Category: Elastics

Spry Springs

This is a challenge about springs.

Say we have a few springs. They each have their nominal lengths and their spring constants. We wrap them all around a rail, with sliding spacers in between. In this way we have created a larger spring. We are challenged to find a way to compute the characteristics of this spring–importantly, the spring constant–in a general way. This should be a short, fun activity! But really, it’s actually a surprisingly interesting and challenging task. For a simpler task, try only the first example below. To practice your math after finding a formula, try all of the examples below!

Spring ConstantsNominal Lengths
2N/m, 5N/m2m, 1m
3N/m, 4N/m, 3N/m3m, .5m, 4.5m
1N/m, 2N/m, 8N/m4m, 1m, 3m
.5N/m, 1N/m, 1N/m2m, 3m, 10m
solution

Esoteric Elastics

This challenge is about elastics.

We begin with 2 elastics. Elastic A has nominal length 3 centimetres and spring constant 2 kilograms per square second. This notation seems unfamiliar but remember that we multiply by the displacement, in metres, and get a force, in mkg/s2. Elastic B has nominal length 5 centimetres and spring constant 3 kg/s2. The long elastic it threaded through the small one. The 2 ends of the long elastic are folded together. 2 identical rods are threaded through them. They are then pulled apart. The elastics are held in place at equal heights on the rods so they cannot move up or down. They are at equal heights and can rotate frictionlessly. The rods are then fastened to the surface of the earth some distance apart. The rods do not sway, bend, or in any way stop being vertical. A weight is placed halfway between the 2 rods, resting on the elastics. It weighs 1 gram. The weight does not cause any friction on the elastics. Elastics A and B are stretched to equal lengths. How far apart are the rods?

SOLUTION

Baffling Bungee

This week’s science challenge requires the principals of physics and chemistry to solve.

Diagram of Baffling Bungee Jump.

Bob the bungee jumper goes bungee jumping over water on a cord made out of C5H8. The thickness of the rope is 3 centimetres. It’s natural length, the length it will have if not acted on by a force, is 1 metre. Bob starts the jump with a velocity vector with a magnitude of 1 metre per second and an angle of 45°. The lowest point of the jump is 1 metre above the water. Afterwards, the cord pulls Bob up to a stable position higher above the water. The challenge is to calculate the elasticity of the rope to figure out exactly how high.

Solution