Hooke's Law & Spring Constant
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flagWhat you'll discover
- arrow_forwardState Hooke’s law and its limit of proportionality
- arrow_forwardMeasure extension with a pointer and scale for increasing loads
- arrow_forwardDetermine k from the slope of an F-x graph
- arrow_forwardPredict and verify k for springs in series and parallel
F = kx, within limits
Hooke’s law says the restoring force of a spring is proportional to its extension: F = kx. The spring constant k (N/m) is the stiffness — how many newtons stretch it one metre. The law holds only up to the elastic limit; stretch a spring too far and it deforms permanently, and your graph bends over.
When a mass m hangs in equilibrium, the spring force balances gravity, so kx = mg. Each 50 g (0.49 N) you add stretches our k = 25 N/m spring by about 2 cm — comfortably readable on a mm scale.
Procedure: load, settle, read
Note the pointer’s zero reading with no load. Add slotted masses one at a time, let the oscillation die out, and read the pointer against the mm scale at eye level. Extension x = reading − zero reading. Take readings while loading AND unloading: if the two disagree, the spring passed its elastic limit and the run must be repeated with smaller loads.
Plot F = mg on the y-axis versus x on the x-axis. A best-fit straight line through the origin confirms Hooke’s law, and its slope is k. Using the graph instead of one reading averages out small reading errors — the same trick as the pendulum experiment.
Series and parallel springs
Two springs in SERIES share the same force but add extensions, so 1/k = 1/k₁ + 1/k₂ — the combination is softer than either spring. Two springs in PARALLEL share the load at the same extension, so k = k₁ + k₂ — stiffer. With k₁ = 25 and k₂ = 40 N/m you get 15.4 N/m in series and 65 N/m in parallel; the simulation lets you verify both numbers.
Error sources: pointer parallax (read square-on), the spring oscillating when you read, zero drift if the spring sags permanently, and forgetting that the hanger itself has mass. These exact points are the expected "precautions" list in the NEB practical copy.