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Classical Mechanics

  • Thread starter auslmar
  • Start date
10
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1. Homework Statement

An object is moving in one-dimensional space with a potential funciton V(x) = constant. Find the equation of motion, x(t). Use x_0 as the initial position and v_0 as the initial velocity at t=0.

2. Homework Equations

initial position = x_0

initial velocity = v_0

3. The Attempt at a Solution

Now, this is for a physical chemistry II course, and I haven't had any Classical Mechanics in about three years (I'm a Chemistry major). Our instructor wanted to have us do a few Classical Mechanics problems for review and perhaps, to bridge to Hamiltonian physics. However, the text doesn't provide any information about classical mechanics, and I've only had minimal success understanding information from the internet regarding my problem. I was mostly wondering if someone could explain or clarify how the potential function, given by V(x) = constant is related to an equation of motion. I know this may seem simple and silly, but please indulge my ignorance, I'm eager to learn. But anyway, from parsing a few sites, I came up with a generic equation:

x (t) = (1/2)a*t^2 + v_0*t + x_0

Where, a is the acceleration, v_0 is the initial velocity, and x_0 is the initial position. I don't know if this is even close to what I'm supposed to be doing, can someone help?

Thanks for your consideration,

Auslmar
 

LowlyPion

Homework Helper
3,079
4
That's pretty much the right equation, but apparently you don't have any acceleration, so with no external forces and potential energy constant it looks like you can drop the ½at² term.

So it reduces then to Xt = xo + vo*t
 
10
0
That's pretty much the right equation, but apparently you don't have any acceleration, so with no external forces and potential energy constant it looks like you can drop the ½at² term.

So it reduces then to Xt = xo + vo*t
So, acceleration nor, gravitational potential play into the derivation of an equation of motion such as this? The following problem on my worksheet is the same as this one except it is given that the potential function is V(x) = A*x, which leads me to believe that it is crucial in developing these equations.

I'm at a loss here.
 

LowlyPion

Homework Helper
3,079
4
So, acceleration nor, gravitational potential play into the derivation of an equation of motion such as this? The following problem on my worksheet is the same as this one except it is given that the potential function is V(x) = A*x, which leads me to believe that it is crucial in developing these equations.

I'm at a loss here.
It played a part. But it was a constant for the dimension of its motion. Hence it had no effect in expressing X(t). So no reason to be at a loss. That's the next problem.

This problem has no V(x) = A*x

Solve them 1 at a time.

Presumably in your next problem for the direction of motion the potential increases at the rate of the constant A. That sounds like gravity then right? Increase potential energy is the change in height times g - gravity?

So your first problem is like a ball rolling on a table? The second like a ball thrown in the air?
 

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