Here's the question you clicked on:
Hunus
Elastic potential energy
|dw:1335300188613:dw| When does the spring have negative potential energy?
Good question! Do you know the expression of this type of potential energy?
Well, when you have the equation \[F_x=-\frac{\partial U}{\partial x}\] what force does F_x represent?
Because if F is the force of the spring, then wouldn't it be positive on the third picture? And if it was positive wouldn't dudx have to be negative?
Your problem is not asking about a negative force, but about a negative energy. For which x can ½kx² be negative?
I'm reading through a book on classical mechanics and I'm having a difficult time understanding when the force is positive\[F_x=−\frac{∂U}{∂x}\]
when F positive dx is negative??
Draw the function U(x)=½kx² For what values of x is the tangent to the curve positive/negative ? As Fx = -dU/dx, you will know the sign of Fx.
dU/dx is the derivative of U with respect to x. Its value is the gradient of the tangent to the curve at point (x,U(x)).
Quote : Well, when you have the equation Fx=−∂U/∂x what force does F_x represent? Answer : it reprensents the force exerted by the spring on the block.