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Jet and conveyor problems
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Force required when mass is added or removed continuously.
When material is continuously added, e.g., sand falling onto a moving belt, the force needed to maintain speed v is F = v dm/dt, and half the power goes into heat.
Sand dropping at 2 kg/s on a belt at 3 m/s needs 6 N.
Apply F = dp/dt to the belt plus new material.
In more detail
Problems involving jets and conveyors apply momentum conservation to the material that enters or leaves a system. The momentum of that material must be included in the equations.
Real-world uses
- Water jets and garden hoses exert forces on nozzles from the momentum of the water.
- Sand conveyors gain mass as material is added, which changes the required force.
- A chute that feeds grain into a moving truck gives the truck extra mass, so the engine must supply more force to keep the speed.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I include the material?
Track the momentum of the material entering or leaving the system at each instant.
Why is it different from a normal collision?
Because the mass of the system changes continuously.
Why does mass added to a moving body need extra force?
The body's momentum grows as its mass grows, and the force must supply that extra momentum change.
Related topics in Momentum & Collisions
Variable mass: rocket equation · Thrust · Multi-stage rockets · Angular momentum · Conservation of angular momentum · Ice-skater spin