How Does Potential Energy Influence Particle Motion in Physics?

[zorro]

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

 

[Doc Al]

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.

 

[zorro]

Thanks a lot!

 

[fizzynoob]

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.

 

[Doc Al]

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.

 

[fizzynoob]

Ha yeah your right, got my U and V mixed up for some reason.