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Springs

Springs. Gravitational Potential Energy. In raising a mass m to a height h , the work done by the external force is equal to GPE :. . GPE = mgh. . Spring Potential Energy. Bungee cords, rubber bands, springs-- any object that has elasticity can store potential energy.

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Springs

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  1. Springs

  2. Gravitational Potential Energy In raising a mass m to a height h, the work done by the external force is equal to GPE: . GPE=mgh .

  3. Spring Potential Energy • Bungee cords, rubber bands, springs-- any object that has elasticity can store potential energy. • Each of these objects has a rest or “zero potential” position (EQUILIBRIUM) • When work is done to stretch or compress the object to a different position elastic potential energy is stored

  4. Spring Potential Energy A spring has potential energy, called elastic potential energy, when it is compressed or stretched. The force required to compress or stretch a spring is: where k is called the spring constant, and needs to be measured for each spring.

  5. Consider Data from Start of Class • If a spring is harder to stretch, will the spring constant be higher or lower? • If a spring is easier to stretch, will the spring constant be higher or lower?

  6. Elastic Potential Energy • Top picture is “rest position”; x = 0 • This is a point where the elastic potential energy = 0 • Bottom picture is “stretched position” • Here elastic potential energy is stored in the spring • PEelast= ½ kx2 where k is the “spring constant” in N/m

  7. Note: Conservation of energy still applies! • When the mass is fully extended or compressed and is at rest…THEN, ALL ENERGY IS POTENTIAL! • BUT • When PE is gone….all energy will convert to KINETIC! (And then we can use KE = 1/2mv2 to do calculations…mass will matter!)

  8. Check for Understanding • What is the formula for GPE? • How do we define GPE? • What is PEelastic? • What is the formula for the FORCE required to compress or stretch a spring?

  9. Check for Understanding • What is a spring constant? • What is the formula for PEelastic? • How are Peelastic and KE related? • Why is there no mass in the PEelasticequation but there is in the KE equation?

  10. Example 1: A spring is hung from a hook and a 10 Newton weight is hung from the spring. The spring stretches 0.25 meters. • What is the spring constant? • If this spring were compressed 0.5 meters, how much energy would be stored? • If this spring were used to power a projectile launcher, which fires a 0.2 kg projectile, with what velocity would the projectile leave the launcher? Assume 0.5 m compression.

  11. Find spring constant:

  12. Find Spring Energy:

  13. Find velocity:

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