Sometimes the force is known and the extension is the unknown, or the spring constant is. A spring with k = 250 N/m is held with a 50 N force. How far does it stretch?
Estimate first. A full meter of extension would need 250 N, and only 50 N is applied: a fifth of a meter.
Exactly: 50 ÷ 250 = 0.2, so the extension is 0.2 m.
One rearrangement of F = kx says that divide in general, and a second finds the spring constant.
Start from the equation you know: F = kx.
Make x the subject: divide both sides by k.
That gives x = F ÷ k.
Make k the subject: divide the force by the extension.
That gives k = F ÷ x.
A spring with k = 250 N/m is held stretched with a 50 N force. Calculate its extension.
Write down the values:
F = 50 N, k = 250 N/m, x = ?
Write down the equation and make x the subject:
x = F ÷ k
Substitute in the values, and calculate:
x = 50 ÷ 250 = 0.2
The extension is 0.2 m.
A luggage-rack spring is held at 0.30 m of extension by a 45 N force. Calculate its spring constant.
Write down the values:
F = 45 N, x = 0.30 m, k = ?
Write down the equation and make k the subject:
k = F ÷ x
Substitute in the values, and calculate:
k = 45 ÷ 0.30 = 150
The spring constant is 150 N/m.
The forward direction works as before: k = 40 N/m at 0.50 m of extension needs 40 × 0.50 = 20, so 20 N.
The questions below mix all three directions; every value arrives already in the unit the answer wants.
A screen-door spring with k = 120 N/m is held open with a 30 N force. Enter its extension, in m.
A keyboard key's spring is held at 0.0040 m of compression by a 2.0 N force. Enter its spring constant, in N/m.
A mattress coil with k = 1800 N/m is squeezed 0.020 m. Enter the force needed, in N.
A spring scale's spring has k = 400 N/m. A steady 64 N load holds it stretched. Enter the extension, in m.
A bike-suspension spring with k = 5000 N/m is squeezed 0.040 m over a curb. Enter the force that squeeze needs, in N.
A clip spring is held at 0.025 m of extension by a 7.5 N force. Enter its spring constant, in N/m.
A trampoline spring with k = 2400 N/m stretches as Yael lands. Enter the force needed to hold it at 0.045 m of extension, in N.
A hand-exerciser spring has k = 600 N/m. Wells squeezes its handles with a steady 90 N force. Enter the spring's compression, in m.
During a quality test, a garage-door spring holds 0.35 m of extension under a 77 N load. Enter its spring constant, in N/m.