How Does Potential Energy Influence Particle Motion in Physics?

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Homework Help Overview

The discussion revolves around a problem involving a particle's potential energy in the x-y plane, given by the equation U=(-7x + 24y) J. Participants are tasked with finding the force acting on the particle and its speed after a certain time, starting from the origin with an initial velocity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of force components from potential energy derivatives and the resulting net force. There is an examination of the particle's speed and acceleration, with some questioning the directionality of velocity and acceleration components.

Discussion Status

Some participants have provided guidance on the correct application of derivatives in relation to force, while others are exploring the implications of potential energy in the context of electric fields. Multiple interpretations of the potential energy function are being discussed, but there is no explicit consensus on the correct approach to the problem.

Contextual Notes

Participants are navigating potential misunderstandings regarding the relationship between potential energy and electric fields, as well as the correct interpretation of derivatives in this context. There is a noted confusion between potential energy and electric potential in the discussion.

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Homework Statement


A particle of mass 5 kg in the x-y plane has its potential energy given by U=(-7x + 24y ) J where x and y are in metre. The particle is initially at origin and has a velocity u=(14.4i + 4.2j)m/s. Find the magnitude of force on the particle and speed of the particle at t=4s.


Homework Equations





The Attempt at a Solution



dU/dx=Fx
dU/dy=Fy
Therefore, Fx= -7N and Fy= 24N
Fnet = 25N

magnitude of u=15m/s
magnitude of acceleration=25/5=5m/s^2
Hence v=15+5x4=35m/s
But the answer is 25m/s
 
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Abdul Quadeer said:
dU/dx=Fx
dU/dy=Fy
Therefore, Fx= -7N and Fy= 24N
Fnet = 25N
Careful. You're missing a minus sign:
Fx = -dU/dx
Fy = -dU/dy

That doesn't affect this answer but will the next.

magnitude of u=15m/s
magnitude of acceleration=25/5=5m/s^2
Hence v=15+5x4=35m/s
But the answer is 25m/s
The velocity and acceleration are not in the same direction. Analyze each velocity component separately, then combine to find the speed.
 
Thanks a lot!
 
Wouldn't -dU/dx give you the x component of the electric field? I think you need to multiply by a factor of charge to find the actual electric force. And don't forget that -dU/dx is actually a partial derivative.
 
fizzynoob said:
Wouldn't -dU/dx give you the x component of the electric field? I think you need to multiply by a factor of charge to find the actual electric force.
Who said anything about electric fields here? U is the potential energy function, not electric potential.
 
Ha yeah your right, got my U and V mixed up for some reason.
 

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