Stretching a spring A spring has a natural length of 10 in....

Stretching a spring A spring has a natural length of 10 in. An $=800-lb$ force stretches the spring to 14 in. Find the force constant. b. How much work is done in stretching the spring from 10 in. to 12 in. $?$ - How far beyond its natural length will a $1600-16$ force stretch the spring?

Stretching a spring A spring has a natural length of 10 in. An $=800-lb$ force stretches the spring to 14 in.
Find the force constant.
b. How much work is done in stretching the spring from 10 in.
to 12 in. $?$
- How far beyond its natural length will a $1600-16$ force stretch the spring?

Key Concepts

Hooke's Law

Hooke's Law is a fundamental principle in mechanics stating that the force required to extend or compress a spring is directly proportional to the displacement from its rest (or natural) length. This linear relationship is mathematically expressed as F = kx, where F is the applied force, x is the displacement, and k is the spring constant that characterizes the stiffness of the spring.

Spring Constant

The spring constant, denoted by k, is a measure of a spring's stiffness. It quantifies the resistance offered by the spring to being deformed. In practical calculations, k is determined by the ratio of the force applied to the displacement produced, meaning that a larger k indicates a stiffer spring requiring more force to achieve the same displacement.

Work Done on a Spring

Work done in stretching or compressing a spring is not constant as the force varies with displacement. It is calculated by integrating the variable force over the distance moved, yielding the formula W = (1/2)kx² for stretching or compressing from the natural length. This concept is essential for understanding how energy is stored as elastic potential energy in the spring.

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