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In this question momentum is conserved along X' direction. But there is a component of mg along the plane which means that there is external force in X' direction. So how is conservation of momentum applied here??

Qmechanic
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Dhruv Bhardwaj
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3 Answers3

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Gravity is a non impulsive force. it means it takes enough time to cause action and does not change momentum in an instant. So in time just before and after collision, momentum is conserved and gravity is neglected for such small time. it will work in all horizontal collisions likeenter image description here

BUT

if ball does not strike horizontally, then Normal and/or friction are impulsive so you cannot conserve momentum even for short durations Ball not striking horizontally

Hemant Kumar
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For the momentum conservation law to be true you must include all interacting parts. You cannot have an external force adding or subtracting momentum out of your system - then obviously momentum isn't conserved for that system. But it is conserved overall, if you included the external part that causes the external force (the planet Earth) in your system.

Compare this with the similarly stated energy conservation law. Energy is always conserved - never destroyed nor brought into existence out of thin air. But obviously, if I define a system that is heated from the outside, then energy is added to my system. Then energy conservation is not fulfilled for my system.

Conservation laws must include all interacting parts to be true.

Steeven
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The momentum is conserved in x direction because there is no external force acting on the center of mass of the ball wedge system, you are correct that the mg component is there along the horizontal but the same force will be applied on the wedge too. Thats why The Momentum is conserved in X direction

Kushagra
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  • In Hemant Kumar answer , the second part ,Momentum Will Be Conserved In Horizontal Direction always remember If there is no external force acting in any direction then momentum will Be Conserved In that direction no matter what, if you throw ball in any direction it's momentum will be conserved in X direction in this example – Kushagra Feb 10 '22 at 17:57
  • No in second part of my answer momentum can't be conserved in any direction(even in x-axis). Since normal force becomes impulsive in y direction it will make friction impulsive in horizontal direction. However in first part friction is non impulsive and can be neglected. – Hemant Kumar Jun 10 '22 at 04:57