What it does
A spring squeezed by a distance x stores energy ½ k x², where k is its stiffness in newtons per metre. When you let go, that energy pushes a block, and by the time the block leaves the spring it has kinetic energy ½ m v². With no friction the two are equal, so the launch speed is v = x √(k/m).
On a rough floor some of the energy is used up as heat. The spring must first beat friction, then it loses μ m g x while pushing, and after the block leaves it slides until friction stops it. This is a teaching model: the block is only pushed, not fixed to the spring. To see how a spring force varies, try spring combinations, and for the idea of work done by a changing force see variable force work.
How to use it
- Set the stiffness k, the compression x and the block’s mass m.
- Leave friction μ at 0 for a smooth floor, or raise it.
- Press Release and watch the block; Reset puts it back.
- Read the stored energy, the launch speed and the sliding distance under the picture.
What each setting does
- Stiffness k: a stiffer spring stores more energy for the same squeeze.
- Compression x: the energy grows with x squared.
- Mass m: a heavier block ends up slower for the same energy.
- Friction μ: how rough the floor is. Zero means smooth.
Worked example
Take k = 100 N/m, x = 10 cm and m = 0.5 kg on a smooth floor. The stored energy is ½ × 100 × 0.1² = 0.5 J, and v = 0.1 × √(100 ÷ 0.5) = 1.41 m/s.
Now add friction μ = 0.2. Then v² = (100 × 0.01 − 2 × 0.2 × 0.5 × 9.8 × 0.1) ÷ 0.5 = 1.61, so v = 1.27 m/s, and the block slides 1.61 ÷ (2 × 0.2 × 9.8) = 0.41 m before it stops.
FAQs
Why does doubling x quadruple the energy? Because the force grows with x and the distance also grows with x, so the work (area under the force graph) grows with x².
Does the block stay joined to the spring? Not in this model. It leaves where the spring reaches its natural length.
Where the numbers come from
- Elastic potential energy ½kx², the work-energy theorem and kinetic friction μmg: standard Class 11 physics (work, energy and power). g = 9.8 m/s². The picture is fibub's own teaching model.
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Last updated 2026-11-10.