Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1310002     The spring force of parallel springs in an exercise apparatus.     1310002
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The piece of exercise equipment shown below includes two handles that are on each end of two parallel springs, each with a stiffness 500 N/m. To build strength, a person holds the two handles and pulls them apart with equal magnitude forces applied in opposite directions to the handles, thus stretching the springs. Neglect the mass of the springs and assume that they are pulled horizontally.

Figure: Two parallel springs between two handles that can be pulled apart.

  1. If a person stretches the springs 5 cm from their relaxed lengths and holds it at rest, what is the net force applied to the system and what magnitude force must he apply to each handle?
  2. What magnitude force must he apply to each handle to stretch it twice as far (10 cm) and hold it at rest?
  3. If the two parallel springs were replaced with a single spring such that the same force would be required to stretch it 10 cm as for the two parallel springs, what would be the stiffness of the single spring?