Calculus based physics - Energy

[XodoX]

Homework Statement

As a particle moves along the x-axis it is acted upon by a single conservative force given by F_x=(22-2.0x)N where x is in m. The potential energy associated with this force has the value +40 J at the origin (x=0). What is the value of the potential energy at x=4 m?

Homework Equations

The Attempt at a Solution

Well, you have to move it so that it is Fx= 2xdx - 20dx ( -dU/dx ) so you have this equation. Then I integrated it and got x^2-20x+C... C is 40 in this case, so you have x^2-20x+40. Since it says potential energy at x=4, I plugged in the 4 and got 4^2-20*4+40= -24. That's not correct, though.

Homework Statement

A spring (k=300N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 1.5 kg block that is initially 0.10m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.20m ( compressing the spring 0.10m) ?

Homework Equations

1/2kx_i²=E_i=mgh_f - energy conservation

The Attempt at a Solution

No idea. This equation above is a guess. I think it should be this one. If it is, you probably have to solve it for something, but I don't know. Solve for k ?

 

[Ericv_91]

For the second question:

You're on the right track thinking about conservation of energy. What will define the energy of the system at the moment the block is dropped? What will define the energy of the system after it has dropped and compressed the spring?