Why study springs elastic Springs are This means

Why study springs? elastic Springs are_______. This means that if you: force them, and a/ apply a ______to deformed(bent out of shape), and b/ they become ______ force then they c/ then you remove the ______, bounce back d/ _________. Many things have some elasticity, and so they behave like springs: metal • wood _______ plastic • concrete humans water • air the sun atoms • quartz speakers water musical instruments • _______________ strings, air, drums… Many elastic objects obey…

Hooke's Law: The compression or elongation x of an ______ equilibrium position (x = 0) ideal spring from its ________ directly proportional is ______________to the applied force Fs. Fs = kx compression: stretching or elongation: x=0 x x Fs stretch or _________. compression More F more ______ Fs

Hooke's Law is often written: Fs = -kx This is because it also describes the force that the spring itself object that is attached ________ exerts on an ______ to it. The negative sign indicates that the direction of oppositeto the spring force is always _______ displacement of the object -x compressed spring: undisturbed spring > 0 Fs ___ Fs x=0 equilibrium _______ position, Fs = __ 0 +x stretched spring: Fs < 0 Fs ___

Ex. A weight of 8. 7 N is attached to a spring that has a spring constant of 190 N/m. How much will the spring stretch? w/ weight w/o weight Given: Fs = 8. 7 N k = 190 N/m Unknown: x =? Equation: Fs = kx 8. 7 N = (190 N/m) x x = 4. 6 x 10 -2 m x 8. 7 N

Fs = kx Ex: A force of 5. 0 N causes the spring to stretch 0. 015 m. How far will it stretch if the force is 10 N? 2 (0. 015 m) = 0. 030 m Fs direct 10 5 . 015 ? x What quantity does the slope represent? slope = = Dy/Dx Compare to Fs = kx Fs/x Solve for Fs/x = k the spring constant, k. The slope represents ________________

What are the units of the spring constant, k? Solve… …for k: units of k: Fs = kx k = [k] = [ Fs/x ]/[Fs = ] x N/m(derived) This can be also seen from the graph: Fs (N) k = the slope = Dy/Dx So k has the same units as Dy/Dx: x (m) N/m

Ex. Comparing two springs that stretch different amounts. spring B Fs spring A Applying the same force F to both springs x. B Which spring stretches more? Which is stiffer? B x. A A greater slope _____ largerk stiffer spring _____ x

Elastic ______ PE - the energy stored in a spring when work is done on it to stretch or compress it PEs = (½)kx 2 Ex. A spring with a spring constant of 370 N/m is stretched a distance 6. 4 x 10 -2 m. How much elastic PE will be stored in the spring? How much work was done to stretch the spring by this amount?

Elastic ______ PE - the energy stored in a spring when work is done on it to stretch or compress it PEs = (½)kx 2 Ex. A spring with a spring constant of 370 N/m is stretched a distance 6. 4 x 10 -2 m. How much elastic PE will be stored in the spring? PEs = (½)kx 2 = (0. 5)( 370 N/m)(6. 4 x 10 -2 m)2 = 0. 76 (N/m)(m 2) = 0. 76 Nm = 0. 76 J How much work was done to stretch the spring by this amount? W = DPE = 0. 76 J

PEs = (½)kx 2 What happens to PEs when you double x? PES prop. to square The PEs quadruples. When you triple x? 9 x more PEs. Ex: The elastic PE stored in a spring is 0. 70 J when it is stretched 0. 010 cm. If the same spring is stretched 0. 030 cm, how much PE will then be stored in it? x changes from 0. 010 to 0. 030 it triples 9 x more PEs 9 x (0. 70 J) = 6. 3 J x

Ex: Plot F vs. x for an ideal spring F F x k = x What does the grey area represent? (½)x. F area = (½)bh = = (½)x(kx) (½)kx 2 = = PEs work doneon the spring, and It represents the ______ energy stored the ___________ in it. W = DPEs

Ex: By looking at the area, you can see why the PE is square of the displacement x: proportional to the ______ F F x k = 1 x 2 x 3 x x 4 A 1 x 1 triangle ____ A area = ____ A so PE = ____ 1 2 3 2 x 4 triangles ____ 4 A area = ____ 4 A so PE = ____ 3 x 9 triangles ____ 9 A area = ____ 9 A so PE = ____

One last warning: deforms If a spring is stretched too much, it ______ permanently, and Hooke's Law (Fs = kx ) _____is no longer valid. _______ Ex: Which of the graphs below shows a spring that obeys Hooke's Law? F F NO A/ C/ NO x F B/ S E Y x x F D/ NO S E Y x YES and NO