angled surface to ball connection

[greycloud]

Hi all

I'm having this confusion about a certain system where I'm not sure how it would act in either of two ways.

Basically system is a weight of one Kilogram falling down and interacting with a body of neglegible weight. the two bodies connect together and start travelling down at the same speed. the weight connects to the weightless body through a circle touching an angled surface of 45 degrees which in turn is connected to the weightless body.

I attached a drawing where the weight is labeled as A while the body of negligable weight is labeled as B.

now given that they are travelling together at same speed I can't decide what is downward force applied by Body A on Body B. is it equal to full weight of A since they are falling together?

or is it half of the weight since they are interacting at a 45 degrees angle?

I highly appreciate your response as I'm scratching my head by now.

Just for clarification: the two lines around the bodies in the drawing are meant to represent rails to guide motion.

 

[JohnRBaker]

If both items 'A' and 'B' are constrained, by the rails, so that they can only move in the same direction, vertically, then it really doesn't make any difference what the face-angle of item 'B' is. The full weight of 'A' will be applied to 'B'.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

 

[hydtools]

The vertical force will always be the weight of A. The angle on B will cause sideward force to be reacted to by the rails for both A and B.

Ted

 

[handleman]

If they are indeed "falling together" the B will not be experiencing the weight of A. If B experienced the weight of A, that means that B is pushing also up on A with a force equal to the force pulling down on it due its own weight, and they'll soon grind to a halt. The vertical component of the force at the interface will equal the friction force of the rails and any wind resistance. If the corresponding horizontal component of the force tends to put the bearings in a bind and increases friction and therefore resistance, then you'll have an iterative process of finding vertical force, finding the horizontal component and therefore the increased friction, and finding a new vertical force. It'll probably converge unless your bearings suck.

 

[greycloud]

Thanks for answering me back. However, why is the force on B the full weight?

lets assume that Weight A just touched body B and they are about to start moving.

 

[hydtools]

Conservation of momentum principle and internal forces are equal and opposite. Neglecting friction.

Ted

 

[chicopee]

Hytools, you can not neglect friction because there will be a side thrust from "A" falling in "B" inclined surface. Friction will be from the roller guides of "A" and "B" bearings and the rolling friction of the rollers onto the rolling surface.

 

[chicopee]

Hytools, ideally, since "B" has no weight then it has no mass therefore conservation of momentum involving the mass of "B' will not apply unless the event took place in space and "A" would not be falling but forced to move from some external force such as compressed spring just released. Without friction the combined "A" and "B" would have the same velocity that "A" had upon impact.

 

[chicopee]

Oops"... unless the event took place in space..." should be rephrased "..if the event took place in space..."

 

[hydtools]

Momentum of zero mass B will be zero. When the masses combine the momentum of the combined masses will be that of mass A before combining. Mass B contribution to the combined mass momentum will be zero. If you add friction, then mass B reacts as a massless body but now friction forces come into play, both for A and B. The reaction of B to A is then that resistance of B friction. The excess force between A and B keeps B moving. If the friction on B were high enough both masses would not move after contact and the force on B would be the weight of A.

Ted

 

[greycloud]

Honeslty I can't get your answer.

opposite forces are equal yes but my main question is wether weight will be divided between two planes or not. one answer I'm thinking about is that weight is acting in same direction of motion meaning there is no angle between force application and motion of body its applied on thus full weight acting on B. Is that what you mean?

how can the weight be applied fully to body B while also exerting reaction on the rails at same time?

 

[77JQX]

The vertical force on B from A is equal to the weight of A less the frictional resistance (in the upward direction) caused by the connection of A to the rails.