Solving a Motion Problem with Work-Energy Theorem

In summary, The point-like object moves from rest along the y-axis until it reaches point A(3,6). Here, the F = 10xy + 15 j.
  • #1
Philip551
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5
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.
 
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  • #2
Philip551 said:
I have been trying to solve the following problem:
I've asked that this be moved to the Homework forum.
Philip551 said:
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.
Philip551 said:
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!
 
  • #3
PeroK said:
I've asked that this be moved to the Homework forum.
Done. :wink:
 
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  • #4
Philip551 said:
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).
 
  • #5
A.T. said:
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.
 
  • #6
Philip551 said:
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.
 
  • #7
A.T. said:
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).
 
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  • #8
ergospherical said:
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.
 
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  • #9
That's fair - me neither.
 
  • #10
A.T. said:
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…?
 
  • #11
I think what A.T. noticed is that at the origin the force points upwards, dragging the particle the wrong way up the parabola.
 
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  • #12
ergospherical said:
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.
 
  • #13
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.
 
  • #14
ergospherical said:
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.
 
  • #15
PeroK said:
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.
 
  • #16
Philip551 said:
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.
 
  • #17
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?
 
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  • #18
Philip551 said:
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?
 
  • #19
PeroK said:
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.
 
  • #20
Philip551 said:
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.
 
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  • #21
Philip551 said:
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.
 
  • #22
The only thing one can say about the velocity at any point is that the ratio of the components of the velocity are known.
 
  • #23
Philip551 said:
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
 
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  • #24
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.
 

FAQ: Solving a Motion Problem with Work-Energy Theorem

What is the Work-Energy Theorem?

The Work-Energy Theorem states that the work done by all the forces acting on an object is equal to the change in its kinetic energy. Mathematically, it is expressed as \( W = \Delta KE \), where \( W \) is the work done, and \( \Delta KE \) is the change in kinetic energy of the object.

How do you define work in the context of the Work-Energy Theorem?

In the context of the Work-Energy Theorem, work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. It is given by the equation \( W = F \cdot d \cdot \cos(\theta) \), where \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and the direction of displacement.

How can the Work-Energy Theorem be used to solve motion problems?

The Work-Energy Theorem can be used to solve motion problems by calculating the work done by all forces acting on an object and equating it to the change in kinetic energy. This allows us to determine unknown quantities such as final velocity, displacement, or the work done by specific forces, given initial conditions and the forces involved.

What are some common forces considered when applying the Work-Energy Theorem?

Common forces considered when applying the Work-Energy Theorem include gravitational force, normal force, frictional force, applied force, and tension. Each of these forces can do work on an object, contributing to the total work done and thus affecting the object's kinetic energy.

Can the Work-Energy Theorem be applied to systems with non-conservative forces?

Yes, the Work-Energy Theorem can be applied to systems with non-conservative forces such as friction or air resistance. In such cases, the work done by non-conservative forces is included in the total work calculation, which then affects the change in kinetic energy of the object. This allows for a comprehensive analysis of the motion, accounting for energy losses due to non-conservative forces.

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