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Hooke's Law — Car Suspension (Worked Example)

Medium
Problem

Each suspension spring of a car has k = 30,000 N/m. When loaded, a spring compresses 0.08 m from its natural length. What force does each spring support?

Given

  • k = 30,000 N/m

  • x = 0.08 m

Find

The spring force F.

Principle

The four springs share the car's weight; per-spring, Hooke's law F = kx gives its load.

Formula

Solution

  1. Write the law: F=kxF = kx

  2. Substitute: F=(30000)(0.08)F = (30000)(0.08)

  3. Multiply: F=2400 NF = 2400\ \mathrm{N}

2400 N

Unit check

N/m × m = N — correct.

What this means physically

2400 N per spring × 4 springs = 9600 N total — supporting roughly a 980 kg car. Suspension springs are stiff because they carry the whole vehicle on small compressions.

Common mistake

Forgetting there are four springs. F = kx gives one spring's force; the car's total weight is shared across all of them.