Spring Force

Compression and Extension  It takes force to press a spring together.  More compression requires stronger force.  It takes force to extend a spring.  More extension requires stronger force.

Spring Constant  The distance a spring moves is proportional to the force applied.  The ratio of the force to the distance is the spring constant (k). x F

Hooke’s Law  The force from the spring attempts to restore the original length.  This is sometimes called Hooke’s law.  The distance x is the displacement from the natural length, L. L+ x L - x L

Spring Constant  Young’s modulus is a from a linear relation like Hooke’s law. Young’s modulus describes a type of material.Young’s modulus describes a type of material. The spring constant describes an object.The spring constant describes an object.  Y and k are related. LL F

Position-dependent Force  The spring force increases in magnitude with increasing displacement.  The slope of the line is the spring constant. F xx stiff spring soft spring

Scales  One common use for a spring is to measure weight.  The displacement of the spring measures the mass. -y F g = -mg F s = -k(-y)

Stiff Springs  Two spring scales measure the same mass, 200 g. One stretches 8.0 cm and the other stretches 1.0 cm.  What are the spring constants for the two springs?  The spring force balances the force from gravity: F = 0 = (- mg ) + (- kx ).  Solve for k = mg/ (– x ).  x is negative.  Substitute values:  (0.20 kg)(9.8 m/s 2 )/(0.080 m) = 25 N/m.  (0.20 kg)(9.8 m/s 2 )/(0.010 m) = 2.0 x 10 2 N/m.

Restoring Force in Motion  When springs are in motion they oscillate.  The motion has a period, T.  Is it like the period of circular motion? next