Solving a Motion Problem with Work-Energy Theorem

[Philip551]

I have been trying to solve the following problem:

Point-like object at (0,0) starts moving from rest along the path y = 2x²-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j. a) Find the work done by F along the path, b) Find the speed of the object at point A

For a) I have applied the formula for work with the integral and have integrated along the path to find the value for work. My first thought about approaching b) was since I know the total work and that the object starts moving from rest, I can use the work-energy theorem to find the speed at A. The problem with that is that I don't know the mass of the object.

 

[PeroK]

I have been trying to solve the following problem:

I've asked that this be moved to the Homework forum.

Point-like object at (0,0) starts moving from rest along the path y = 2x²-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j. a) Find the work done by F along the path, b) Find the speed of the object at point A

For a) I have applied the formula for work with the integral and have integrated along the path to find the value for work.

Sounds good.

My first thought about approaching b) was since I know the total work and that the object starts moving from rest, I can use the work-energy theorem to find the speed at A. The problem with that is that I don't know the mass of the object.

That is indeed a problem!

 

[berkeman]

I've asked that this be moved to the Homework forum.

Done.

 

[A.T.]

Point-like object at (0,0) starts moving from rest along the path y = 2x²-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j.

Are i & j the unit vectors of x & y? If yes, then I don't quite see how it gets from (0,0) at rest to (3,6).

 

[Philip551]

Are i & j the unit vectors of x & y? If yes, then I don't quite see how it gets from (0,0) at rest to (3,6).

I may have been unclear. It starts at (0,0) being at rest and then the F is applied to the object.

 

[A.T.]

I may have been unclear. It starts at (0,0) being at rest and then the F is applied to the object.

I get that. My question was what i & j are.

Have you plotted the path function? What is F at (0,0)? If F is the total force then it would have to be tangent to the path initially.

 

[ergospherical]

If F is the total force then it would have to be tangent to the path initially.

My guess is that the particle is constrained to the path (e.g. bead along smooth wire).

 

[A.T.]

My guess is that the particle is constrained to the path (e.g. bead along smooth wire).

I still don't see how it gets from rest at (0,0) to (3,6), given that F.

 

[ergospherical]

That's fair - me neither.

 

[haruspex]

I still don't see how it gets from rest at (0,0) to (3,6), given that F.

Isn’t it just the word "total" that's the problem? Should say it is constrained on a smooth wire and an external force is applied…?

 

[ergospherical]

I think what A.T. noticed is that at the origin the force points upwards, dragging the particle the wrong way up the parabola.

 

[A.T.]

I think what A.T. noticed is that at the origin the force points upwards, dragging the particle the wrong way up the parabola.

@Philip551 Are you sure you posted the correct formulas?

If mass is really not given, then it suggests a) should deliver a result that answers b) without knowing the mass.

 

[PeroK]

I'm often suspicioius of these questions that play fast and loose with units and dimensions. It looks like something somebody just made up without too much thought of any physics. I wouldn't be surprised if they never thought to check the mathematical functions they slapped together made physical sense.

 

[haruspex]

I think what A.T. noticed is that at the origin the force points upwards, dragging the particle the wrong way up the parabola.

Ok, so F would have to be just one of the forces applied. The rest are whatever's required to move it along that path. But then, we'd have no idea what the final velocity is even if we knew the mass.

 

[A.T.]

I'm often suspicioius of these questions that play fast and loose with units and dimensions. It looks like something somebody just made up without too much thought of any physics. I wouldn't be surprised if they never thought to check the mathematical functions they slapped together made physical sense.

I also remember cases of websites that offer free exercises which are not solvable, so you buy their paid tutorials.

 

[bob012345]

I have been trying to solve the following problem:

Point-like object at (0,0) starts moving from rest along the path y = 2x²-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j. a) Find the work done by F along the path, b) Find the speed of the object at point A

As pointed out by others, this problem seems inconsistent. Where did this problem come from? Homework assignment or did you found it on your own? What is the exact statement of the problem? Thanks.

 

[Philip551]

This problem came from a past exam paper from my university's physics department. The exact wording is: Point-like object at O(0,0) is at rest and starts moving, without experiencing any friction, along the curve y = 2x^2-4x until it reaches point A(3 m, 6 m). The force applied to the object is F = 10xy i + 15 j. (i) Calculate the work done by F along the OA path. (ii) What is the speed of the object at point A?

 

[PeroK]

This problem came from a past exam paper from my university's physics department. The exact wording is: Point-like object at O(0,0) is at rest and starts moving, without experiencing any friction, along the curve y = 2x^2-4x until it reaches point A(3 m, 6 m). The force applied to the object is F = 10xy i + 15 j. (i) Calculate the work done by F along the OA path. (ii) What is the speed of the object at point A?

Do you understand why that problem makes no physical sense?

 

[Philip551]

Do you understand why that problem makes no physical sense?

I think I do. To summarise, if the object were free, it would only move in the y direction so not in the aforementioned path and if it were constrained to that path, we wouldn't be able to find the velocity since we can't calculate the other forces' work in order to apply the work-energy theorem.

 

[bob012345]

This problem came from a past exam paper from my university's physics department. The exact wording is: Point-like object at O(0,0) is at rest and starts moving, without experiencing any friction, along the curve y = 2x^2-4x until it reaches point A(3 m, 6 m). The force applied to the object is F = 10xy i + 15 j. (i) Calculate the work done by F along the OA path. (ii) What is the speed of the object at point A?

It would be nice to ask whoever wrote that exam question what they were thinking.

 

[PeroK]

I think I do. To summarise, if the object were free, it would only move in the y direction so not in the aforementioned path and if it were constrained to that path, we wouldn't be able to find the velocity since we can't calculate the other forces' work in order to apply the work-energy theorem.

The force is initially in the positive y direction, but the curve the particle is supposed to follow is initially in the negative y and positive x direction.

 

[bob012345]

The only thing one can say about the velocity at any point is that the ratio of the components of the velocity are known.

 

[haruspex]

I think I do. To summarise, if the object were free, it would only move in the y direction so not in the aforementioned path and if it were constrained to that path, we wouldn't be able to find the velocity since we can't calculate the other forces' work in order to apply the work-energy theorem.

No, that's not it.
Consider a bead sliding on a frictionless wire. The constraining forces are always perpendicular to the motion, so do no work. The work-energy theorem applies.
The two flaws are:
- failing to specify the mass in part ii.
- the applied force would not have caused it to move in the stated direction

 

[bob012345]

It seems this would work out if it was a bead on a frictionless wire and the applied force was meant to be F=15 i +10xy j instead.