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*Question:* The force required to slowly stretch a spring
varies from 0N to 105N as the spring is extended by 13cm
from its unstressed length. What is the force constant of the spring?
What work is done in stretching the spring? Assume that the spring
obeys Hooke's law.
*Answer:*
The force that the spring exerts on whatever is stretching it
is , where is the force constant, and is the extension
of the spring. The minus sign indicates that the force acts in the opposite
direction to the extension. Since the spring is stretched slowly, the force
which must be exerted on it is (almost) equal and opposite to .
Hence,
. We are told that N when m. It
follows that

The work done by the external force in extending the spring from 0 to is

Hence,

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** Up:** Conservation of energy
** Previous:** Worked example 5.2: Dragging
Richard Fitzpatrick
2006-02-02