Spring Stretch Game

About Stretch

In Stretch a spring hangs from a bracket with a block attached. The block shows its mass in kilograms and the spring is labeled with its stiffness, written as k in newtons per meter. You slide to the number of centimeters you expect the spring to stretch under the block.

It is a physics problem, but you are not meant to solve it on paper. The idea is to develop a feeling for how a stiffness and a load combine: a stiff spring barely moves, a soft one sags, and doubling the weight doubles the stretch. The slider is logarithmic because answers range from half a centimeter to more than a meter.

How to play

1. Read the stiffness k and the mass on the block. Gravity is 9.8 meters per second squared.
2. Estimate the weight of the block in newtons. One kilogram weighs about 10 newtons.
3. Divide that force by the stiffness to get the stretch in meters, then think in centimeters. A 1 kg block on a 1000 N/m spring stretches 1 cm.
4. Move the slider to your estimate and lock in. The spring then stretches to show the truth.

A spring of known stiffness carries a weight. Slide to how many centimetres it stretches. A stiffer spring stretches less, a heavier weight stretches it more. The slider is logarithmic.

How scoring works

The score is based on the ratio between your answer and the true stretch, on a logarithmic scale, so being twice too high costs the same as being twice too low. A perfect answer scores 100, and the score falls to 0 when you are off by a factor of about 2.6 on level 1, or by about 1.8 on level 10.

The time limit is 16 seconds on level 1 and 12 seconds on level 10. The stretch is always between 0.5 cm and 100 cm. On the first levels the stiffness and masses come from short lists of round numbers, so that you can find the answer by simple arithmetic.

What it trains

Stretch trains proportional reasoning with two inputs, the kind of thinking behind rubber bands, trampolines, car suspension, weighing scales and even the way a diving board bends. It teaches you to treat stiffness as a conversion factor between force and displacement.

It is also a gentle practice in order-of-magnitude arithmetic. You do not need the third digit; knowing whether the answer is closer to 1 cm, 10 cm or 100 cm is already worth most of the points.

Tips for a higher score

• Memorize the anchor: a 1 kg mass pulls with about 10 newtons, and 10 newtons on 1000 N/m is 1 cm. Everything else is a multiplication or division of that anchor.
• Scale from the anchor. A mass of 5 kg is five times as heavy, and a stiffness of 200 N/m is five times softer, so the stretch is 25 times bigger, about 25 cm.
• Check the order of magnitude before the details: is it millimeters, centimeters or a meter? The logarithmic slider rewards that first step.
• Remember that a softer spring gives a bigger stretch. Players often move the slider the wrong way when the stiffness is the unusual number.
• Use the picture: the spring in the drawing stretches in proportion to the answer, so you can compare your feeling with the result.

The idea behind it

Hooke's law, published by Robert Hooke in 1678 as the Latin phrase 'ut tensio, sic vis', states that the force needed to stretch a spring is proportional to the extension: F equals k times x. It holds as long as the spring is not stretched beyond its elastic limit.

A real spring also has a mass of its own and can oscillate, and very long stretches can bend or permanently deform it. The game assumes an ideal, massless spring that stays within the elastic range, which is a good approximation for the numbers used here.

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