# Potential Energy as a function of x

1. Nov 19, 2007

### KvnBushi

[SOLVED] Potential Energy as a function of x

1. The problem statement, all variables and given/known data
Take U = 5 at x = 0 and calculate potential energy as a function of x, corresponding to the force:
$$8e^{-2x}$$

2. Relevant equations
$$W_{net} = U_i - U_f$$
$$W = \int_a^b F_x dx$$

3. 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?

Last edited: Nov 19, 2007
2. Nov 19, 2007

### 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).

3. Nov 19, 2007

### 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)

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

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

4. Nov 19, 2007

### KvnBushi

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