Chapter 2 Review of Forces and Moments - Brown University

Forces exerted by springs
A solid object (e.g. a rubber band) can be made to exert forces by stretching it. The forces exerted by a
solid that is subjected to a given deformation depend on the shape of the component, the materials it is
made from, and how it is connected to its surroundings. Solid objects can also exert moments, or torques
– we will define these shortly. Forces exerted by solid components in a machine or structure are
complicated, and will be discussed in detail separately. Here, we restrict attention to the simplest case:
forces exerted by linear springs.
A spring scale is a good example of a linear spring. You can attach it
to something at both ends. If you stretch or compress the spring, it
will exert forces on whatever you connected to.
The forces exerted by the ends of the spring always act along the line
of the spring. The magnitude of the force is (so long as you don’t
stretch the spring too much) given by the formula
F = k( L−
a)
where a is the un-stretched spring length; L is the stretched length,
and k is the spring stiffness.
In the SI system, k has units of N/m.
Note that when you draw a picture showing the forces exerted by a
spring, you must always assume that the spring is stretched, so that
the forces exerted by the spring are attractive. If you don’t do this,
your sign convention will be inconsistent with the formula
F = k( L− a)
, which assumes that a compressed spring (L