Potential Energy - Potential function problem.

[Alpha Russ Omega]

Hello:
I'm having trouble starting a certain problem.

A potential function is given by U(x) = 12 x^2. What will be the acceleration (in meters/second ^2) of a 2 kg mass, when it is at the position x = 0.2 m?

Any help will be highly appreciated.

 

[quasar987]

How is the potential energy function related to the force? And in turn, how is force related to acceleration?

 

[Alpha Russ Omega]

How is the potential energy function related to the force? And in turn, how is force related to acceleration?

Hmmm... Well, here is what I can think of from what I've learned in class:

1. The potential energy function is tied into a conservative force for x. Maybe I can go with the formula of: F cons. x = - ∂U/∂x
   
2. Force is related to acceleration by: F net = (mass) x (acceleration) Thus: *acceleration = (mass) / (F net)

Am I on the right track?

*EDIT: acceleration = (F net) / (mass)

 

[teclo]

Hmmm... Well, here is what I can think of from what I've learned in class:

1. The potential energy function is tied into a conservative force for x. Maybe I can go with the formula of: F cons. x = - ∂U/∂x
   
2. Force is related to acceleration by: F net = (mass) x (acceleration) Thus: acceleration = (mass) / (F net)

Am I on the right track?

yes. now, put all the equations together and solve for acceleration.

 

[Alpha Russ Omega]

Alrighty, so by taking the derivative of 12x^2 I get 24x. To get the Force would I multiply 0.2 meters by 24 ?

B.T.W.: (Thank you for all the replies.)

 

[quasar987]

That's right.

 

[teclo]

not quite, but almost. you forgot the negative when calculating the force.

 

[teclo]

because acceleration does not equal mass/force (you still forgot the negative)

 

[Alpha Russ Omega]

Oh my goodness! (brain fart) I see my mistake now. a = Fnet / mass
Thus being: (-4.8)/(2 kg) = -2.4 m/s^2



Thank you folks for all your help!