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Gravel is dropped vertically onto a horizontal conveyor belt at a constant rate of 500 g s ⁻¹ . If the conveyor belt moves at a constant speed of 7.2 km h ⁻¹ , the extra force required to keep the belt moving at this speed is :

Options

  1. A3.6 N
  2. B1000 N
  3. C3600 N
  4. D1 N

Correct answer

D. 1 N

Step-by-step solution

The rate of mass falling on the belt is dm dt = 500 g s ⁻¹ = 0.5 kg s ⁻¹ . The velocity of the conveyor belt is v = 7.2 km h ⁻¹ = 7.2 5 18 m s ⁻¹ = 2 m s ⁻¹ . The extra force required to keep the belt moving is equal to the rate of change of momentum of the falling gravel in the horizontal direction. F = v dm dt F = 2 0.5 = 1 N . Answer: 1 N

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