Calculating the Weight of a Moving Object Using Momentum and Force

[Eitan Levy]

Homework Statement

A snake with a mass equals to m is placed on a scale. The length of the snake is L. Suddenly the snake starts moving with a constant velocity v₀. What does the weight display at the moment the snake starts moving?

Homework Equations

F=dP/dt

The Attempt at a Solution

First I tried to understand what force the snake is affected by. I think gravity, normal and some force F that causes it to move.
I tried to find the combined force on the snake at that moment. Before it starts moving it has a momentum of 0, and then it has a momentum of mv₀.
So I get this: ∑F=N+F-mg=dP/dt=m*dV/dt
I know what the change in momentum is but I struggle to use to actually find the exact value of ΣF. Could anyone provide some guidance?

Also, I struggle to understand how the length of the snake is relevant to the question.

 

[PeroK]

Well, I don't know what this question is all about. For example, ##v_0## is a speed not a velocity. And normally in physics an instantaneous change in velocity corresponds to an idealised scenario where you cannot analyse the forces.

 

[Eitan Levy]

Well, I don't know what this question is all about. For example, ##v_0## is a speed not a velocity. And normally in physics an instantaneous change in velocity corresponds to an idealised scenario where you cannot analyse the forces.

I need to find what is displayed on the scale the moment the snake starts moving. What you said is the reason I am struggling. The exact way the question is written is: "A snake with a length of L and a mass of m is placed on a scale. At the moment t=0 the snake begins to move upwards with a constant velocity v₀. What will be displayed on the scale when t=0?".

Does that help?

 

[PeroK]

I would move on to another problem.

 

[Eitan Levy]

I would move on to another problem.

That would be quite a problem considering I have to submit the final answer.

 

[DaveE]

This is a very poorly worded question, sorry you have to deal with it.
1) An instantaneous change in velocity requires infinite force.
2) Why a snake, is only part of it moving, as a real snake would? How much of the snake is moving?

If you can't ask for clarification, then maybe you could rewrite the question by making clarifying assumptions and then answer it. Make reasonable assumptions that change the problem as little as possible and communicate them clearly. Try not to do it in a way that insults the instructor (re. his ability to write good exam questions). Then solve it using the techniques the instructor expects you to use.

 

[PeroK]

That would be quite a problem considering I have to submit the final answer.

I suppose you could ask yourself that if something is moving at constant velocity what can you say about that?

 

[Eitan Levy]

This is a very poorly worded question, sorry you have to deal with it.
1) An instantaneous change in velocity requires infinite force.
2) Why a snake, is only part of it moving, as a real snake would? How much of the snake is moving?

If you can't ask for clarification, then maybe you could rewrite the question by making clarifying assumptions and then answer it. Make reasonable assumptions that change the problem as little as possible and communicate them clearly. Try not to do it in a way that insults the instructor (re. his ability to write good exam questions). Then solve it using the techniques the instructor expects you to use.

If that helps I believe only a part of it is moving (At t=0at least).

 

[gneill]

I suspect that this will turn out to be a variation of the "chain falling onto a scale" or "stream of sand falling onto a scale" type question (only in reverse).

Presumably the whole snake does not start moving at once. Perhaps it begins with the head. After this, at a constant rate, more of the snake is being elevated. So there's a dP/dt involved...

 

[Eitan Levy]

I suppose you could ask yourself that if something is moving at constant velocity what can you say about that?

Well the combined force on the snake would be 0. Though I am not sure if it's relevant because this happens when t>0.

 

[Eitan Levy]

I suspect that this will turn out to be a variation of the "chain falling onto a scale" or "stream of sand falling onto a scale" type question (only in reverse).

Presumably the whole snake does not start moving at once. Perhaps it begins with the head. After this, at a constant rate, more of the snake is being elevated. So there's a dP/dt involved...

This analogy helped me a lot actually. I think I understand now.

 

[neilparker62]

Can't we just say the scale reading increases momentarily - the snake has to exert a downward force in order to start moving upward. ?

 

[haruspex]

Can't we just say the scale reading increases momentarily - the snake has to exert a downward force in order to start moving upward. ?

No. E.g. if the whole snake somehow were to spring into the air at speed v₀ in an instant then the force would be infinite.
I would go with @gneill's interpretation.

 

[PeroK]

Okay, so the question should be something like:

A snake charmer places a snake of mass ##m## and length ##L## on a scale and begins to play his magic pungi. At time ##t=0## in response to the mesmerising music the snake begins to uncoil upwards, with its head moving at a constant upward speed of ##v_0## ...

 

[neilparker62]

Okay, so the question should be something like:

A snake charmer places a snake of mass ##m## and length ##L## on a scale and begins to play his magic pungi. At time ##t=0## in response to the mesmerising music the snake begins to uncoil upwards, with its head moving at a constant upward speed of ##v_0## ...

Ok - well in this case perhaps the 'correct' model is of two objects connected by a compressed spring. When the 'spring' releases, conservation of momentum applies and the scale pan experiences an equal and opposite impulse to that applied to (applied by!) the snake.

 

[kuruman]

I think I have an answer to this problem but not without assumptions. We are asked to find the "weight display at the moment the snake starts moving". Question: Is this moment before or after the snake reaches speed v0? If before, we need to know the details of how the snake accelerates from v = 0 to v = v₀. My assumption is that the snake reaches constant velocity v₀ instantaneously and that we are asked to find the reading on the scale when the snake's head has reached terminal any part of the snake that's moving has velocity v₀. Arguably, under this assumption, the reading is constant and extends to t = 0. The answer is obtained simply and incorporates all three of the given parameters.

Edited to clarify a point raised in #18.

 

[haruspex]

Ok - well in this case perhaps the 'correct' model is of two objects connected by a compressed spring. When the 'spring' releases, conservation of momentum applies and the scale pan experiences an equal and opposite impulse to that applied to (applied by!) the snake.

No, a spring is not the right model. That would imply an acceleration, neither infinitesimal nor infinite, for the snake as a whole.
Stick with @gneill's and @PeroK 's model, but with the head being infinitesimal in size.

 

[haruspex]

I think I have an answer to this problem but not without assumptions. We are asked to find the "weight display at the moment the snake starts moving". Question: Is this moment before or after the snake reaches speed v₀? If before, we need to the details of how the snake the snake accelerates from v = 0 to v = v₀. My assumption is that the snake reaches constant velocity v₀ instantaneously and that we are asked to find the reading on the scale when the snake's head has reached terminal velocity v₀. Arguably, under this assumption, the reading is constant and extends to t = 0. The answer is obtained simply and incorporates all three of the given parameters.

I do not understand your model.
You mention reaching constant velocity instantaneously (the snake as a whole?) then refer to reaching terminal velocity.
@PeroK 's model is fine, with the caveat in post #17.

 

[kuruman]

I do not understand your model.
You mention reaching constant velocity instantaneously (the snake as a whole?) then refer to reaching terminal velocity.
@PeroK 's model is fine, with the caveat in post #17.

My model is essentially the model by @PeroK. A plot of the speed of the tip of the snake's head as a function of time is parallel is parallel to the time axis at v₀. I felt that a clarification of "at the moment the snake starts moving" was needed.

 

[haruspex]

My model is essentially the model by @PeroK. A plot of the speed of the tip of the snake's head as a function of time is parallel is parallel to the time axis at v₀. I felt that a clarification of "at the moment the snake starts moving" was needed.

Ok, but that's not how post #16 reads.
I regard the "moment it starts moving" as a blunder. As you note/imply, it leaves the question unanswerable because the velocity of the tip is a step function. Further, the criterion is unnecessary. The reading will not change again as long as the snake maintains its head speed but is stiil in contact with the pan.

 

[kuruman]

Ok, but that's not how post #16 reads.

I edited #16 to clarify it. Thanks.

 

[Andrew Mason]

I agree with all of you that this is a poorly worded problem. It might make sense if the snake had a uniform mass per unit length, m/L, which is not obvious.

If the snake is uncoiling upward at constant speed v, the the upward rate of change of momentum is determined by the rate at which mass is added to the upward flow.

AM

 

[neilparker62]

I agree with all of you that this is a poorly worded problem. It might make sense if the snake had a uniform mass per unit length, m/L, which is not obvious.

If the snake is uncoiling upward at constant speed v, the the upward rate of change of momentum is determined by the rate at which mass is added to the upward flow.

AM

Perhaps we are indeed meant to make the assumption about uniform mass per unit length.

 

[kuruman]

Perhaps we are indeed meant to make the assumption about uniform mass per unit length.

Yes, because otherwise one will need the linear mass density of the snake to solve the problem. Even if the snake were simply modeled as a prolate ellipsoid (head) a cylinder (body) and a cone (tail) of uniform mass density, the problem would be unnecessarily complicated and would detract from the main idea which (in my opinion) is an application of ##F=\frac{dP}{dt}.## Furthermore, if all parts of the snake moved at speed v₀ and the snake's linear mass density were not uniform, one would have to know ##\frac{dm}{dx} \vert _{x=0}## in order to answer the question.

Given that the author of the problem intended it to be solvable, one has to make enough simplifying assumptions until it is. A well crafted problem enunciates the appropriate assumptions up front and precludes ambiguity about how one ought to proceed in order to solve it. A badly crafted problem cannot be solved no matter what the simplifying assumptions. There also is a gray area of so-so crafted problems that elicit discussion about the formulation of the appropriate simplifying assumptions. This problem belongs in the gray area.

 

[neilparker62]

Given that the author of the problem intended it to be solvable, one has to make enough simplifying assumptions until it is. A well crafted problem enunciates the appropriate assumptions up front and precludes ambiguity about how one ought to proceed in order to solve it. A badly crafted problem cannot be solved no matter what the simplifying assumptions. There also is a gray area of so-so crafted problems that elicit discussion about the formulation of the appropriate simplifying assumptions. This problem belongs in the gray area.

To misquote terribly your motto: "I know one thing, I know not enough !"