Notation within homework question

[mike_302]

Homework Statement

A particle moving along the x-axis is subject to a conservative force such that the potential energy of the particle is given by U(x,y)=2x + x^3 where x and y are in meters, U is in joules. When the particle moves from (2,0) to the origin, the work done by the conservatice force is:
A) b) c) d) (the choices don't matter... I have the right value, wrong sign)

Homework Equations

delta(U) = change in potential energy.

The Attempt at a Solution

Okay, my real question here is: What does this notation U(x,y) really mean?

And I checked the solution for this problem, and it says U(initial) - U(final)... Why is this? Since when is the change in a value equal to initial - final ?

 

[Mark44]

The notation U(x, y) is used to indicate that U is a function of two variables, x and y. The formula you show, however, is a function of x alone.

the potential energy of the particle is given by U(x,y)=2x + x^3 where x and y are in meters

Is there a typo in this formula? Should it be U(x, y) = 2x + y^3?

 

[tiny-tim]

… I checked the solution for this problem, and it says U(initial) - U(final)... Why is this? Since when is the change in a value equal to initial - final ?

Hi mike_302!

(try using the X₂ tag just above the Reply box )

Change in potential energy = minus the work done

ie ∆PE = -W

so the work done will be -∆PE = U_initial - U_final

 

[mike_302]

Okay, I completely see why it's U_i-U_f now but that U(x,y) notation seems messed up because there's no typo :P That's how it is written, and I get the answer using JUST x, so I guess it should've said U(x)= ...

Oh well!

 

[tiny-tim]

… that U(x,y) notation seems messed up because there's no typo :P That's how it is written, and I get the answer using JUST x, so I guess it should've said U(x)= ...

No, because potential is a function of position, and has to be defined at every position …

for example gravitational potential is U(x,y,z) = -gz.