Answer:
.
Step-by-step explanation:
The question has given the force it takes to stretch this spring by a particular length. With that information, the amount of work completed in order to stretch this spring by a different length can be found using the following steps:
- Find the spring constant
of the spring from the restoring force and the corresponding displacement of the spring, and - Apply the equation for the elastic potential energy
of ideal springs to find the energy required to stretch the spring by the given distance.
Note the unit conversion during the calculations- all values should be measured in standard units, with distances measured in meters.
To find the spring constant
of an ideal spring, divide the restoring force by the change in the length of the spring.
.
In this question, it is given that an external force of
is needed to increase the length of the spring by
(note the unit conversion.) In other words, the restoring force on the spring would be
in response to a change in length of
. The spring constant would be:
.
For an ideal spring of spring constant
, if the length of the spring is changed by
, the elastic potential energy
stored in that spring would be:
.
The spring constant in this question is
, whereas the displacement of the spring needs to be
(again, note the unit conversion.) The elastic potential energy stored in this spring would be:
.
(Note that
.)
In other words, when an external force stretches this spring by
from the equilibrium position, the amount of work done on the spring would be
.