Задание 4 — Водопад зажигает свет

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⏸ 05:00

Level 1

Task 4 — "The Waterfall Lights Up the Camp"

Situation. As darkness falls, a snow leopard creeps closer and closer to the camp — its growls and rustling can be heard nearby. The only defense is bright light: predators are afraid of fire and electric lamps.

Deep in the island, the team found a small waterfall. The squad's engineer suggested: set up a water wheel, connect it to a coil of copper wire between pieces of magnetite — and you get a generator. Falling water turns the wheel, the wheel turns the coil, the coil produces current.

The waterfall's height is h = 3 m. Three lamps were connected to the generator. The lamps' combined power is P = 12 W. The efficiency of the system (wheel + generator) is η = 20%. The night lasts 8 hours.

Given:

P_lamps = 12 W
η = 0.20
h = 3 m
t = 8 h = 28,800 s
ρ = 1,000 kg/m³
g = 10 N/kg

Goal: light the lamps in time to scare off the snow leopard and save the camp

Check

η = P_lampsP_water η — system efficiency
P_lamps — lamp power (W)
P_water — waterfall power (W)

P_water = m × g × ht P_water — water power (W)
m — water mass (kg)
g — free-fall acceleration (N/kg)
h — waterfall height (m)
t — time (s)

A = P_lamps × t A — energy (J)
P_lamps — lamp power (W)
t — time (s)

How does current arise? Gravity pulls the water down the waterfall → the water falls onto the water wheel's blades → the wheel starts spinning → the wheel is connected to the coil through an axle → the coil spins → current arises.

How does the coil's rotation produce current? Step 1 — The coil has free electrons:
The coil is made of copper wire. In copper, electrons aren't rigidly bound to atoms — they can move freely inside the wire.

Step 2 — The magnetic field acts on moving charges:
The magnetite creates a magnetic field. When the coil spins, the electrons inside the wire move together with it through this field.
By Ampère's law, the magnetic field pushes moving charges along the wire.

Step 3 — Electrons start moving along the wire:
The magnetic field pushes the electrons not across the wire, but along it — from one end of the coil to the other.
The movement of electrons along the wire is exactly what electric current is.

Step 4 — The coil keeps spinning continuously:
As long as the coil keeps spinning, the electrons keep getting pushed → the current flows continuously.

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🏆 CONGRATULATIONS!
BONUS AWARDED — 5 POINTS! 🎁

Askar S.