Potential Energy as a function of x

[KvnBushi]

[SOLVED] Potential Energy as a function of x

Homework Statement

Take U = 5 at x = 0 and calculate potential energy as a function of x, corresponding to the force:
8e^{-2x}

Homework Equations

W_{net} = U_i - U_f
W = \int_a^b F_x dx

The Attempt at a Solution

\int 8e^{-2x} dx = -4e^{-2x} = W(x)

W(x) = -4e^{-2x} = U_i(x) - U_f(x)
U_f(x) = U_i(x) + 4e^{-2x}
U_f(x) = 5 + 4e^{-2x}

correct answer: U(x) = 1 + 4e^{-2x}

Any ideas how i went wrong?

 

[Sourabh N]

You were working with definite integral, I guess. when you integrated 8exp(-2x), you should have put the limits (x = 0 and x = x).

 

[KvnBushi]

SOLVED

W(x) = \int 8e^{-2x} = -4e^{-2x} + C ( I forgot the C earlier)
W(x) = U_i(x) - U_f(x)
-4e^{-2x} + C = 5 - U_f(x)
U_f(x) = 5 - 4e^{-2x} - C

SOLVE FOR C

U(0) = 5 = 5 - 4(1) - C
C = 4

SOLVE FOR U(x)

U_f(x) = 5 - 4e^{-2x} - 4

U_f(x) = 1 - 4e^{-2x}

 

[KvnBushi]

You were working with definite integral, I guess. when you integrated 8exp(-2x), you should have put the limits (x = 0 and x = x).

I am going to try this way as well when I get back from eating. Cheers!