2.8 Spring Forces

Describe the force exerted on an object by an ideal spring.

• An ideal spring has negligible mass and exerts a force that is proportional to the change in its length as measured from its relaxed length. A nonideal spring either has nonnegligible mass or exerts a force that is not proportional to the change in its length as measured from its relaxed length.
• The magnitude of the force exerted by an ideal spring on an object is given by Hooke’s law:
• The force exerted on an object by a spring is always directed toward the equilibrium position of the object–spring system.

Describe the equivalent spring constant of a combination of springs exerting forces on an object.

• A collection of springs that exert forces on an object may behave as though they were a single spring with an equivalent spring constant keq.
  • i. The inverse of the equivalent spring constant of a set of springs in series is equal to the sum of the inverses of the individual spring constants. Derived equation: TOPIC 2.8 Spring Forces
  • ii. The equivalent spring constant of a set of springs arranged in series is smaller than the smallest constituent spring constant.
  • iii. The equivalent spring constant of a set of springs arranged in parallel is the sum of the individual spring constants. Derived equation: BOUNDARY STATEMENT AP Physics C: Mechanics only expects students to find the effective spring constant of systems of springs that are arranged either in series or in parallel and does not expect students to find the effective spring constant of a system in which springs are arranged in both series and parallel.