cm = 0.1 m

mass m, = 25.0 gm = 0.025 kg

using F= k(dx) = mg

k * 0.1m = 0.025 * 9.81

k = 2.4525 N/m

Part 2

spring stretches by dx = 22.3 cm = 0.223 m

using F= k(dx) = mg

2.4525 N/m * 0.223 m = mass * 9.81

mass = 0.5575 kg = 55.75 gm

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