Video Transcript
The amount of force it takes to
compress a spring can be approximated using the formula 𝐹 equals 𝑘𝑥, where 𝐹 is
the force in newtons, 𝑘 is the spring constant in newtons per millimeter, and 𝑥 is
the displacement or the change in the length of the spring in millimeters. The given table shows the spring
constants for seven different types of springs. The relationship between the value
of the extension for one of the springs is plotted in the figure shown, with the
force represented on the 𝑦-axis and the compression on the 𝑥-axis. Which type of spring does this plot
refer to?
Before we do anything else, let’s
go ahead and label this graph. The 𝑥-axis is the compression, a
measure of millimeters. The 𝑦-axis is the measurement of
force, which is measured in newtons. We know that the force equals the
spring constant times a compression 𝑥. And if we divide both sides of this
equation by 𝑥, we can say that the spring constant 𝑘 equals the force divided by
the compression 𝑥. This is important because in order
for us to identify which type of spring is shown on the graph, we’ll need to find
out which spring constant is shown.
On this graph, we have the
coordinates of 𝑥 being the compression and 𝑦 being the force. On our 𝑥𝑦-axis, we’re dealing
with the values 𝑥 and 𝐹. If we look at the first point, we
have a point at four, 80. This is a compression of four
millimeters and a force of 80 newtons. We also see a point at eight, 160,
a compression of eight millimeters and a force of 160 newtons.
To calculate the constant, we take
those 80 newtons and divide it by four millimeters. And we could divide 160 newtons by
eight millimeters. 80 divided by four is 20. The first point is 20 newtons per
millimeter. And 160 divided by eight is also 20
newtons per millimeter. You can see this on the graph if
you go up 20 newtons in force, you’ll go to the right one millimeter, up 20 newtons
and right one millimeter. And only one of our springs has
this relationship between force and compression. The type A spring has a constant of
20 newtons per millimeter. And so, this is a graph of type
A.
