Vada tests a landing-leg spring from her camera drone, holding it at a series of extensions and recording the force each time.
Three readings is a list. Is there a way to see the spring's whole behavior at a glance, and read off its spring constant?
The drone spring's three holds in numbers: 5.0 N at 0.05 m, 10 N at 0.10 m, 20 N at 0.20 m.
Here is the force-extension graph of those holds: extension on the x-axis in m, force on the y-axis in N, one dot per hold.
The dots line up: a straight line through the origin. Doubling the extension doubles the force, exactly Hooke's law.
Now read the spring constant from the line. Pick a point on it: 20 N at 0.20 m.
k is the force per meter of extension: k = 20 ÷ 0.20 = 100, so k = 100 N/m.
The force-extension graph shown carries a spring's straight line through the origin. What does the line's slope give?
A steeper line means more newtons per meter: a stiffer spring. A shallower line means a softer one.
Read the slope from a point far up the line, where the gridlines are easy to read; any point on the line gives the same k.
A force-extension graph for a drawer spring shows a straight line through the origin, passing through 12 N at 0.30 m of extension. Calculate the spring constant.
Write down the values, read from the line:
F = 12 N at x = 0.30 m
Write down the relation:
k = F ÷ x
Substitute in the values, and calculate:
k = 12 ÷ 0.30 = 40
The spring constant is 40 N/m.
The force-extension graph shown has a straight line through the origin passing through 15 N at 0.10 m of extension. Enter the spring constant, in N/m.
On one grid, a door spring's line reaches 30 N at 0.10 m of extension, and a toy spring's line reaches 30 N at 0.60 m. Calculate both spring constants.
Door spring, read from its line: k = 30 ÷ 0.10 = 300, so 300 N/m.
Toy spring, read from its line: k = 30 ÷ 0.60 = 50, so 50 N/m.
The door spring's line is the steeper one: more newtons per meter.
The door spring's k is 300 N/m; the toy spring's is 50 N/m.
The force-extension graph shown has a straight line through the origin passing through 14 N at 0.40 m of extension. Enter the spring constant, in N/m.
The force-extension graph shown for a camper-van step spring is a straight line through the origin passing through 240 N at 0.30 m of extension. Enter the spring constant, in N/m.
The graph shown carries two straight lines through the origin: a ski-rack spring's line reaching 60 N at 0.20 m of extension, and a bed-frame spring's line reaching 60 N at 0.50 m. Which spring is stiffer?
A physics class tests a resistance-machine spring. The force-extension graph shown is a straight line through the origin passing through 42 N at 0.15 m of extension. Enter the spring constant, in N/m.