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  By Newton’s law of reaction the spring pushes back with an equal and opposite force.  This is sometimes called Hooke’s law.

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)

Work with Variable Force  The force applied to a spring increases as the distance increases.  The work must be calculated over each separate interval.  The work increases over a small interval as the force increases. F xx

Area under a Curve  Separate the total distance into steps  x.  The product within a small step is the area of a rectangle F  x.  The total equals the area between the curve and the x axis. F xx

Work on a Spring  For the spring force the force makes a straight line.  The area under the line is the area of a triangle. F=kx x

Integral Form of Work  The work can be found by taking the area under any force curve.  This technique in calculus is the integral. next F x