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Understanding the Scenario
In this scenario, a train is moving at a constant velocity of 10 m/s while rain is falling vertically with zero horizontal velocity. The rain adds mass to the train at a rate of 5 kg/s. To maintain its velocity, the train's engine must counteract the effects of this added mass.
Key Concepts
- Conservation of Momentum: When the rain collects in the train, it effectively increases the train's mass, requiring additional force to maintain its velocity.
- Force Calculation: The additional force needed can be calculated using the principle of momentum change.
Applying the Principles
- Mass Addition: The rain adds 5 kg of mass per second. Therefore, the train's mass increases by this amount continuously.
- Momentum Change: The momentum change per second due to the added mass (5 kg) moving at the train's speed (10 m/s) is given by:
Change in momentum = mass flow rate × velocity
= 5 kg/s × 10 m/s = 50 kg·m/s
- Force Requirement: According to Newton’s second law, the force required to maintain this momentum change is equal to the rate of change of momentum.
Conclusion
- Additional Force: The additional force required by the engine to maintain the same velocity of the train, considering the mass being added by the rain, is 50 N (Newtons).
This analysis shows how the train's engine must compensate for the increased mass due to rain to sustain its uniform motion.
And open carriage in a good strain is moving with a uniform velocity o...
CHANGE IN MOMENTUM= mass flow rate × velocity
∆p=5×10
∆p=50
ACCORDING TO NEWTON'S SECOND LAW : rate of change of momentum is directly proportional to the applied force .
SO,
required additional force is 50N.
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