Measuring the Spring Constant – an Introduction
A common technique used to evaluate the spring constant is illustrated in Figure 1.The spring
is hung vertically and a body of mass m is attached to the lower end of the spring. The spring
stretches a distance of d from its initial position under the action of the load (stretching force)
m*g. Because the spring force is upward, it must balance the weight, m*g, downward when
the system is in rest. In this case, we apply Hooke’s Law to give:
Fs … spring force
k … spring constant
g ... acceleration of free fall
m … mass
d … elongation
Fs = k*d = m*g
k = m*g / d
Figure 1
d
m
F = k*d
Figure1: Determining the spring constant.
The elongation, d, of the spring is due to
the suspended weight, m*g. Because the
upward spring forces balance the weight
when the system is in equilibrium, it
follows that k = m*g / d
m*g
Quicklab: Measure the Spring Constant
The spring is stretched in stages by hanging masses from one end. Each time the load is
changed, the elongation of the spring is measured. The elongation is the difference between
the stretched length of the spring and its original unstretched length.
The readings can be used to plot a graph load versus elongation.
1.) Write the readings in a table (load m*g in N and elongation d in m). The load is calculated
by multiplying the mass [kg] with g = 9.81m/s² (the acceleration of free fall) m*g.
Reading #
1
2
3
4
5
Weight: m*g [N]
Elongation: d[m]
2.) Plot a graph of load versus elongation
m*g [N]
d [m]
3.) Determine the slope of the line through the data points. The spring constant may be
determined according to k = m*g / d.
Words
spring
spring constant
to evaluate
to determine
elongation
due to
suspended
to balance
weight
equilibrium
initial
load
Hooke’s Law
Feder
Federkonstante
berechnen, auswerten
bestimmen
Auslenkung
verursacht durch
hängend
im Gleichgewicht halten
Gewicht
Gleichgewicht, Balance
anfänglich
Last
Hooke’sches Gesetz