Lab work No.7, Task No.23 · goals 8.4.2.12, 8.4.2.14, 8.4.2.15
Situation. Deep in the island, the team found a small waterfall of height h = 3 m. The team's engineer suggested: install a water wheel, connect it to a coil of copper wire between pieces of magnetite — this makes a generator. The falling water spins the wheel, the wheel spins the coil, the coil produces current.
The generator was connected to 4 carbon arc lamps. Total lamp power P = 12 W. System efficiency (wheel + generator) η = 20%. The night lasts 8 hours.
a) What power must the waterfall deliver for the lamps to stay lit?
b) What water flow rate is needed — how many liters per second?
c) How much energy will the lamps consume over the night?
Given:
Plamps = 12 W
η = 0.20
h = 3 m
t = 8 h = 28,800 s
ρ = 1,000 kg/m³
g = 10 N/kg
Find: Pwater, V (L/s), A
η = PlampsPwaterη — system efficiency Plamps — lamp power (W) Pwater — waterfall power (W)
Pwater = m × g × htPwater — water power (W) m — water mass (kg) g — free-fall acceleration (N/kg) h — waterfall height (m) t — time (s)
A = Plamps × tA — energy (J) Plamps — 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.