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. 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

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.

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?

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  PE elast = ½ kx 2 where k is the “spring constant” in N/m

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 = 1/2mv 2 to do calculations…mass will matter!)

Check for Understanding – What is the formula for GPE? – How do we define GPE? – What is PE elastic ? – What is the formula for the FORCE required to compress or stretch a spring?

Check for Understanding – What is a spring constant? – What is the formula for PE elastic ? – How are Pe elastic and KE related? – Why is there no mass in the PE elastic equation but there is in the KE equation?

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. a)What is the spring constant? b)If this spring were compressed 0.5 meters, how much energy would be stored? c)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.

Find spring constant: Q: kU: N/mI: F= 10N x= 0.25 m D: S: 1 For: F=-kx M: F=- kx 10N =- (k) (-0.25m) 40N/m = k E:

Find Spring Energy: Q: PE spring U: J I : k=?? x= 0.5 m D: S: 1 For: E spring = 1/2kx 2 M: E spring = 1/2kx 2 E spring = (1/2)(40N/m)(0.5m) 2 E spring = (20N/m)(0.25m 2 ) E spring = 5 J E:

Find velocity: Q: vU:m/s I: E=?? x= 0.5 m m= 0.2 kg D: S: 1 For: E kinetic = 1/2mv 2 M: E kinetic = 1/2mv 2 5 kgm 2 /s 2 =(1/2)(0.2kg)(v 2 ) 50 m 2 /s 2 = v 2 7m/s = v E: