Springs Essential Questions: Can a spring do work?

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Presentation transcript:

Springs Essential Questions: Can a spring do work? Can a spring store energy? How does the tension relate to…?

What factors affect the tension in a spring?

The tension in a spring is related to: The material used to make it. The thickness of the “wire” used in the winding. The shape and size of the spring. The change of length (compared to its relaxed length).

What is the mathematical relationship between…

What is the mathematical relationship between… the change of the spring’s length (m) and the amount of tension (N) in the spring? the tension in the spring (N) and the change of length (m) of the spring?

Hooke’s “Law” Tension (N) Change of length (m)

Work done BY a spring W = (F)(Dr) cosj ONLY used when F is CONSTANT W = ∫F(x)∙dx or W = area “under” F vs x graph Where x is the CHANGE OF LENGTH For a Hookian spring, W = ½ kxi2 – ½ kxf2 (does not apply to a progressive spring)

Solve this problem A spring is stretched from a relaxed length of 10 cm to a length of 15 cm. As a result, it experiences 20N of tension throughout its coils. A) What is the spring’s constant (in N/m)? B) How much work was done BY the spring? C) How much work was done ON the spring? #26

Work Done by a general variable force W = ∫F(x)∙dx or W = area “under” F vs x graph Note: x, y, z and r are interchangeable position symbols in this equation, but have different directional meanings Examples: CH7 #34, 38, 36, 41

POD The string in a compound bow exerts a force on an arrow that is shown to be equal to: F(x) = 11400x3 -6750x2 + 2000x Once the archer releases the string, it is in contact with a 0.35kg arrow for 0.50m. Determine the work the bow does on the arrow, and the speed the arrow attains.