A spring with k = 60 N/m hangs from a workshop beam. Xenia holds it at 0.10 m of extension with a 6.0 N force.
At 0.20 m it takes 12 N. At 0.30 m, 18 N.
The forces climb in step with the extension: 6.0 N, then 12 N, then 18 N. Is there a rule in the numbers?
Check the pattern against k. This spring's constant is 60 N/m: 60 N for each full meter of extension.
At 0.10 m of extension, a tenth of a meter: 60 × 0.10 = 6.0, so 6.0 N. That matches Xenia's first hold.
At 0.20 m: 60 × 0.20 = 12, so 12 N. At 0.30 m: 60 × 0.30 = 18, so 18 N. All three holds match.
This is Hooke's law: the force needed to stretch or compress a spring is proportional to the extension.
Proportional means the trade is exact. Double the extension, and the force needed doubles. Triple it, and the force triples.
From 0.10 m to 0.20 m, Xenia's extension doubled, and the force went from 6.0 N to 12 N: doubled.
Which relation is Hooke's law for a spring?
Compression works the same way. Squeeze the same spring 0.10 m shorter than its natural length, and holding it there takes the same 6.0 N.
A pogo-stick spring has k = 8000 N/m. Calculate the force needed to compress it by 0.030 m.
Write down the values:
k = 8000 N/m, x = 0.030 m, F = ?
Write down the equation:
F = kx
Substitute in the values, and calculate:
F = 8000 × 0.030 = 240
The compression takes 240 N.
A drawer spring has k = 80 N/m. Enter the force needed to hold it at 0.30 m of extension, in N.
A clipboard spring needs 4.0 N to hold 0.020 m of extension. What force holds 0.040 m?
The extension doubles, from 0.020 m to 0.040 m.
Hooke's law is proportional: double the extension, double the force.
F = 4.0 × 2 = 8.0
Holding 0.040 m takes 8.0 N.
A trampoline spring needs 50 N to hold 0.10 m of extension. The extension is doubled to 0.20 m. What happens to the force needed?
A garage-door spring has k = 350 N/m. Enter the force needed to hold it at 0.20 m of extension, in N.
A pen's spring has k = 400 N/m. Clicking the pen compresses the spring by 0.012 m. Enter the force the click needs, in N.
A spring with k = 150 N/m is held at 0.10 m of extension. Which change doubles the force needed?