The Time Ratio of Objects A and B with Constant Power: How Do They Compare?

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Homework Help Overview

The problem involves two objects, A and B, both of the same mass, being pushed under different conditions: object A with a constant force and object B with a constant power. The goal is to find the ratio of the time taken by both objects to travel a distance s while their velocities increase from v to 2v.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the time taken for object A using kinematic equations but struggles with finding a similar expression for object B under constant power. Some participants suggest using energy considerations and integrating velocity as a function of power and time to derive position.

Discussion Status

Participants are exploring different methods to approach the problem, including energy considerations and integration techniques. There is an ongoing dialogue about eliminating variables such as mass and power from the equations, indicating a productive exchange of ideas without a clear consensus yet.

Contextual Notes

Participants are working within the constraints of the problem as stated, with a focus on deriving relationships rather than providing direct solutions. The discussion includes references to external resources for further understanding of motion with constant power.

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Homework Statement


Object A of mass m is pushed with a constant force, another object B of the same mass is pushed with a force that does work at constant rate. Velocity of both objects increase from v to 2v and they move a distance of s. Find the ratio of the time taken by objects A and B to move the distance s


Homework Equations





The Attempt at a Solution


Firstly, for object A
s = 1/2(v + 2v)t
t = 2s/3v

Object B has constant power, thus
F1v = F2(2v)
But I don't know how to find an expression for the time taken by object B in term of v and s
 
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Use energy considerations.

First: What is the total change in energy?

Second: Find the velocity as a function of P and t and integrate this to obtain the position as a function of time.

Now you can use these to equations to eliminate P.

Good luck :)

Edit: For more info on motion with constant power, see https://kb.osu.edu/dspace/bitstream/1811/2458/1/V30N04_218.pdf
 
change in energy = work done = 3/2 mv2
3/2 mv2 = Pt
v = (2Pt/3m)1/2
integrating this term, i get
s = 1/3 (8Pt3/9m)1/2

But how do i eliminate m and p?
 
Indeed.

Try looking at the first equation again. Can't you use that to eliminate the ratio P/m?
 

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