Statics · free game
Counterweight Crane
Slide the counterweight so the resultant of every weight stays inside the outrigger base. One control, one equation.
The hook load grows as the rope takes up — walk the counterweight out to match it.
Counterweight d0.25 m
- Simple definition
- A body stays put when its forces and its turning effects both cancel, which lands the resultant inside its base.
- Example
- A 4 t counterweight 2.8 m behind the mast balances a 1.6 t load 7 m out, so the crane does not tip.
How the physics works
Taking moments about the mast, the counterweight turns the rig back with W_c·d while the jib, the ice and the hook turn it forward. The readout is that sum, live.
Divide the net moment by the total weight and you get the line of action of the single equivalent force — the same weighted average that locates a centre of mass. The rig stands only while that line falls between the pads.
The jib carries its own weight uniformly, so it becomes one force at its centroid. The ice thickens towards the tip, so its resultant sits two thirds of the way out — much further than a uniform strip of the same peak, which is why lift 03 bites.
Take moments about the rear pad and one unknown disappears; ΣF_y = 0 then hands you R_rear = ΣW − R_front. The bars on the pads are those two numbers drawn to scale.
While the rope takes up, W_p climbs from zero. While the trolley runs out, a grows. Both make the balancing distance a function of time, so a correct answer at t = 0 is wrong two seconds later.
Balancing the mast is not balancing the base. When the front leg is shorter than the rear one, the safest lift leaves a deliberate backward moment rather than a zero one.