36:38 I understand that the centripetal force effectively acts inward but in this model surely it should be modelled as acting outwards? This would allow you to balance the equations in order to find the required velocity.
Every force has an equal and opposite reaction and they are balanced. That is Newton's third law, I think. In this case the weight component is trying to pull the marble outwards and the centripetal force is supplied by the horizontal component of the normal force exerted by the surface of the cone.
No . The centripetal force is a centre seeking force, so it will always point into the circle. In this model, the centripetal force is the horizontal component of the normal force, and by resolving vertically you can find an expression of N (mg / sin α) then substitute it into the expression of the centripetal force, and you should get that the centripetal force = mg cot α. From there you can equate that to the equation for centripetal force (mv^2)/r [note that r = H tan α] and you get that v = √HG. Now you have an expression for the velocity in terms of the height of the cone, you can just equate it to the expression for velocity at the end of the ramp, so √HG = √2gh and square both sides and rearrange to get that the vertical height (h) of the ramp should be H/2 so that the marble has enough velocity to move in a horizontal circle.
The centripetal force is a force required for circular motion. Any force that acts inwards towards the center of the circle can ACT as the centripetal force. The CENTRIFUGAL force is the pseudo force corresponding to the centripetal force, which only exists in the frame of the rotating body. So, this will act ouwards. For this problem you can do one of 2 things: 1) Find the net force towards the center and say that it PROVIDES the necessary centripetal force, thus you can equate them. 2) Shift to the marble's frame- here obviously the marble is at rest and undergoes no acceleration, so now you can say that the net force towards the center is balanced by the outwards CENTRIFUGAL force. Of course, they both give the same answer.
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36:38 I understand that the centripetal force effectively acts inward but in this model surely it should be modelled as acting outwards? This would allow you to balance the equations in order to find the required velocity.
Every force has an equal and opposite reaction and they are balanced. That is Newton's third law, I think. In this case the weight component is trying to pull the marble outwards and the centripetal force is supplied by the horizontal component of the normal force exerted by the surface of the cone.
No . The centripetal force is a centre seeking force, so it will always point into the circle. In this model, the centripetal force is the horizontal component of the normal force, and by resolving vertically you can find an expression of N (mg / sin α) then substitute it into the expression of the centripetal force, and you should get that the centripetal force = mg cot α. From there you can equate that to the equation for centripetal force (mv^2)/r [note that r = H tan α] and you get that v = √HG. Now you have an expression for the velocity in terms of the height of the cone, you can just equate it to the expression for velocity at the end of the ramp, so √HG = √2gh and square both sides and rearrange to get that the vertical height (h) of the ramp should be H/2 so that the marble has enough velocity to move in a horizontal circle.
The centripetal force is a force required for circular motion. Any force that acts inwards towards the center of the circle can ACT as the centripetal force.
The CENTRIFUGAL force is the pseudo force corresponding to the centripetal force, which only exists in the frame of the rotating body. So, this will act ouwards.
For this problem you can do one of 2 things:
1) Find the net force towards the center and say that it PROVIDES the necessary centripetal force, thus you can equate them.
2) Shift to the marble's frame- here obviously the marble is at rest and undergoes no acceleration, so now you can say that the net force towards the center is balanced by the outwards CENTRIFUGAL force.
Of course, they both give the same answer.
Does anyone have the final solution for the marble problem?
i got H/2