Two springs hang side by side in a lab: a thick door spring and a thin toy spring. Wells hangs the same 10 N weight from each.
The thin spring stretches 0.20 m; the thick one only 0.05 m. Same force, different stretch. How do we put a number on a spring's stiffness?
The same 10 N stretches the thin spring 0.20 m but the thick spring only 0.05 m.
The thick spring resists more: it needs a greater force to produce the same stretch. It is the stiffer spring.
First, a name for the stretch itself. The stretch, measured from the spring's natural length, is called the extension.
Now the stiffness number. Ask of each spring: how much force would one full meter of extension need?
The thick spring: 10 N produced 0.05 m, so each meter would need 10 ÷ 0.05 = 200, which is 200 N.
The thin spring: 10 ÷ 0.20 = 50, so 50 N for each meter.
So k = 200 N/m means 200 N produces 1 m of extension. A bigger k means a stiffer spring.
The same 6.0 N weight hangs from two springs in turn: a clipboard spring stretching 0.02 m, and a toy spring stretching 0.10 m. Which spring is stiffer?
A luggage-scale spring stretches 0.06 m when a 9.0 N bag hangs from it at rest. Calculate its spring constant.
Write down the values:
force = 9.0 N, extension = 0.06 m, k = ?
Write down the relation:
k = force ÷ extension
Substitute in the values, and calculate:
k = 9.0 ÷ 0.06 = 150
The spring constant is 150 N/m.
A mattress coil is labeled k = 2500 N/m. What does the label say in plain words?
k is the force needed per meter of extension.
A full meter of extension would need 2500 N.
That is a large force for a small spring: the coil is stiff.
Each meter of extension would need 2500 N; the coil is a stiff spring.
A spring stretches 0.25 m when a 30 N weight hangs from it at rest. Enter its spring constant, in N/m.
A screen-door spring stretches 0.30 m when held with a 48 N force. Enter its spring constant, in N/m.
Four bike-suspension springs are labeled 800 N/m, 1200 N/m, 2000 N/m, and 3500 N/m. Which spring is stiffest?
A catalog lists a rowing-machine replacement spring as k = 900 N/m. The gym's worn old spring needed 450 N to hold one full meter of extension. Which spring is stiffer?
Type the two-word name for the force needed per meter of extension.